Manipulation of Population Distributions, Fragmentation Processes and Nonlinear Optical Processes by Coherent, Adiabatic Interactions

Transcription

1 Manipulation of Population Distributions, Fragmentation Processes and Nonlinear Optical Processes by Coherent, Adiabatic Interactions Thomas Halfmann Dr. rer.nat., Juniorprofessor Technische Universität Kaiserslautern Habilitationsschrift 1

2 Sapere aude (Horaz, Epistulae ) in memoriam Prof. Dr. med. W. Kreienberg cover figure : Experimental demonstration of electromagnetically-induced transparency. upper row : a probe laser, tuned to an atomic resonance in Mercury, is significantly absorbed after transmission through a cell with Mercury vapour. The remaining intensity distribution shows distortions and deviations from the original Gaussian intensity profile due to pronounced filamentation. lower row : when a dressing laser is introduced in the system and controls the optical properties of the medium, the probe laser is transmitted without absorption losses. The Gaussian intensity distribution is also restored. 2

3 Contents 1. Introduction and motivation 7 2. Coherent interactions between light and matter Incoherent versus coherent excitation in two-level systems Rapid adiabatic passage (RAP) Stark chirped rapid adiabatic passage (SCRAP) Coherent population transfer in three-level systems : Stimulated Raman Adiabatic Passage (STIRAP) Stimulated hyper-raman adiabatic passage (STIHRAP) Retroreflection-Induced Bichromatic Adiabatic Passage (RIBAP) Dark resonances and electromagnetically-induced transparency (EIT) Laser-Induced Continuum Structure (LICS) Stimulated Raman Adiabatic Passage (STIRAP) via a Continuum Enhancement of nonlinear optical processes in coherently prepared media Coherent manipulation by adiabatic processes : Experimental results Manipulation of population distributions Coherent population transfer by stimulated hyper-raman adiabatic passage Coherent population transfer by Stark-chirped rapid adiabatic passage Dark resonances involving Rydberg states probed by ionization suppression Power broadening revisited : Lineshapes in coherent excitation Coherent Population Transfer by Retroreflection-Induced Bichromatic Adiabatic Passage Coherent Population Transfer via Continuum States Manipulation of fragmentation processes Laser-induced continuum structure (LICS) in multiple continua Modification of autoionization lineshapes Suppression of incoherent losses in Stark-chirped rapid adiabatic passage (SCRAP) by laser-induced continuum structure (LICS) 41 3

4 3.3 Manipulation of frequency conversion processes Frequency conversion enhanced by Stark-chirped rapid adiabatic passage High-order stimulated Raman scattering induced by ultrashort (fs) laser pulses Generation of short-wavelength radiation by interaction of a nanosecond and a femtosecond laser pulse Generation of short-wavelength radiation in organic molecules Probing attosecond (as) pulse trains by phase control techniques Preparation of coherent superpositions in three-state systems Summary and outlook Acknowledgements References Attachments Manipulation of population distributions N.V. Vitanov, T. Halfmann, B.W. Shore, and K. Bergmann, Laser-Induced Population Transfer by Adiabatic Passage Techniques Review Article, Ann. Rev. Phys. Chem. 52, 763 (21) K. Böhmer, T. Halfmann, L.P. Yatsenko, B.W. Shore, and K. Bergmann, Stimulated Hyper-Raman Adiabatic Passage III : Experiment, Phys. Rev. A 64, 2344 (21) T. Rickes, L.P.Yatsenko, S.Steuerwald, T. Halfmann, B.W.Shore, N.V.Vitanov, and K.Bergmann, Efficient Adiabatic Population Transfer by Two-Photon Excitation Assisted by a Laser-Induced Stark Shift, J. Chem. Phys. 113, 534 (2) T. Halfmann, K. Böhmer, L.P. Yatsenko, A. Horsmans and K. Bergmann, Coherent Population Trapping involving Rydberg States in Xenon probed by Ionization Suppression, Eur. Phys. J. D 17, 113 (21) T. Halfmann, T. Rickes, N. Vitanov, and K. Bergmann Lineshapes in Coherent Two-Photon Excitation Opt. Comm. 22, 353 (23) 4

5 N.V. Vitanov, B.W. Shore, L.P.Yatsenko, T. Halfmann, T. Rickes, K. Böhmer, and K. Bergmann, Power Broadening Revisited : Theory and Experiment Opt. Comm. 199, 117 (21) A. Peralta-Conde, L.P. Yatsenko, J. Klein, M. Oberst, and T. Halfmann Experimental Demonstration of Retroreflection-Induced Bichromatic Adiabatic Passage, Phys. Rev. Lett., to be submitted T. Peters, L.P. Yatsenko, and T. Halfmann Experimental Demonstration of Coherent Population Transfer via a Continuum Phys. Rev. Lett., submitted 7.2 Manipulation of fragmentation processes K. Böhmer, T. Halfmann, L.P. Yatsenko, D. Charalambidis and K. Bergmann, Laser-Induced Continuum Structure in the Two Ionization Continua of Xenon Phys. Rev. A 66, 1346 (22) M. Stellpflug, M. Johnsson, I. D. Petrov, and T. Halfmann Investigation of Auto-Ionizing States in Xenon by Resonantly Enhanced Multi-Photon Ionization Eur. Phys. J. D 23, 35 (23) T. Peters, I.D. Petrov, V.L. Sukhorukov, T. Halfmann, U. Even, A. Wünnenberg, and H. Hotop Experimental and Theoretical Investigation of even mp 5 1/2 nl Autoionizing Resonances in the Rare Gas Atoms Ne, Ar, Kr, and Xe J. Phys. B. 38, S51 (24) L.P. Yatsenko, V. Romanenko, B.W. Shore, T. Halfmann and K. Bergmann Two-photon excitation of metastable hydrogen (2s) assisted by laser-induced chirped Stark shifts and continuum structure Phys. Rev. A 71, (25) 7.3 Manipulation of nonlinear optical processes T. Rickes, J.P. Marangos, and T. Halfmann Enhancement of Third-Harmonic Generation by Stark-Chirped Rapid Adiabatic Passage Opt. Comm. 227, 133 (23) E. Korsunsky, T. Halfmann, J.P. Marangos, M. Fleischhauer, and K. Bergmann Analytical Study of Four-Wave Mixing with Large Atomic Coherence Eur. Phys. J. D 23, 167 (23) S.A. Myslivets, A.K. Popov and V.V. Kimberg, T. Halfmann, J.P. Marangos, T. F. George Nonlinear-Optical Vacuum-Ultraviolet Generation at Maximum Coherence Controlled by a Laser-Induced Stark Chirp of Two-Photon Resonance Opt. Comm. 29, 335 (22) 5

6 E.Sali, K.Mendham, T.Halfmann, and J.P.Marangos Highly-Transient Stimulated Raman Scattering with a 2-Colour Femtosecond Pump Opt. Lett. 29, 495 (24) T. Halfmann, N. Hay, J.W.G. Tisch, and J.P. Marangos Generation of Vacuum Ultraviolet Radiation by Sum Frequency Mixing of a Femtosecond and a Nanosecond Laser Opt. Comm. 182, 229 (2) N. Hay, R. de Nalda, T. Halfmann, K.J. Mendham, M.B. Mason, M. Castillejo, and J.P.Marangos, Pulse Length Dependence of High-Order Harmonic Generation in Dissociating Cyclic Organic Molecules, Phys. Rev. A 62, 4183(R) (2) N. Hay, R. de Nalda, T. Halfmann, K.J. Mendham, M.B. Mason, M. Castillejo, and J.P.Marangos, High Order Harmonic Generation from Organic Molecules in Ultra-Short Pulses, Eur. Phys. J D 14, 231 (21) E. Hertz, N.A. Papadogiannis, G. Nersisyan, C. Kalpouzos and D. Charalambidis, T. Halfmann, G.D. Tsakiris Probing Attosecond Pulse Trains using Phase Control Techniques Phys. Rev. A 64, 5181(R) (21) N. Sangouard, S. Guerin, L.P. Yatsenko, and T. Halfmann, Preparation of coherent superposition in a three-state system by adiabatic passage, Phys. Rev. A 7, (24) all publications of the author can also be downloaded from 6

7 1. Introduction and motivation For many decades lasers have been most extensively used to study and investigate atomic and molecular systems and processes [Dem98]. As such studies focused mainly on the understanding of the system or process under observation, lasers were commonly used as a tool to probe, detect and investigate. Going far beyond these applications in the last decade lasermatter interactions were also found to permit the efficient manipulation of atomic and molecular systems and properties, which raised considerable attraction to a large scientific community. The control scenarios do not exclusively rely on the strength of the laser-matter interaction only. A rich variety of, very often on the first glance surprising phenomena arises when the coherence of the exciting radiation field is taken into account [Sho9]. Laser-based control techniques offer numerous possibilities for applications. Among these are e.g. the generation of population inversion, control of atomic and molecular photofragmentation processes, steering chemical reactions, manipulation of optical properties, i.e. absorption, the index of refraction as well as nonlinear optical, e.g. frequency conversion, processes. The latter are of significant interest to extend the wavelength regime, accessible by conventional laser systems, e.g. to the regime of short-wavelength, extreme-ultraviolet radiation [Wal82]. The field of coherent laser-matter interaction exhibits a variety of different approaches to steer atomic and molecular processes. Among these are techniques based on quantum interference between different excitation pathways from an initial to a target state, either a bound state or belonging to fragmentation continua [Sha94,Sha99,Sha]. These methods are often termed phase control techniques, as constructive or destructive interference is usually controlled by the relative phase of the exciting radiation fields. Such, the excitation of bound state transitions or fragmentation processes, e.g. ionization or dissociation, as well as branching ratios between different excitation or fragmentation channels can be controlled. The interactions by phase control techniques can, at least in principle, be implemented with laser systems of arbitrary intensities. The techniques work for weak interactions as well as strong couplings. However, if interaction of atomic or molecular systems with radiation fields of high intensities is considered to control the media, approaches based on pulse-shaping of ultrashort (fs) laser pulses have been shown in the last decade to provide powerful tools [Ass98,Bri1a,Bri1b, Jud92,Lev1,Mes99,Rab,Ricb,Tan85,War93,Wei99b,Wei]. Pulse-shaping techniques combine either phase control by interference of different excitation pathways, induced by the manifold of frequency components in the huge spectrum of an ultrashort (fs) laser pulse, as 7

8 well as time-domain processes by steering wave packets on molecular energy surfaces. These techniques have been used successfully to manipulate media in the gas, liquid and solid phase, control excitations between bound states, fragmentation processes as well as branching ratios between different fragmentation channels and nonlinear optical processes [Bri1a,Bri1b]. In contrast to the coherent control techniques discussed above the research program presented in this work focuses on the development and application of laser-matter interactions, based on adiabatic passage processes [Ber98,Vit1b] 1. Such processes are usually implemented with laser systems of moderate intensities in the regime up to some GW/cm 2. On one hand such intensities already permit strong modifications of atomic and molecular level systems, also involving multi-photon transitions and couplings between bound and continuum states, but on the other hand these intensities are not yet strong enough to dominate the inner-atomic potential. As a main advantage compared to other coherent control techniques adiabatic passage processes offer robustness with respect to fluctuations in the experimental parameters, e.g. laser intensities, detunings, pulse delays or shapes, provided some limits are kept in view. Such, applications for coherent, adiabatic interactions to manipulate population distributions [Vit1b], fragmentation processes [Kni9,Boe2,Cav91,Cav93,Cav95,Cav98,Era97,Fau93, Hal98,Hut88,Sha91,Shn96,Yat98b,Yat99b] and optical properties in atomic and molecular media [Har97,Mar98,Phi], in the gas phase as well as in selected solid state systems, e.g. doped solids [Ham97a,Ham97b,Ham,Hem1,Wei99a] and nanostructures [Sch96,Sch97, Sch99], have been successfully demonstrated. The projects presented here deal with the development and investigation of new techniques for coherent, adiabatic interactions as well as extended applications of such processes. In section 2 principles of coherent light-matter interaction in two- and three-level systems, also involving continuum states will be briefly reviewed. In section 3 experimental and theoretical results, obtained by the author, together with coworkers and cooperation partners, focused on the investigation and application of coherent, adiabatic techniques to manipulate population distributions, fragmentation processes and nonlinear optical frequency conversion processes are summarized. Details on the experimental and theoretical results are discussed in the publications, collected in the attachments. 1 In the following, references with participation of the author, T. Halfmann, are set in blue fonts 8

9 2. Coherent interactions between light and matter 2.1 Incoherent versus coherent excitation in two-level systems A two-level system of a ground state 1 and an excited state 2 driven by a single, incoherent radiation field (see fig. 1, l.h.s.) is commonly described by rate equations, involving the fundamental processes of stimulated absorption and stimulated emission as well as spontaneous emission. The equations read : dn dn 1 2 = B 21 = B 12 u ( ω) N 2 u ( ω) N 1 dt + A with the changes of the populations dn i in state i, the energy density of the radiation field u(ω) and the Einstein coefficients B 12 for stimulated absorption, B 21 for stimulated emission and A 21 for spontaneous emission of photons. Spontaneous emission can be neglected in the population dynamics, if the lifetime of the excited state is much longer than the interaction time with the radiation field. dt 21 N 2 dt 2 populations [%] state 1 state time [arb. units] Fig. 1 : Two-level system driven by an incoherent radiation field on resonance. Level scheme and population dynamics. The continuous driving field is switched on at time t =. All population is in the ground state at the beginning of the interaction. In the case of saturation half of the population is transferred to the excited state. Considered the radiation field is strong or the interaction time is long enough, a maximum of 5 % of the population in the ground state can be transferred to the excited state. This is termed saturation of the transition. The equal distribution of population mirrors the equal probabilities for stimulated absorption and emission, described by the relevant Einstein coef- 9

10 ficients with B 12 = B 21. Thus, in the case of incoherent excitation, population inversion is not possible in a two-level system. If the two-level system is driven by a strong, coherent radiation field, the model presented above is no longer valid. While the rate equations are based on perturbation theory, i.e. the description of the system in the basis of the bare states (the eigenstates of the system without the interaction with the radiation field), the correct treatment for strong, coherent interaction needs to go beyond perturbation theory. As the radiation field strongly affects the system, new eigenstates, the dressed states, will arise from the Hamiltonian involving the laser-matter interaction. The Hamiltonian H = H atom + H Interaction for a two-level atom interacting with a strong, coherent radiation field (see fig. 2, l.h.s.), reads in Schrödinger representation and considering electric dipole interaction as [Sho9] : H = µ Ecos( ωt) µ Ecos( ωt) hω with the electric field strength E and the frequency ω of the driving field, the resonance frequency ω and the transition dipole moment µ. The Hamiltonian can be rewritten involving rotating wave approximation and transformation to the Dirac (interaction) representation : H = h 2 Ω Ω with the Rabi frequency Ω = µe / Σ and the detuning from resonance = ω ω. The dressed states, i.e. the eigenstates of the Hamiltonian including the interaction with the radiation field, read : a a with the mixing angle Θ defined by + = cos Θ 1 sin Θ 2 = sin Θ 1 + cos Θ 2 tan Θ = Ω Ω The new eigenvalues of the system, i.e. the energies of the dressed states, yield : 2 ± ω = ± 1 2 Ω

11 Thus, on resonance ( = ) the eigenstates are separated by an amount ω + - ω - = Ω, called the Autler-Townes splitting [Sho9]. Ω 2 populations [%] state 1 state time [arb. units] Fig. 2 : Two-level system driven by a strong, coherent radiation field. Level scheme and population dynamics. The continuous driving field is switched on at time t =. The detuning is set to =. All population is in the ground state at the beginning of the interaction. During the interaction the populations exhibit Rabi oscillations. In contrast to the case of incoherent excitation the population dynamics for coherent interaction exhibit oscillations of the bare state population as a most prominent feature. For zero detuning the population in the excited state flips between % and 1 %. In the case of fluctuations in the laser intensity, frequency or phase these oscillations average to the case of equal (5 %) population distribution between the ground and the excited state, as expected. If the exciting radiation is pulsed and appropriately timed, i.e. switched off, when the transfer reaches 1 %, complete population inversion is possible in the system (see fig. 3). This transfer technique is called Π pulse with respect to the area, covered by the time-varying Rabi frequency. However, the Π pulse technique suffers from fluctuations, e.g. in the laser intensity, frequency or phase, as the frequency and phase of the Rabi oscillations depend critically upon these parameters [Sho9]. Thus, for practical use, Π pulses are no appropriate choice to generate population inversion. 11

12 Ω 2 populations [%] state 1 state time [arb. units] Fig. 3 : A pulse with area A = Ω(t) dt = n π ( n ; here n = 5) inverts the population distribution in a two-level system. The detuning is set to =. 2.2 Rapid adiabatic passage (RAP) In contrast to the Π pulse technique, stable and robust population transfer, not effected by fluctuations in the experimental parameters can be implemented by means of adiabatic passage processes. To study the possibility of complete population transfer between the ground and the excited state the dressed state dynamics have to be considered. Complete population transfer in a two-level system via e.g. the dressed state a - is possible, if at the beginning of the interaction all population is prepared in the dressed state a -, thus the initial bare state 1 aligns parallel to a - for early times. At the end of the interaction a - must align parallel to the excited state 2 in order to project all the population from the dressed state onto the target bare state. Regarding the definition of the dressed state a - = sin Θ 1 + cos Θ 2 these conditions read : for t : a 1 if sin Θ 1 (cos Θ ), i. e. / Ω for t + : a 2 if cos Θ 1 (sin Θ ), i. e. / Ω + i.e. the detuning has to change from a large negative to large positive value during the interaction in order to provide complete population transfer via the dressed state a -. Thus the center frequency of the driving radiation pulse has to be chirped, such that the laser frequency is driven through the atomic resonance. Provided the transfer process is adiabatic, which means no population is exchanged between the two dressed states during the process, thus the 12

13 state vector of the system follows the motion of the dressed state a - in the Hilbert space, all the population can be transferred by a chirped pulse from the ground to the excited state (see fig. 4). This technique is called rapid adiabatic passage (RAP) [Loy74,Loy76,Gri75a, Gri75b,Gri76,Vit1b]. The specification rapid indicates, that the interaction time has to be short with respect to the lifetime of the excited state, otherwise population will flow back to the ground state during the process. A full theoretical treatment reveals conditions for adiabatic following, essentially a minimum pulse intensity or coupling strength, i.e. the transition has to be strongly driven or saturated, as well as a minimum chirp rate [Vit1b]. 1 lations [%] popu state 1 state laser electric field [arb. units] time [arb. units] time [arb. units] Fig. 4 : Rapid adiabatic passage (RAP): the frequency of the exciting radiation pulse is modulated by a linear chirp (r.h.s., lower row) and driven through resonance during the interaction. Such all population is transferred from the ground state to the excited state (r.h.s., upper row). 13

14 2.3 Stark chirped rapid adiabatic passage (SCRAP) RAP works as a stable and robust possibility for efficient population transfer, provided the excited transition can be strongly driven, i.e. saturated, and the radiation pulse can be chirped in a controlled way. This is usually implemented with rather short (ps) radiation pulses., which can be chirped by methods based on dispersion. Longer (ns) pulses would offer the advantage of higher pulse energies and longer interaction times, thus also weaker resonances and a larger number of atomic or molecular systems could be driven in saturation. Due to the small bandwidth of ns pulses, usually they are hard to chirp in a controlled way. To overcome these difficulties, an extension of RAP was suggested : Stark-chirped rapid adiabatic passage (SCRAP) [Rica,Vit1b,Yat99a]. 1 populations [%] state 1 state 2 i time [arb. units] Ω 2 laser intensities [arb. units] 5 pump laser Stark laser time [arb. units] Fig. 5 : Two-level system driven by a pump laser and a second (Stark) laser pulse in the SCRAP process : coupling scheme and population dynamics. As the Stark laser pulse drives the atomic transition frequency through resonance with the pump laser, initially detuned from resonance, population flows in a RAP process from the ground to the excited state. 14

15 The basic idea is to replace the frequency chirp of the exciting pulse laser pulse across the atomic resonance by a modulation of the atomic resonance, driven by a laser with fixed carrier frequency. Thus, the atomic resonance is chirped rather than the laser pulse. The modulation of the atomic resonance is implemented by a second, strong radiation pulse, inducing dynamic Stark-shifts (see fig. 5). The coupling scheme is as follows : a pump laser excites a (single- or multi-photon) transition from the ground to an excited state. The pump laser frequency is detuned from the atomic resonance. The Stark shifting laser pulse is introduced into the system with a time delay, either preceeding or following the pump laser pulse. In the latter case the rising wing of the Stark laser will induce dynamic Stark shifts of the upper state. Stark shifts of the ground state are usually negligible. Thus the upper state rp. the atomic transition frequency will be driven through resonance with the pump laser pulse as in RAP the laser frequency is driven across the atomic transition frequency. Population will flow now in a RAP process from the ground to the excited state. The decaying wing of the Stark laser will drive the system a second time through resonance, but this will not matter, as the pump pulse is already off. In the case of the pulse sequence Stark laser pulse preceeding pump laser pulse the population dynamics are obviously the same. Finally, two important features of SCRAP should be stressed : the technique is applicable to both single- as well as multi-photon transition. The Stark shift, usually associated with a strongly pump-laser driven multi-photon transition does not matter for the population transfer, provided the shifts induced by the Stark-laser are larger. Moreover SCRAP can also be implemented in inhomogeneously, e.g. Doppler broadened media, permitted the laser-induced Stark shifts cover the full range of the inhomogeneous broadening. In this case all atoms will be driven in a RAP process through resonance, irrespective of what their exact transition frequency is. 2.4 Coherent population transfer in three-level systems : Stimulated Raman Adiabatic Passage (STIRAP) As in two-level systems, coherent excitation in multi-level system also exhibit considerable differences to incoherently driven processes. Consider a three-level system in lambda-type configuration (see fig. 6) : the pump laser couples the initial state 1 to an intermediate state 2, the Stokes laser connects the intermediate state 2 and the target state 3. If the aim is to transfer population from the initial to the target state, the intuitive pulse sequence pump preceding Stokes pulse would be the obvious pulse sequence. Such, in the case of saturation, 5 % of the population could be transferred from the initial to the intermediate state and subse- 15

16 quently, 5 % of the population in the intermediate state, i.e. 25 % of the total population will be transferred to the target state. This coupling scheme is called stimulated emission pumping (SEP, type I). For coincident laser pulses, the population will be equally distributed in all three states, thus the transfer efficiency will be 33 % (SEP, type II) [Dai95]. 1 populations [%] state 1 state 2 state 3 laser intensities [arb. units] time [arb. units] pump laser Stokes laser time [arb. units] Fig. 6 : Coupling scheme and population dynamics for a three-level system driven by STIRAP. All the population is transferred during the STIRAP process from the initial to the target state without being stored in the intermediate state. Thus no losses can occur due to decay from the intermediate state. To investigate the possibilities for complete (1 %) population transfer, the dressed states of the coherently driven three-level system have to be analyzed. The Hamiltonian of the system reads in Dirac notation rotating wave approximation, with the pump and Stokes laser tuned to the single-photon resonances [Sho9,Ber98,Vit1b] : 16

17 H h = Ω 2 P Ω Ω P S Ω S with the Rabi frequencies Ω P and Ω S of the pump- and Stokes laser driven transitions. The dressed states, as derived from the Hamiltonian, read : a a ± 1 = 2 ( sin Θ 1 m 2 + cos Θ 3 ) = cos Θ 1 sin Θ 3 with the mixing angle Θ defined by sin Θ = Ω P / [Ω 2 P + Ω 2 S ] 1/2 or cos Θ = Ω S / [Ω 2 P + Ω 2 S ] 1/2. The dressed state a does not involve any contribution from the intermediate bare state 2. Thus it provides a direct coupling between the initial state 1 and the target state 3. The conditions for complete transfer of population to the target state read : for t : for t + : a a 1 3 if if cos Θ sin Θ 1 (sin Θ ), Ω 1 (cosθ ), Ω P S ( t ), Ω ( t + ), Ω S P ( t ) ( t + ) At the beginning of the interaction the Stokes laser has to be on (and off at the end of the interaction), while the pump laser is off at the beginning (and on at the end), i.e. the Stokes laser precedes the pump laser pulse, which is a counter-intuitive pulse sequence. Then all the population is transferred completely from the initial to the target state (see fig. 6) in a stimulated Raman adiabatic passage (STIRAP) process. A detailed theoretical treatments for equal Rabi frequencies Ω P = Ω S = Ω yields the condition for adiabatic following Ω τ à 1, with the pulse duration τ [Ber98,Vit1b]. 2.5 Stimulated hyper-raman adiabatic passage (STIHRAP) The STIRAP technique driven on single-photon resonances is a well established tool [Ber98,Hal96,Vit1b]. However in many atomic or molecular systems multi-photon excitations are necessary to populate high lying states. Thus an extension of STIRAP to involve also multi-photon transitions needs to be provided. In the simplest case a two-photon rather than a single-photon transition is driven either by the pump or the Stokes laser (see fig. 7). In contrast to STIRAP this coherent coupling is called stimulated hyper-raman adiabatic passage (STIHRAP) to emphasize the multi-photon coupling [Yat98a,Gue98,Boe1]. As multi-photon transition between two states 1 and 2 are mediated by off-resonant couplings to a manifold of intermediate states i, such off-resonant couplings also induce Stark 17

18 shifts of the levels 1, 2 and 3. These Stark shifts are usually of the same order of magnitude as the two-photon coupling or Rabi frequency [Gue98]. Due to the level shifts the resonance condition between the states 1 and 2 rp. 2 and 3 is not met all during the interaction. Therefore the population transfer process will be strongly affected, i.e. the transfer efficiency will be lowered. Only in special cases multi-photon excitations in STIHRAP permit as efficient population transfer as in the case of single-photon excitations by STIRAP. Fig. 7 : Coupling scheme for STIHRAP, involving a two-photon transition driven by the pump laser and a single-photon transition driven by the Stokes laser. Other states, coupled far off resonance, induce perturbing Stark shifts to the resonantly coupled states, which can reduce the population transfer efficiency dramatically 2.6 Retroreflection-Induced Bichromatic Adiabatic Passage (RIBAP) The techniques for the generation of population inversion in two-level systems, as discussed above, demand frequency-chirped lasers or dynamic Stark-shifts for experimental implementation. It was recently proposed, that even without such setups, a process called retroreflection-induced bichromatic adiabatic passage (RIBAP) [Yat3], permits efficient coherent population transfer in two-level systems. The technique uses a single laser beam, which intersects a particle beam slightly tilted away from normal incidence, thereby inducing a controlled Doppler-shift. A subsequent retroreflection produces effectively a two-pulse bichromatic field in the rest frame of each particle. The retroreflected beam is slightly temporally delayed with respect to the incoming beam and has a reduced intensity. 18

19 Rabi frequencies [arb.units] populations [%] state 1 state Ω 1 Ω time [arb. units] Fig. 8 : RIBAP : Principle coupling scheme (l.h.s.), pulse sequence and population dynamics (r.h.s.). The principle coupling scheme for RIBAP is depicted in fig. 8 (l.h.s.). A two-level system of states 1 and 2 is driven by two coherent radiation fields. The Rabi frequencies are Ω 1 and Ω 2. The frequencies of the incoming and retroreflected radiation field are, due to the Dopplershift, symmetrically detuned by from the transition frequency ω. The laser pulses are temporally delayed, but still partially overlapping. The time evolution of the system in the basis of the bare states 1 and 2 shows a rather complicated dynamics (see fig 8, r.h.s.). In contrast to the adiabatic processes, discussed in the above sections, the population dynamics here are not smooth, but exhibit fast oscillations. Nevertheless, these oscillations damp by constructive quantum interference at the end of interaction to constant values, i.e. complete population transfer. The time evolution cannot be understood in simple terms and in the system of the bare states. Therefore, the dressed state picture of quasi energies, as derived from calculations based on Floquet theory, will be considered in the following (see fig. 9, for details see [Yat3]). The quasi energies belong to the eigenstates of the Floquet Hamiltonian in the two-level system. The eigenstates can be written as n,j where n denotes the photon number state and j the atomic state 1 or 2. Population transfer from the bare state 1 to the 19

20 bare state 2 corresponds in the lowest order of n to an evolution of the Floquet eigenstates from,1 to 1,2. Fig. 9 shows the quasi energies for different ratios α of the driving Rabi frequencies. To permit complete population transfer, the system has to pass the first crossing of the quasi energies diabatically, the second crossing needs to be avoided, i.e. the system evolves adiabatically. No further crossings should take place in the first order of the RIBAP process. Such, only for a ratio α <> and α <> 1 population is transferred coherently from the initial to the target state. Rabi frequencies [arb. units] 2 Ω 1 t 1 t 2 2 Ω 1 t 1 t 2 Ω 2 t 3 2 Ω 1 t 1 t 2 Ω 2 t 3 es [arb. units] quasi energi 1,5 1,,5, 2,2> 1,1> 1,2>,1> 1,5 1,,5, 2,2> 1,1> 1,2>,1> 1,5 1,,5, 2,2> 1,1> 1,2>,1> time [arb. units] time [arb. units] time [arb. units] (a) (b) (c) Fig. 9 : The Floquet quasi energies for different ratios of the driving Rabi frequencies α = Ω 2 /Ω 1. (a) α =, i.e. only one laser pulse interacting with the system: at times t 1 and t 2 the system passes twice diabatically through the crossings of the quasi energies. This corresponds to coherent population return to the initial state,1 (compare sect ). (b) α =.5, i.e. RIBAP configuration : the first crossing at t 1 is passed diabatically, the second crossing at t 2 is avoided. As the coupling decreases with the reduced intensity of the second pulse, no further diabatic crossing with higher Floquet states occurs at later times. The system evolves and remains in state 1,2. (c) α =1, i.e. both pulses equally strong. As in the RIBAP case the first crossing at t 1 is passed diabatically and the second crossing at t 2 is avoided. But as the intensity of the second pulse is still strong at later times t 3 another diabatic crossing to state 1,1 takes place, leaving the system after the interaction in the ground state. 2.7 Dark resonances and electromagnetically-induced transparency (EIT) STIRAP provides complete transfer of population from an initial state 1 to a target state 3, using an intermediate state 2 only to mediate the coupling, but not to store population. In contrast incoherent techniques, e.g. SEP, use the intermediate state 2 to store population 2

21 [Dai95]. Thus, as state 2 is subject to radiative decay, fluorescence will be observed during the interaction (see fig. 1). If STIRAP is implemented in the system, rp. the laser pulses are delayed such that the Stokes pulse precedes the pump pulse, no population will be stored in state 2 and no fluorescence will be observed any more. A dark resonance appears in the fluorescence from state 2, which is a necessary condition for STIRAP [Ber98,Vit1b]. The population is trapped in the dark state a or, at the end of the interaction, in state 3. In a configuration, closely related to STIRAP, it is possible to trap the population in the initial state 1 rather than the target state 3. This works, if the laser pulses are coincident and only the Stokes laser is strong, while the pump laser is weak, i.e. Ω P τ P á 1 and Ω D τ D à 1 (see fig. 1). The system can be described in terms of a strongly coupled sub-system of state 2 and 3 and a weakly coupled state 1. The interaction with the strong Stokes laser (in this case usually called dressing laser) and weak pump laser (in this case usually called probe laser) will not effect state 1, but the sub-system will exhibit strong modifications, i.e. dressed states different from the bare states arise. The dressed states of the sub-system read in the case of the dressing laser tuned to resonance (see also above): ± 1 a = m 2 ( 3 2 ) The dressed states are separated by the Autler-Townes splitting, the dressed energies differ from the energies of the bare states (see above). The pump laser couples the initial state 1 to each of the dressed states. The total absorption probability of the probe laser is calculated by : P µ µ 1a + E + µ E µ + + P 1a P 2 1a 1a 2 With the electric field E P of the probe laser and the transition dipole moments from the initial state to the dressed states µ 1a : µ µ 1a+ 1a = 1 µ a = 1 µ a + = = ( 1 µ 3 1 µ 2 ) = µ 2 ( 1 µ µ 2 ) = + 1 µ 2 As the dipole moments are of the same value, but different sign, the absorption probability of the probe laser cancels to zero, thus the two transitions from the ground state exhibit destructive quantum interference. This phenomenon is called electromagnetically-induced transparency (EIT) [Har97,Mar98]. EIT was shown to be an efficient tool to manipulate media in order to suppress absorption losses [Har97,Mar98,Hal1], manipulate the index of refraction 21

22 and store light in a medium [Phi1,Tur2], stimulate lasing without inversion[fry93] and enhance frequency conversion processes [Dor98, Dora,Dorb,Jai96,Mer99]. With respect to the population dynamics in the medium, all the population is now trapped in the initial state 1, no population resides in state 2 after the interaction and a dark resonance appears in the decay channels, e.g. fluorescence [Alz76,Ari76,Ari96]. A detailed analysis shows, that some population flows during the process to the intermediate state, but coherently returns the ground state. The dark resonances are very pronounced, as the decay from state 2 is completely suppressed, thus the coherently prepared resonances offer a significantly increased contrast with respect to incoherent excitation. Moreover the minimum bandwidth is determined by the lifetime of the target state 3, which is usually a metastable state, i.e. the bandwidth of the dark resonance is very small. Therefore dark resonances can be used in high resolution spectroscopy, e.g. as applied to metrology, or to measure magnetic fields [Alz76]. 1 fluorescense signal [arb. units] detuning dressing laser [arb. units] Fig. 1 : Electromagnetically-induced transparency. A strong dressing laser couples an intermediate and a target state, a weak probe laser connects the ground state to the intermediate state. Due to destructive interference between the transitions from the ground to the dressed states in the strongly coupled sub-system, no population resides in the intermediate state. Therefore no decay, e.g. fluorescence, will be observed any more and a dark resonance shows up in the spectrum, when the dressing laser is tuned across the resonance between the excited states. The probe laser passes the medium then without any absorption losses. 22

23 2.8 Laser-Induced Continuum Structure (LICS) The preparation of dark resonances by EIT is usually implemented in systems of bound states only. The question arises, whether coherent interactions can also be prepared in systems including continuum states. As a continuum is usually viewed as a simple loss channel, it cannot maintain coherence. However this simple picture is not true for coherent preparation of continuum states. Consider a coupling scheme, closely related to the one, implemented in EIT, now involving an intermediate state, which is no longer bound, but belonging to a continuum, e.g. an ionization or a dissociation continuum (see fig. 11, l.h.s.). The dressing laser couples an, initially not populated excited state 2 to the continuum e. The interaction is considered to be strong, i.e. Γ D τ D à 1, with the fragmentation rate Γ D. In the dressed state picture the strongly coupled sub-system of the bound state and the continuum leads to dressed states, which are a combination of the bound state 2 and the continuum states e. Therefore the continuum, which was flat and structureless before the interaction, exhibits now bound state character, i.e. it shows resonance-like properties. The phenomenon is called laserinduced continuum structure (LICS) [Kni9,Boe2,Cav91,Cav93,Cav95,Cav98,Era97,Fau93, Hal98,Hut88,Sha91,Shn96,Yat98b,Yat99b]. The modification of the continuum can be detected by a weak probe laser, i.e. Γ P τ P á 1, photoionizing or dissociating population from a ground state 1. Probe and dressing laser are coincident. As in EIT a dark resonance will appear in the continuum. Thus, when the dressing laser is switched on, the probe laser will no more ionize or dissociate the population from the ground state any more. Fig. Fig. 11 : Coupling scheme for LICS (l.h.s.), quantum interference between fragmentation pathways in LICS (center) and autoionization resonances as a phenomenon, closely related to LICS (r.h.s.) 23

24 LICS can also be described in terms of quantum interference. As the dressing laser is strong, it will also induce off-resonant couplings to other bound states in the system. A two-photon Raman-type coupling, mediated by one dressing and one probe laser photon transfers population from the ground state 1 to the excited state 2, which is subsequently photofragmented by the strong dressing laser (see fig. 11, center). Thus, there are two ways to ionize population from the ground state : either directly by absorption of one probe laser photon or by the multiphoton (2+1) resonantly enhanced photofragmentation process described above. These two pathways interfere, either constructively, leading to an enhancement of the photofragmentation cross section - or destructively, leading to a dark resonance in the fragmentation cross section. This situation is closely related to autoionization resonances, where an excited state is coupled to a continuum by inner-atomic (see fig. 11, r.h.s.) interactions. Population in a ground state can be either excited directly to the continuum or via the autoionizing state, which is subsequently ionized by the inner-atomic couplings. Both pathways interfere, the contrast between the constructive and destructive interference is given by the Fano-parameter q, which is essentially the ratio of the ionization rates via the autoionizing state and the direct fragmentation process. The above discussion also holds true for predissociating states in molecules. In this sense LICS is an artificially prepared autoionizing state, exhibiting the same properties as any autoionization resonance. In contrast to an autoionization resonance the energetic position as well as the shape of a LICS can be controlled by external parameters, e.g. laser frequency and choice of the excited state 2. Problems with respect to coherent population trapping in purely bound state systems arise due to Stark shifts induced by the strong dressing laser pulse as well as competing loss channels, e.g. photofragmentation of the excited state by the probe laser. In the simplest case LICS is implemented in system with a single continuum. In more complex systems, multiple fragmentation channels can be addressed. This is the case if different fragmentation channels appear in parallel, e.g. a molecule dissociating in physically or chemically distinguishable channels - or ionization processes in an atom, leaving the ionic core in different energy levels. Such processes are described by a manifold of continua. LICS prepares each of these continua, thus each fragmentation channel is manipulated [Cav98,Boe2,Shn96]. If the fragmentation channels are coupled by inner-atomic interactions, the continuum resonances will, in general, exhibit different lineshapes. By appropriately tuning the laser frequency, the ratio between the fragmentation channels can be manipulated. 24

25 2.9 Stimulated Raman Adiabatic Passage (STIRAP) via a Continuum Coherent population transfer by stimulated Raman adiabatic passage (STIRAP) is a wellestablished tool to manipulate population distribution in systems of purely bound states [Vit1b]. Although STIRAP uses an intermediate state to provide a coupling between the initial and the target state, there is never any population stored in the intermediate state. Thus the population transfer is not hindered by losses from this state. There has been much interest in the possibility of using also ultra-fast decay channels, i.e. continuum states as the intermediary for STIRAP [Car92, Car96, Dör97, Nak94, Pas97, Tra99, Una98, Vit97, Yat97]. Investigations on laser-induced continuum structure (LICS) have already proven the possibility of coherent interactions via continuum states. However, conventional work on LICS deals only with population losses to the continuum and trapping of population in the initial bound state; no population transfer occurs between the bound states. Fig 12 : Simplified coupling scheme for STIRAP via a continuum (l.h.s.). Coupling scheme including off-resonantly excited states and pump laser induced incoherent loss channel (r.h.s.) The coupling scheme for STIRAP via a continuum is depicted in fig.12. The pump laser couples the initial bound state to a continuum, the Stokes laser induces a coupling between the continuum and the discrete target state (see fig. 12, l.h.s). The pulse sequence is counterintuitive, i.e. the Stokes laser pulse precedes the pump laser pulse. In comparison to purely bound state systems, major problems arise in the coupling scheme, involving continuum states (see fig. 12, r.h.s). As the bound-continuum transitions have to be strongly driven in order to permit adiabatic evolution of the system during the transfer process, the high laser intensities will also excite off-resonant couplings to all other states outside the pure three-level system. 25

26 Thus, dynamic, i.e. time-dependent Stark-shifts of the initial and target will be induced. Therefore, the two-photon resonance between the bound states cannot be maintained during the transfer process. To overcome these perturbing effects, it was proposed to use auxiliary laser fields to compensate the dynamic Stark-shifts [Yat97] Alternatively, a static detuning of the pump and tokes lasers from exact two-photon resonance can be adjusted to minimize the deviation from the dark resonance during the interaction time [Yat97]. Moreover, even if population is transferred to the target state during the time, when the Stokes and pump laser temporally overlap, the falling portion of the pump laser pulse will induce ionization losses, as the pump laser also couples the target state to higher continuum states. Because the transition rates to higher continuum states are usually smaller than the transition rates to the lower states these incoherent losses will not reduce the transfer efficiency to zero, provided the pump laser intensity is not too strong. The limits will be determined by the minimum intensity necessary to drive the STIRAP process and the maximum intensity by the onset of significant incoherent ionization losses [Yat97]. As both the dynamic Stark-shifts and the incoherent losses perturb the STIRAP process and reduce the transfer efficiency, complete coherent population transfer via a continuum is theoretically not possible. The transfer efficiency will be much smaller then 1 %. However, incoherent techniques, e.g. stimulated emission pumping (SEP), do not permit any transfer of population via ultra-fast decay channels, i.e. continua. Therefore coherent population transfer, induced by STIRAP, offers even greater advantages in such environments compared to purely bound state systems E = µ 2 2 c t t E Enhancement of nonlinear optical processes in coherently prepared media As the population distributions in a medium determine any optical property of the system, co- herent preparation of a medium will also modify nonlinear optical properties and processes. If the aim is to enhance nonlinear optical, i.e. frequency conversion, processes, the wave equation for the propagation of a radiation field in a medium determines the conditions for appropriate control mechanisms. The wave equation in the standard form reads : or for the frequency (Fourier) components and ε : 2 P ω + c ε ( z, t) = i ( z, t) t z ε 2 26

27 The wave equations show, that the polarization is the physical property to be controlled in order to manipulate any optical response of the medium to the incoming or generated radiation fields ε. In a two-level system the polarization reads ƒ = N Óµ = N ÓY µ Y c 1 c 2 *, with the number of atoms N, the dipole operator µ and the state vector Ψ = c c 2 2, including the amplitudes c 1 and c 2. 1 populations, coherence [%] population state 1 population state 2 coherence time [arb. units] laser intensities [arb. units] 5 pump Stark probe VUV time [arb. units] Fig. 13 : Population and coherence dynamics in a two-level system driven on a two-photon transition by the SCRAP process. When population is transferred from the ground to the excited state, a nonpersistent maximum coherence is established. The coherence can be used in four-wave mixing processes, e.g. difference- (DFM) or sum-frequency mixing (SFM), driven with an additional probe laser pulse to provide short-wavelength, vacuum-ultraviolet radiation with enhanced conversion efficiency. As the expression for polarization shows, reaches a maximum, if the product of the amplitudes (c 1 c 2 *) is maximized. The product (c 1 c 2 *) is called the coherence of the system and is equal to the off-diagonal element ρ 12 of the density matrix describing the two-level system. The coherence, thus the polarization, reaches a maximum for equal amplitudes c 1 = c 2 * = ½. 27

28 Such, the system is prepared in the state of maximum coherence, i.e. a coherent superposition of the ground and excited state with equal amplitudes. The polarization in the medium cannot reach higher values compared to the case of the maximum coherence, therefore any frequency conversion process in the medium will be driven with the maximum possible efficiency. As the coherence in the system depends on the population distribution, any technique, which permits the preparation of a coherent superposition state will enhance subsequent nonlinear optical processes, e.g. electromagnetically-induced transparency was shown to permit the preparation of a maximum coherence [Har96,Jai96,Kor2,Mer99,Sok98,Sok] in three-level systems. In a two-level system rapid adiabatic passage [Vit1b] rp. Stark-chirped rapid adiabatic passage [Rica] can be used to prepare the state of maximum coherence (see fig. 13). When population is transferred from a ground to an excited state by SCRAP, i.e. on a twophoton transition driven by ultraviolet radiation, during the process an equal distribution of population between the two coupled states is prepared and a maximum coherence is established. As the SCRAP process proceeds towards complete population transfer, this coherence is not persistent, but decays on the timescale of the interaction, i.e. the duration of the exciting pump laser pulse. Still the non-persistent maximum coherence can be used in a frequency conversion process. The conversion process is e.g. driven by another probe laser, timed appropriately with the maximum coherence in order to generate a four-wave mixing signal at the frequencies ω signal = 2 ω pump ± ω probe, which indicates sum- and difference frequency mixing processes. If the wavelength of the probe laser is located in the visible regime, sum frequency mixing with the ultraviolet pump laser easily provides radiation in the signal wave in the vacuum- or extreme ultraviolet spectral region. As the system is prepared by SCRAP in the state of maximum coherence the conversion efficiency will be significantly enhanced with respect to conventional four-wave mixing [Kor3,Mys2,Ric3]. 28

29 3. Coherent manipulation by adiabatic processes : Experimental results The results, discussed in the following sections are obtained from projects, planned, directed or carried out by the author in the years 2 25, some in cooperation with partners. The projects dealt with coherent preparation of bound state two- or three-level systems, manipulation of fragmentation processes in systems involving continuum states as well as investigations on nonlinear optics in coherently prepared media. The results are given in a summarized form, only prominent data are presented as viewgraphs. For a detailed discussion see the publications in the attachments. 3.1 Manipulation of population distributions Coherent interactions, mediated by adiabatic processes, permit the efficient manipulation of population distributions in two-, three- or multi-level systems of atomic or molecular species. A review to the theory and experimental implementation of such processes can be found in ref. [Vit1b], which was written under participation of the author Coherent population transfer by stimulated hyper-raman adiabatic passage The STIRAP-technique in pure three-level systems, involving single-photon excitations only, provides an established tool to transfer population completely from a ground to a target state [Ber98,Vit1b]. As already discussed above (see chap. 2.5), an extension of the technique to systems involving also multi-photon excitations suffers from laser-induced Stark-shifts. These perturb the population dynamics and, in the worst case, suppress any efficient, coherent population transfer [Gue98,Yat98a]. The possibilities and limitations of stimulated hyper-raman adiabatic passage (STIHRAP) were investigated experimentally in a three-level system, involving a two-photon transition, driven by the pump laser (see fig.14, l.h.s.) [Boe1]. In contrast to STIRAP, involving only single-photon excitations, for STIHRAP the dependence of the transfer efficiency on the experimental parameters, e.g. laser frequencies, is more complicated (see fig.14, r.h.s., lower trace). It was found that STIHRAP permits coherent population transfer if the laser frequencies are appropriately detuned from the transition frequencies, such that the perturbing dynamic Stark shifts induced by the pump-laser are at least partially compensated. Moreover, for other choices of laser detunings, other transfer schemes are also possible, e.g. efficient population transfer to the intermediate state by coupling schemes, that are closely related to 29

30 Stark-chirped rapid adiabatic passage (SCRAP) (see above, chap. 2.3, and below, chap ) [Rica]. Ion signal (arb. units) (a) (b) Ion signal (arb. units) Pump detuning D (GHz) P Fig. 14 : Coupling scheme for STIHRAP, implemented in metastable Helium atoms (l.h.s.) : The metastable states of Helium were prepared by electron impact in a gas discharge [Halb] prior to the interaction with the laser pulses. The pump laser couples the metastable state 2 3 S 1 to the intermediate state 3 3 S 1 in a two-photon transition. The intermediate state is coupled to the target states 2 3 P,1,2 which can be selected by appropriate choice of the Stokes laser frequency. The population transferred to the target state(s) is state-selectively probed by (1+1 ) resonantly enhanced multi-photon ionization with a probe laser. Ion signal as a probe for the population in the target states 2 3 P 1,2 versus pump laser detuning from exact two-photon resonance (r.h.s.) : When the Stokes laser is switched off (a) population is transferred by the pump laser, tuned on resonance, to the intermediate state and subsequently by radiative decay to the target state. When the Stokes laser is switched on (b), a complicated pattern of the ion signal versus the pump laser detuning arises. The population transfer is enhanced on two-photon resonance, but also outside the resonance regions of considerable population transfer evolve. The numbers in squares indicate specific transfer processes which are analyzed in detail in ref. [Boe1]. 3

31 3.1.2 Coherent population transfer by Stark-chirped rapid adiabatic passage (SCRAP) The investigations on STIHRAP in metastable Helium (see above, chap ) already revealed evidence for coherent population transfer involving laser-induced Stark shifts. Therefore the same atomic system with slightly modified coupling scheme and experimental setup was used to demonstrate also the possibilities of Stark-chirped rapid adiabatic passage (SCRAP) for efficient coherent population transfer [Rica]. transfer efficiency [%] Experiment Numerical Simulation Ω = 3.6 ns -1 S = 845 ns pump laser two-photon detuning [ns -1 ] Ω = 4.6 ns -1 S = 77 ns -1 Fig.15 : Coupling scheme for coherent population transfer by Stark-chirped rapid adiabatic passage (SCRAP) in metastable Helium atoms (l.h.s.) : The metastable states of Helium were prepared by electron impact in a gas discharge [Halb] prior to the interaction with the laser pulses. The pump laser couples the metastable state 2 3 S 1 and the target state 3 3 S 1 slightly off-resonance. A Stark-laser, with central frequency far off any atomic resonance, provides laser-induced Stark shifts to drive the twophoton transition through resonance with the pump laser. After the interaction with the pump and Stark laser pulse, the population in the excited state is probed by ionization with a probe laser pulse. When the pump laser is detuned appropriately from exact two-photon resonance, the SCRAP process drives all the population from the ground to the excited state. Transfer efficiency to the target state versus pump laser detuning for two different Stark laser intensities rp. Stark shifts (r.h.s.) : Efficient population transfer occurs for the pump laser detuned from exact two-photon resonance, the transfer process is less depending upon the pump laser frequency, if the Stark shift rp. the Stark laser intensity is increased (compare upper and lower trace). 31

32 The coupling scheme and results on the observed transfer efficiency are depicted in fig. 15 : The pump laser excites a two-photon transition between a ground and a target state, a Starklaser provides laser-induced Stark shifts to drive the atomic transition frequency through resonance with the pump laser. Efficient, coherent population transfer close to 1 % was observed, if the experimental parameters, e.g. pump laser frequency, laser intensities and delay between pump and Stark laser are chosen appropriately [Rica]. Deviations from the 1 % barrier of complete population transfer are due to radiative losses from the target state after the SCRAP process has finished. The transfer efficiency is not modified by fluctuations in the experimental parameters, provided certain limits, which are due to the conditions for adiabatic evolution, are kept in view. These conditions mainly demand minimum values for the pump laser intensity and the Stark shift. The results were analyzed in details and coincided with numerical simulations [Rica]. The SCRAP process proved to be a reliable and robust tool to manipulate population distributions, already involving multi- rather than a one-photon transition Dark resonances involving Rydberg states probed by ionization suppression Dark resonances are a well established tool to observe pronounced and spectrally narrow resonances in atomic and molecular media [Alz76,Ari76,Ari96]. Usually the resonances are excited in a lambda-type level scheme, with a stimulated absorption process, excited by the probe laser and a stimulated emission process, driven by the dressing laser (compare sect. 2.7). Nevertheless, dark resonances rp. electromagnetically-induced transparencies [Har97,Mar98] can also be prepared in systems involving multi-photon excitations [Mar98, Dor98,Dora,Dorb]. In the project, discussed here, dark resonances in a ladder-type coupling scheme, involving three-photon excitation of highly excited Rydberg states, were investigated. The dark resonances, observed in resonantly enhanced multi-photon ionization of an intermediate state, exhibited a contrast, which was significantly enhanced with respect to techniques, based on incoherent excitation (see fig. 16) [Hal1]. Ionization was essentially completely suppressed, provided the intensity of the dressing laser was high enough. The data also indicate multi-level interactions, induced by isotope distributions and shifts as well as hyperfine splittings. 32

33 19s [3/2] 1 2s [3/2] 1 22s [3/2] 1 23s [3/2] 1 ion signal [a.u.] 1 18d [1/2] 1 19d [1/2] 1 2d [1/2] 1 21d [1/2] 1 22d [1/2] 1 15 GHz 1 dressing laser frequency 18d [3/2] 1 19d [3/2] 1 2d [3/2] 1 21d [3/2] 1 22d [3/2] 1 1 Fig. 16: Dark resonances in the vicinity of Rydberg states in Xenon. Coupling scheme and experimental results. A probe laser couples the ground state 5p 6 1 S of Xenon to the intermediate state 5p 5 6p [1/2]. Absorption of another probe laser photon leads to multi-photon (2+1) resonantly enhanced ionization of the Xenon atoms. The dressing laser strongly couples the intermediate state 5p 5 6p [1/2] to excited Rydberg states. When the dressing laser frequency is tuned across the resonance between the intermediate and the Rydberg state, the ionization signal breaks down to zero, i.e. the intermediate state is no longer populated and a dark resonance shows up. All the population of the system is now trapped in the ground state. Some dark resonances exhibit sub-structure, which is due to hyperfine splittings and isotope distributions Power broadening revisited : Lineshapes in coherent excitation A simple and prominent example for the principle differences between coherent and incoherent excitation is the, on the first glance well-understood phenomenon of powerbroadening of spectral lines. Consider a radiation field exciting a transition in a two-level system, while the fluorescence from the excited state is observed. The bandwidth of the laser-induced fluorescence is expected to increase, if the laser intensity is increased above the saturation intensity - as at higher intensities the excitation probability saturates in the line center, while it still increases outside the line center [Dem98]. A detailed analysis shows, that this only holds true, if 33

34 the excitation process is incoherent. In contrast, the lineshapes, obtained after coherent excitation, depend critically upon the timing of the excitation process and the probing process, which detects the population transferred to the upper state [Hal3,Vit1a]. ion signal [arb. units] ion signal [arb. units] ion signal [arb. units] 1,,8,6,4,2, 1,,8,6,4,2, 1,,8,6,4,2, (a),5 GHz (b) 1,1 GHz (c) 2,5 GHz.75 GW/cm GW/cm GW/cm detuning [GHz] LIF-Signal [arb. units] LIF-Signal [arb. units] LIF-Signal [arb. units] 1,,8,6,4,2, 1,,8,6,4,2, 1,,8,6,4,2 (d) 28 MHz (e) 27 MHz (f) 26 MHz.75 GW/cm GW/cm GW/cm 2, detuning [GHz] Fig. 17 : Powerbroadening in a coherently driven two-level system. Coupling scheme : The pump laser excites population from the ground state 5p 6 1 S to the upper state 5p 5 6p [1/2] on a two-photon transition. Another photon from the pump laser serves to ionize some upper state population. Alternatively fluorescence from the upper state to lower lying states is observed. The lifetime of the excited state is longer than the laser pulse duration. Spectra obtained in ionization (left column, (a,b,c)) and fluorescence (right column, (d,e,f)) for different pump laser intensities : When the intensity of the pump laser is increased, the ionization spectra show significant power broadening, while the fluorescence spectra remain almost unchanged. This is due to the time delay in the probing process, when fluorescence is observed, i.e. the radiative decay occurs mainly after the excitation process, while the pump-laser induced ionization happens during the excitation process. It was shown theoretically and experimentally by the author and cooperation partners, that powerbroadening does not occur, if the probing process takes place after the excitation proc- 34

35 ess [Hal3]. For overlapping excitation and probing process the spectral line will broaden when the intensity of the exciting radiation field increases. Thus, the appearance of powerbroadening depends upon the nature of the probing process (see fig. 17) Coherent Population Transfer by Retroreflection-Induced Bichromatic Adiabatic Passage The technique of retroreflection-induced bichromatic adiabatic passage (RIBAP) [Yat3] was proposed as a surprising mechanism to prepare population inversion in a two-level system (see sect. 2.6) In the RIBAP process a two-level system is exposed to two radiation fields, symmetrically detuned to either sides of the transition frequency. By constructive quantum interference between the two off-resonant transitions population is driven completely from the ground to the excited state. So far RIBAP had not been experimentally demonstrated. transfer efficiency (%) , -2,5-2, -1,5-1, -,5,,5 1, 1,5 2, 2,5 3, pump laser tuning [GHz] Fig. 18 : Coherent population transfer by RIBAP in metastable Helium atoms. Coupling scheme : The metastable state 2s 3 S 1 is coupled by two counter-propagating, suitably delayed pump radiation fields to the excited states 3p 3 P 1,2..The closely spaced excited states can be considered in the experiment as a single state. The population transferred to the excited states is monitored by photoionization with an additional probe radiation field after interaction with the pump laser pulses. Experimental data : Calibrated ion signal versus pump laser tuning. For each pump radiation field alone, the transition frequency is Doppler-shifted from the center frequency (blue and green line). The maximum transfer efficiency on the Doppler-shifted resonances is 5 %. The incoherent sum of the two excitation pathways would yield an ion signal according to the dashed line. Almost no transfer would be observed between the Doppler-shifted transitions. The maximum efficiency could not exceed 5 %. In contrast, when both laser beams are coherently interacting during the RIBAP process with the atomic system, a broad plateau of complete population transfer arises (red line). 35

36 RIBAP was experimentally implemented for the first time by the author and coworkers [Per5]. Helium atoms in the metastable triple state were driven by coherent interaction with two counter-propagating and temporally delayed radiation pulses, tuned in the vicinity of the transition frequency between the initial metastable state and excited states (see fig. 18). The lasers intersected the atomic beam of Helium atoms under an angle, which was different from normal incidence. Such Doppler-shifts of the transition frequency were induced. The sign of the Doppler-shifts was different for the two counter-propagating laser beams. The maximum transfer efficiency, expected for incoherent excitation by the two radiation fields, cannot exceed 5 %. Moreover no population transfer should be possible on the center of the resonance, as the transitions, induced by the two radiation fields, are Doppler-shifted. In contrast, by coherent interaction, complete population transfer on a broad frequency plateau, which included the center of the resonance, was observed (see fig. 18). The data are a striking example for the surprising features and the efficiency of coherent interactions [Per5] Coherent Population Transfer via Continuum States Coherent population by stimulated Raman adiabatic passage (STIRAP), implemented in systems of purely discrete states, found numerous applications in atomic and molecular physics [Vit1b]. While an extension of the STIRAP technique to systems involving also continuum states was theoretically proposed already many years ago [Car92, Car96, Dör97, Nak94, Pas97, Tra99, Una98, Vit97, Yat97], coherent population transfer via a continuum had never been demonstrated experimentally so far (see also sect. 2.9). The author and coworkers implemented the first successful experiment of coherent population transfer by STIRAP via the ionization continuum in Helium atoms (see fig. 19) [Pet5]. Such, several percent of the population in the metastable singlet state of Helium were transferred via coherent interaction with the ionization continuum to an excited discrete state. The laserinduced couplings were implemented with rather slow (ns) radiation pulses, while the ionization continuum exhibits an ultra-fast (fs) decay channel. It was experimentally confirmed, that the population transfer was indeed due to coherent interaction, mediated by two radiation pulses in a counter-intuitive pulse sequence, i.e. in STIRAP configuration. In contrast, a pulse sequence, attributed to stimulated emission pumping (SEP; pump pulse preceding Stokes pulse) via off-resonant excitation to the manifold of all other states in the system, did not yield any transfer at all [Pet5]. 36

37 Population [%] E kin =.25 ev E kin =3.31 ev 2-1,5-1, -,5,,5 1, 1,5 Laser tuning [GHz] Fig. 19 : Coherent population transfer via the ionization continuum in Helium atoms. Coupling scheme : The pump laser and the Stokes laser couple the intially populated state 2s 1 S to the target state 4s 1 S via the ionization continuum (solid lines). The pump laser can also ionize population transferred to the target state (dotted line). The photoelectrons, generated by pump laser induced ionization of the initial state and target state were separately detected as a measure for the population in the two discrete states. Experimental data : Measured electron signals versus tuning of the pump laser in the range of the two-photon resonance for Stokes laser preceding pump laser pulse. The circles and the triangles indicate slow and fast electrons respectively. The signal from the slow electrons shows a minimum, i.e. a dark resonance, while the fast electron signal reaches a maximum, which clearly indicates population transfer to the target state. 37

38 3.2 Manipulation of fragmentation processes Laser-induced continuum structure (LICS) in multiple continua In a previous project the author demonstrated the preparation of pronounced laser-induced continuum resonances in the single ionization continuum of Helium [Hal98]. Thanks to the implementation with lasers of excellent coherence properties, the observed resonances exhibited a strongly enhanced contrast with respect to laser-induced continuum resonances, reported so far in the literature [Kni9,Cav91,Cav93,Cav95,Cav98,Era97,Fau93,Hut88,Sha91, Shn96]. As an extension of the latter project the manipulation of multiple fragmentation continua was planned. Such continua are of interest for applications in physical chemistry, i.e. the control of photodissociation processes or chemical reactions [Sha94,Sha99,Sha,Cav98, Shn96]. As a test case the two-fold ionization continuum in Xenon was chosen. Following photoionization the ionic core of Xenon can be left in two fine structure components (see fig. 2). The experimental investigations showed the efficient manipulation of both ionization channels by laser-induced continuum structure. Dark resonances with a manipulation depth up to 8 % were observed [Boe2]. As both channels behave the same way with respect to the variation of the ionization cross section with the laser detuning, switching between the channels was not possible. This may be due to a lack of coupling between the two ionization continua. A detailed analysis of atomic parameters has to be subject to extended theoretical calculations, as the standard method of multi-channel quantum defect theory failed to explain the clear experimental data [Boe2]. The lineshape of the laser-induced continuum structures is determined by the Fano-parameter q, which indicates the ratio between the Raman-type coupling of the excited bound states (in the case of the experiment discussed above between the states 5p 5 6p [1/2] and 5p 5 9p [1/2]) via all other bound states and the coupling via the continuum (see also above, chap. 2.8). As the continuum resonances are almost symmetric and do hardly exhibit any enhancement, the Fano-parameters are close to zero [Boe2]. 38

39 12 fast electrons (%) q=.21 Γ=59 MHz slow electrons (%) q=.6 Γ=6 MHz dressing laser tuning (GHz) Fig. 2 : Coupling scheme and ionization cross sections versus probe laser detuning. The state 5p 5 6p [1/2] state is excited from the ground state 5p 6 1 S by two photons. The dressing laser couples the state 5p 5 9p [1/2] to the two-fold ionization continuum. The laser-induced continuum resonance is probed by one-photon ionization from the state 5p 5 6p [1/2]. The process leading to the formation of LICS with coincident probe and dressing pulses is separated from the excitation process by a suitable time delay. The electrons generated in the two ionization continua are separated by their kinetic energy (fast electron belonging to the lower continuum and slow electrons belonging to the upper continuum). When the probe laser is tuned across two-photon resonance between the excited states 5p 5 6p [1/2] and 5p 5 9p [1/2], pronounced and spectrally narrow dark resonances show up in the ionization cross sections. Fit parameters for the Fano-parameters q and bandwidth Γ are given in the figure Modification of autoionization lineshapes As in the case of LICS, the lineshape of an autoionization resonance is described by the Fanoparameter q. The parameter depends strongly on the quantum numbers of the excited states rp. the excitation pathway. Thus, different excitation pathways to the same autoionizing target state will change the lineshape of the observed resonance. This was demonstrated experimen- 39

40 tally and confirmed by theoretical calculations for autoionizing states in Xenon, populated by multi-photon (2+1 ) excitation via different intermediate states [Ste3] d' 16 s' P 1/2 cross section [arb. units] d' 21 2 s' 9 cm -1 Xe 358,2 358,4 358,6 358,8 359, 359,2 359,4 359,6 probe laser wavelength [nm] P 1/2 d' s' cross section [arb. units] s' 7 cm d' Xe cm probe laser wavelength [nm] Fig. 21 : Coupling schemes and autoionization spectra in Xenon for multi-photon (2+1 ) resonantly enhanced excitation from the ground state via different intermediate states to target autoionizing states 5p 5 ( 2 P 1/2 ) ns or 5p 5 ( 2 P 1/2 ) nd. If an intermediate state belonging to the ionic core configuration 2 P 3/2 is chosen (upper row, red data), the spectrum exhibits only window-type nd -resonances, while no contributions from ns -states are visible. If an intermediate state belonging to the ionic core configuration 2 P 1/2 is selected (lower row, blue data), both the nd - as well as the ns -resonances are visible. Thus for both types of resonances the Fano-parameters, i.e. autoionization lineshape, have significantly changed with the different intermediate states. 4

41 Autoionization resonances, which were clearly visible in spectra following excitation via a specific intermediate state seem to vanish, when another intermediate state is chosen (see fig. 21). As autoionization resonances are also important for frequency conversion processes to yield short-wavelength radiation (see fig. 22) [Blo77,Kni83] these investigations are closely related to the projects on nonlinear optical processes (see below, chap. 3.3) THG intensity [arb. units] d' s' Xe 5 278,5 279, 279,5 28, probe laser wavelength [nm] Fig. 22 : In comparison to the data, presented in fig. 21 we also monitored the lineshape of autoionization resonances in Xenon, as revealed in third-harmonic generation without any intermediate states involved. As there is no preference now for any intermediate state core configuration, both ns - as well as the nd -resonances are visible. Besides the spectra discussed above, also data on autoionization resonances so far not sufficiently well investigated had been collected. New level energies and quantum defects have been measured in cooperation with partners. The experimental setup, implemented by the author and coworkers, permitted the determination of atomic parameters for even mp 5 nl resonances in Neon with high accuracy [Pet4] Suppression of incoherent losses in Stark-chirped rapid adiabatic passage (SCRAP) by laser-induced continuum structure (LICS) A major problem for strongly driven, coherent excitations are subsequent incoherent losses, mediated by multi-photon excitations, induced by the driving radiation fields. Such, otherwise 41

42 successful implementations of coherent population transfer, e.g. by Stark-chirped rapid adiabatic passage on two-photon transitions in hydrogen atoms [Yat99a], are hindered by multiphoton photoionization losses. To overcome this problem, a combination of Stark-chirped rapid adiabatic passage (SCRAP) and laser-induced continuum structure (LICS) was proposed to permit both coherent excitation as well as suppression of incoherent ionization losses. The key feature of the technique is a temporally suitably delayed dressing laser pulse, which serves both to modify the ionization cross sections as well as induce dynamic Stark-shifts to drive a SCRAP process. We show theoretically that the technique permits the preparation of population inversion between the ground state and the metastable state in hydrogen atoms with significantly reduced photoionization losses of the total population. 42

43 3.3 Manipulation of frequency conversion processes Frequency conversion enhanced by Stark-chirped rapid adiabatic passage Nonlinear optical processes, i.e. frequency conversion processes, are of considerable interest to extend the wavelength regime, accessible by coherent radiation sources. The efficiency of such conversion processes is usually rather small due to the small nonlinear optical susceptibilities in the medium. This holds especially true for the generation of short-wavelength, vacuum- or extreme ultraviolet radiation, which is of interest for applications in laser lithography, high-resolution microscopy or spectroscopy of highly excited atomic or molecular species. Coherent preparation of the nonlinear optical medium may serve to overcome the small conversion efficiencies. Such, electromagnetically-induced transparency (EIT) was implemented to reduce losses due to reabsorption of the generated vacuum-ultraviolet radiation [Har97,Mar98,Dor98,Dora,Dorb] or to enhance the generation of ultraviolet radiation by preparation of a maximum coherence [Har96,Jai96,Mer99,Sok98]. However EIT applied to a lambda-type level scheme does not permit the generation of radiation with much shorter wavelength, as the coupling scheme involves both stimulated absorption and emission processes (see above). If multi-photon transitions are used instead to reach highly excited states, EIT suffers at higher intensities, as STIRAP rp. STIHRAP (see above, chap. 2.5) from dynamic Stark shifts [Boe1,Gue98,Yat98a] These limitations are overcome, if SCRAP [Rica] is used to prepare the medium. In the approach discussed here a two-level system, driven on a two-photon transition, is prepared in the state of maximum coherence by SCRAP. The maximum coherence is used in a thirdharmonic generation process to yield extreme-ultraviolet radiation at λ = 71 nm (see fig. 23) [Ric3]. The experiment was performed in a dense, supersonic jet of Krypton atoms, which serve as a typical medium for the generation of short-wavelength radiation. The main results from this specific experiment on third-harmonic generation [Ric3] as well as from more general analytical [Kor3] and numerical simulations [Mys2] of four-wave mixing processes in SCRAP-prepared media are as follows : (a) SCRAP enhances the generation of extreme-ultraviolet radiation in Krypton by more than one order of magnitude with respect to conventional frequency conversion (see fig. 23) (b) The preparation of a maximum coherence by SCRAP is not effected by inhomogeneous broadening in the medium, provided the laser-induced Stark shifts are larger than the Doppler 43

44 width. This is an interesting feature with regard to applications, as usually dense, gaseous media, which are subject to Doppler broadening are used for efficient frequency conversion techniques. (c) SCRAP offers the biggest enhancement with respect to conventional frequency conversion in the case of moderate laser intensities, right at the edge of saturation. There is no need in higher laser intensities to exploit the advantages of SCRAP. 25 Stark laser ON Stark laser OFF THG signal [arb. units] pump laser tuning [GHz] Fig. 23 : Third-harmonic generation in Krypton supported by SCRAP : coupling scheme and thirdharmonic yield versus pump laser detuning. The pump laser at λ = 213 nm excites the 4p 6 1 S Ø 4p 5 5p [ ½] two-photon transition. Another photon from the pump laser couples the excited state to the continuum. A strong laser at λ = 164 nm provides dynamic Stark shifts for the SCRAP process.. When the Stark laser is switched off, conventional resonantly enhanced (2+1) third-harmonic generation yields only low conversion efficiency (red data points), enhanced in the vicinity of the atomic resonance. When the Stark shift laser is switched on, the system is driven in the SCRAP process and a maximum coherence is prepared on the 4p 6 1 S Ø 4p 5 5p [ ½] two-photon transition. The conversion efficiency is enhanced by about a factor of 22 (blue data points) with respect to the case of conventional third-harmonic generation. 44

45 3.3.2 High-order stimulated Raman scattering induced by ultrashort (fs) laser pulses The preparation of a maximum coherence in the experiment discussed in the previous section was implemented with rather long (ns) laser pulses in order to fulfill the condition for adiabatic following. This condition essentially gives lower limits for the pump laser intensity and the Stark shift [Rica]. In terms of the Rabi frequency it means, that the relevant transition has to be strongly driven, i.e. a large product of Rabi frequency and interaction time (see above, chap. 2.2 and 2.4) is needed. Thus, a transition can be either strongly driven if the laser intensity is weak, but the interaction time is long - or the interaction time is short, but the laser intensity is high. wavelength [nm] sideband intensity [arb. units] without OPG with OPG H 2 Ti:sapphire CPA laser broadband spectrometer optical fiber 8 nm, 1 fs, 2 mj, 1 Hz CaF 2 white light Tunable (OPG) KDP 4 nm BBO BBO Tunable,4,6,8 1, 1,2 1,4 frequency [1 15 Hz] diffuser Gas-filled capillary Fig. 24 : High-order stimulated Raman scattering in Hydrogen molecules. Experimental setup and spectrum of the anti-stokes sidebands. When a pump laser only at λ = 8 nm excites the Hydrogen molecules, the Raman anti-stokes sidebands vanish in the background, only the fundamental radiation is visible in the spectrum (red data points). When a second (Stokes) radiation pulse, provided by an OPG is introduced into the system and tuned to a Raman transition in Hydrogen, strong anti-stokes sidebands arise in the spectrum (blue data points). The sidebands are strong enough to be clearly visible on a screen. 45

46 For conventional laser systems the best combination of laser intensity and pulse duration, rp. interaction time, is given by nanosecond (ns) or long picosecond (ps) pulses [Vit1b]. These systems are, in general, best to drive adiabatic processes. Laser systems providing ultrashort (fs) radiation pulses are usually not appropriate for coherent preparation. On the other hand, ultrashort (fs) pulses are a proper choice to drive nonlinear optical, e.g. frequency conversion processes. Thus coherent preparation of the nonlinear optical medium also by fs pulses would be convenient. If proper preparation of a maximum coherence is not possible, even less efficient stimulation of a coherence can support nonlinear optical processes. The effect of stimulation of molecular coherences to drive Raman scattering processes was investigated in cooperation with the group of Prof. Dr. J.P. Marangos at Imperial College, London (UK). Such, the generation of Raman sidebands in Hydrogen (H 2 ) and Methane (CH 4 ) was dramatically increased by stimulating two-photon transitions with ultrashort (fs) radiation pulses, thus not providing a maximum, but still an enhanced coherence in the system (see fig. 24). The sidebands were generated with an efficiency in the order of 1 % [Sal4]. In order to tune to the relevant molecular transitions, broadly tunable ultrashort radiation pulses were required. These were provided by an optical parametric generator (OPG) and amplifier system, setup by the author. An important application of the efficient high-order stimulated Raman scattering process as discussed above is the generation of attosecond (as) pulses [Ant96,Chr97,Dre1,Sal1]. As the (fs) Raman sidebands are phaselocked with respect to each other, they could be superimposed to form an attosecond radiation pulse. Similarly the generation of ultrashort (fs) radiation pulses by preparation of a maximum coherence in Hydrogen molecules, excited by ns radiation pulses has already been reported in literature [Sok1] Generation of short-wavelength radiation by interaction of a nanosecond and a femtosecond laser pulse The considerations, discussed above revealed the important differences between coherent preparation of media with rather long (ns) or ultrashort (fs) radiation pulses. While nanosecond lasers are a good choice to drive adiabatic processes [Vit1b], femtosecond pulses are very appropriate to drive nonlinear optical processes. A combination of both such laser systems in the excitation of nonlinear optical media would be most desirable. To explore such possibilities, the four-wave sum-frequency mixing process of a nanosecond and a femtosecond laser pulse in a jet of Xenon atoms was investigated by the author [Hala]. The mixing process 46

47 was found to yield vacuum-ultraviolet radiation with efficiencies, comparable to related nonlinear optical interactions, e.g. high-order harmonic generation Generation of short-wavelength radiation in organic molecules High-order harmonic generation, induced by ultrashort (fs) radiation pulses, serves as an efficient tool to provide short-wavelength radiation. Usually the technique is implemented in rare gases, as such media offer sufficiently large nonlinearities and high ionization potentials, which permit a low threshold for the minimum attainable wavelength [Pro97]. Nevertheless, molecules as the nonlinear optical media, offer advantages, as giant resonances can enhance some modes in the harmonic spectrum. Thus, in a project, conducted in the group of Prof. Dr. J.P. Marangos, Imperial College, London (UK) under participation of the author, cyclic organic molecules as the nonlinear optical media were investigated. These systems were shown to yield conversion efficiencies for selected harmonics, which are comparable to the yield in Xenon, as the most efficient atom for high-order harmonic generation. The power dependence of the generation efficiency for different pulse durations revealed that photofragmentation processes play an important role. For longer radiation pulses, the harmonics are not only generated by the parent molecule, but also by fragments, while for shorter pulses photofragmentation does not affect the nonlinear optical process [Hay,Hay1] Probing attosecond (as) pulse trains by phase control techniques The generation of ultrashort, sub-femtosecond laser pulses is a topic of considerable scientific interest [Ant96,Chr97,Dre1,Sal1]. Besides the preparation of such pulses, their detection is, already from the principal point of view, not a simple task. In a proposal, planned and directed by Greek cooperation partners, a technique based on phase control to determine the relative phase and amplitude of the frequency components in an attosecond pulse was suggested [Her1]. The attosecond pulse is supposed to be generated by superposition of highorder harmonics. The method is based on quantum interference between multi-photon ionization channels, induced by the fundamental laser frequency and the high-order harmonics, yielding the relative phase of each harmonic. This information permits the evaluation of the temporal structure of the attosecond pulse. As the technique relies on quantum interference involving ionization continua, it is also closely related to the topics, discussed above (see chap. 3.2). 47

48 3.3.6 Preparation of coherent superpositions in three-state systems As in two-level systems, excited e.g. by SCRAP [Rica], the preparation of coherent superpositions [Kor3,Mys2,Ric3], is also possible in three-level system by adiabatic processes. Such, coupling schemes, closely related to EIT [Har97,Mar98] or STIRAP [Ber98,Vit1b], were shown to permit the preparation of non-persistent maximum coherences [Jai96,Mer99,Sok], which can be used for frequency conversion processes. A combination of STIRAP-type coupling schemes, involving pump- and Stokes-laser driven one-photon excitations, and dynamic Stark shifts, induced by a third laser, are proposed by the author and coworkers to permit the preparation of arbitrary, persistent coherent superpositions of any combination of states in three-level systems of lambda-, ladder- and V-type configuration [San4]. Specific three-level schemes for frequency conversion processes, enhanced by coherently prepared maximum coherences in Mercury vapour are also suggested. 48

49 4. Summary and outlook In the present work coherent, adiabatic interactions were shown to permit the efficient manipulation of population distributions, fragmentation processes and nonlinear optical processes in media, involving bound-bound as well as bound-continuum couplings. Major results have been obtained on the following subjects : (a) Techniques for efficient coherent population transfer, among them Stark-chirped rapid adiabatic passage (SCRAP), stimulated hyper-raman adiabatic passage (STIHRAP) and retro-reflection induced bichromatic adiabatic passage (RIBAP) were investigated with respect to related coherent or incoherent techniques, applications and limitations. The first experimental demonstrations of STIRAP via continuum states and RIBAP were performed. (b) Atomic photofragmentation processes in multiple continua were significantly manipulated by laser-induced continuum structure (LICS). The most pronounced and spectrally narrow laser-induced continuum resonances were observed. (c) Third-harmonic generation in an atomic medium, coherently prepared by Stark-chirped rapid adiabatic passage (SCRAP) was shown to be enhanced by more than one order of magnitude with respect to conventional frequency conversion, permitting efficient generation of short-wavelength, extreme-ultraviolet radiation. The key features of the technique were investigated extensively, both experimentally and theoretically. (d) In cooperative projects, closely related to coherently enhanced third-harmonic generation (see above, (c)), frequency conversion processes driven by ultrashort (fs) radiation pulses were studied. Such, coherently stimulated efficient Raman sideband generation, the effect of fragmentation processes in molecular media on high-order harmonic generation and efficient sum frequency mixing schemes were investigated. (d) Interactions, based on coherent population trapping were shown to permit the manipulation of spectral lineshapes, i.e. the suppression of powerbroadening and the preparation of pronounced dark resonances also in ladder-type level schemes, involving multi-photon excitations. (e) In cooperative projects, closely related to the coherent manipulation of fragmentation continua (see above, (b)), autoionization resonances in rare gases were investigated. The modification of autoionization lineshapes was studied and spectroscopic parameters determined from the experimental data. 49

50 The successful implementation of coherent interactions, as discussed above, will be extended in future projects. Subject to these projects will be the investigation and development of new coherent interactions, the implementation of new applications for existing schemes of adiabatic preparation and implementation of adiabatic interactions in other than gaseous media. The planned experiments will focus in particular on nonlinear optical frequency conversion processes in media, prepared by STIRAP and SCRAP in extended and modified coupling schemes to enlarge the accessible wavelength regime. Moreover, in cooperation with partners, possibilities to combine preparation of nonlinear optical media by rather long (nanosecond) laser pulses and frequency conversion in such media, driven by short (pico- or femtosecond) radiation pulses will be a subject of future investigations. To exploit coherent interactions also in environments, offering high densities, projects on adiabatic processes in solids are planned. Such the number of applications for coherent, adiabatic interactions should be significantly enlarged to permit stimulating input to a broad field of laser-based research. 5

51 5. Acknowledgements The research program presented above would have been impossible to carry out without the help, assistance and significant personal and scientific support from friends, coworkers and cooperation partners all across the world. I like to mention some of them in this section though I am aware, whatever I say or write, can never be complete and enough. First of all I have to acknowledge the tremendous support by Prof. Dr. K. Bergmann, TU Kaiserslautern. It would take a long time to mention all the advices, ideas, opportunities, motivation, backing, coaching, mentoring, that was given to me for free - as well as financial support and a lot of nice and fancy equipment for my laboratory, when I started from scratch. Where ever my professional life will lead me to, I hope, I will be able to give at least a small fraction of all this support back in the future. Danke, Klaas. The members of my laboratory, among them postdocs, graduate (PhD) students and diploma students, had the pleasure - and also the pain - to run, usually in close and active cooperation with myself, the research projects. Dr. K. Böhmer, Dr. T. Rickes, Dr. M. Johnsson, Dr. S. Guerin, Dr. K. Temelkov, the graduate (PhD) students T. Peters, A. Peralta-Conde, M. Oberst, J. Klein and M. Stellpflug as well as the diploma students J. Könsgen, A. Horsmans, A. Mühlbauer, and L. Brandt, together with technical support by R. Walther and L. Meyer, were and some still are the backbone of the laboratory. Therefore I have to say Dankeschön! for all the time, you spent with and at the complicated setups and experimental arrangements - sometimes successfully, sometimes loosing against the forces of evil, which every experimentalist has to fight day by day. Anyway, we never gave up and never will surrender. During my - still short - career in science I had the pleasure to cooperate with a large number of scientists from the entire world, many became friends in the years of the cooperation. Among the cooperation partners I like to mention the hosts of my postdoctoral time, Prof. Dr. P.L. Knight, F.R.S. and Prof. Dr. J.P. Marangos, both Imperial College, London (UK). Prof. Dr. J.P. Marangos also became my closest cooperation partner later, participated in many of the projects discussed here, gave me the opportunity to share laser time at a laser system providing ultrashort (fs) laser pulses - and always enriched my scientific and private life with plenty of ideas. Ta, Jon. Another close scientific connection, established in several years of common scientific efforts was due to cooperation with the group of Prof. Dr. M. Shapiro, 51