Coherent interaction of femtosecond extreme-uv light with He atoms

Coherent interaction of femtosecond extreme-uv light with He atoms Daniel Strasser, Thomas Pfeifer, Brian J. Hom, Astrid M. Müller, Jürgen Plenge, and Stephen R. Leone Departments of Chemistry and Physics, and Lawrence Berkeley National Laboratory, University of California, Berkeley, California 9472 We show experimentally that spectral phase manipulation of ultra-short extreme-uv light pulses can induce and control coherent transient excitation of the He(1s3p) excited state by the nonresonant components of the broadband EUV light. The spectral phase manipulation of the 15th harmonic of an intense 85 nm, 8 fs pulse is achieved by propagation of the EUV light through a variable optical density of He gas. The acquired spectral phase due to the dispersive interaction of the off-resonance components in the EUV pulse with the He(1s3p) resonance enhances and modifies the transient excitation. The temporal evolution of the coherently-prepared transient He(1s3p) amplitude is probed by ionization to the continuum with a 4 nm, 8 fs pulse. PACS numbers: 42.65.Ky, 32.8.Qk In the near infrared (8 nm) regime, ultra-short laser pulses are routinely used for coherent control of atomic and molecular quantum processes [1 3]. In particular, shaping of the spectral phase of fs pulses is used to selectively enhance [4 6] or attenuate [7] resonant vs. nonresonant pathways of multi-photon absorption in Rb atoms. Coherent control of fundamental systems systems such as the He atom requires access to fs pulses in the extreme- UV (EUV) regime. In recent years, various ultra-short EUV light sources have become available. High harmonic generation (HHG), based on intense 8 nm laser pulses focused into rare gases, provide short duration (ps to as) coherent EUV pulses [8]. Other types of sources include synchrotron radiation, using the so called pulse slicing technique [9], plasma based EUV lasers [1] as well as free electron laser projects[11]. Ultra-short EUV pulses, in synchronism with IR and visible short laser pulses, were proposed and applied to probe the temporal evolution of photo-initiated dynamics in atomic[12, 13] and molecular systems [14 17]. In recent work, pulse shaping of high harmonic generation pulses by transmission through thin Al foils was demonstrated experimentally to provide attosecond pulse trains [18]. In addition, calculations of coherent control with intense EUV pulses [19] show the possibility to maximize or minimize a nonresonant two-photon He(1s1s) He(1s3s) excitation by shaping the spectral phase of the EUV light. In this paper we demonstrate experimentally the application of pulse shaping and control of coherent transients in the emerging field of ultra-short EUV pulses based on the use of dispersion around an absorption resonance. We show experimentally that shaping the spectral phase of the 15th harmonic of 85nm by propagation through He gas enhances the nonresonant transient excitation of the He(1s3p) excited state. The spectral phase of the nonresonant components in the EUV pulse are controlled by changing the He optical thickness; consequently the temporal profile of the transient excitation of the He(1s3p) state by the shaped pulse is modified. The time-dependent transient population of the He(1s3p) state is probed by time-resolved ionization to the continuum with a 4 nm (8 fs) pulse, and the result is shown to follow a characteristic temporal function that depends on the He optical thickness along the propagation path of the EUV pulse. Since the pulse shaping presented here is decoupled from the high harmonic generation process, it can be applied to the other types of ultra-short EUV sources [9 11] and allow coherent control of benchmark processes, such as the He(1s3p) transition. The experimental setup, previously described [2], is shown schematically in Fig. 1. At 1 khz repetition rate, the 85 nm, 2.9 mj, and 8 fs Ti:sapphire laser pulses are split into two arms. One arm (7% of the power) is focused into a pulsed Ar gas jet to generate coherent, ultrafast, high order harmonics of the fundamental 85 nm radiation. The 15th harmonic is selected and refocused by grazing incidence optics; a spherical grating in zeroth order and toroidal grating in first order direct the beam to the interaction region, typically delivering 3 1 6 photons/pulse [2]. The other arm (3% of the power) is doubled in a BBO crystal to produce typically 18 µj 4 nm pulses, which intersect the EUV beam at an 1.5 angle in the interaction region. At the interaction region an effusive He beam crosses the laser beams at a right angle. The energy of the emitted photoelectrons is analyzed by an 1.3 m long time-of-flight(tof) magnetic-bottle spectrometer. The photoelectron background spectrum is removed by blocking every other 4 nm pulse and subtracting the photoelectron spectrum produced by the EUV pulse alone from the spectrum produced by both the EUV and 4 nm. The TOF spectrum consists of a single peak arriving at the detector 2.1 µs after the laser pulse, corresponding to 1.6 ev photoelectron kinetic energy. The peak appears only for positive time delays of the 4 nm pulse, at which the EUV pulse arrives first, in agreement with the following ionization scheme: He(1s1s) + 53.7 nm He(1s3p) excitation (both resonant and nonresonant), followed by ionization

2 after a time delay t, He(1s3p) + 4 nm He + +e (1.6 ev). The TOF spectrum is recorded as a function of the time delay between the EUV and 4 nm pulses, which is controlled by a variable delay stage (see Fig. 1). The measurements are performed with a He effusive beam with low backing pressure, in order to maintain an ambient He pressure in the interaction region vacuum chamber below 1.3 1 4 Pa. A dedicated leak valve attached to the grating vacuum chamber is used to introduce He gas (up to 6 1 2 Pa) along the optical path of the EUV light on its way to the interaction region. Changing the optical thickness of the resonant medium shapes the EUV spectral phase by the dispersion near the absorption resonance. photoelectrons (counts) 2 1 5 1 15 2 25 3 time (ps) Ti: Sapphire 8 nm, 8fs 2.9 mj @ 1kHz Spherical Ar grating Pulsed Jet time delay BBO toroidal grating 4nm He leak valve He effusive beam FIG. 1: experimental setup. Magnetic Bottle e TOF Figure 2 shows a sequence of the photoelectron count rates as a function of the EUV pulse, 4 nm pulse time delay, and the He optical density. At first no He is leaked into the grating chamber, shown by the filled circles ; then the He optical thickness is increased slightly by leaking He into the grating chamber, shown by the and + symbols (higher He optical thickness). The time delay was scanned with 1 fs steps and the photoelectron spectra from 4 laser pulses were collected at each step. The signal is proportional to the time-dependent population of the He(1s3p) state. For negative time delays (4 nm arrives before EUV pulse) the He(1s3p) population is vanishing (the fluctuations in the signal are due to the subtracted background photoelectrons). At t = the population rises with a 3 fs rise time, limited by the instrumental response time due to the EUV pulse front tilt on the grating and the 8 fs duration of the 4 nm probe pulse [2]. With no additional optical density of He in the path of the EUV beam, shown by the filled circles, the population slowly decreases due to the long 1.76 ns lifetime of the He(1s3p) state [12]. For delay times considerably longer than the EUV pulse duration, the population of the He(1s3p) excited state depends only on the amplitude of the resonant frequency content of the excitation pulse. The amplitude and phase of the nonresonant spectral components in the EUV pulse do not affect the transition probability at t. The and + symbols in Fig. 2 show the pump-probe signals recorded with 4.2 1 4 and 12 1 4 Pa of He introduced along the propagation FIG. 2: Photoelectron yield as a function of the pump-probe delay time for different He pressures along the propagation path of the EUV pulse : He leak valve closed, : 4.2 1 4 Pa, + : 12 1 4 Pa. All plots on actual measured counts scale. path of the EUV pulse. When the He optical thickness is increased, the long-lived component of the excited state population is decreased, since the He gas effectively absorbs the resonant frequencies of the EUV pulse. On the other hand the nonresonant components of the EUV pulse, whose amplitudes do not decrease due to propagation through the He gas, acquire an antisymmetric spectral phase about the resonant frequency due to the strong dispersion around the He absorption line. These components give rise to a transient excited He(1s3p) state population that emerges with an increase of the He optical thickness. Even though the resonant component of the EUV pulse is almost completely absorbed before the interaction region, as shown by the + symbols in Fig 2, significant transient population is excited by the nonresonant part of the EUV light. At its peak, the nonresonant excitation is equivalent to the resonant absorption of the unmodified EUV pulse (filled circles). Therefore, by timing the delay of the 4 nm pulse we control the amount of nonresonant EUV light that is physically absorbed by He atoms in the effusive beam. An aspect of the spectral phase shaping due to propagation in a resonant medium is the influence of enhanced transient population amplitudes on resonant pump-probe experiments, giving rise to temporal profiles that are not due to the excited state evolution dynamics. Indeed, in a recent paper [12] such enhanced transient population was reported as an artifact in a pump-probe study of the He(1s2p) radiative lifetime at high sample pressures, and the result was attributed to a combination of absorption of the resonant frequency and an AC-Stark broadening. We note here that the reported artifact was most likely due to spectral phase shaping.

The temporal evolution of an excited state amplitude, excited by the electric field of a short pulse with spectral content E(ω) and a spectral phase φ(ω), can be estimated by its first-order term a 1 e(t) given by time-dependent perturbation theory. With the approximation of an infinite lifetime of the excited state, the result can be written as a (1) e (t) = µ [ iπe(ω )u(t) + ] dω E(ω)eiφ(ω) ω ω ei(ω ω)t (1) where µ is the transition dipole moment, ω is the resonant frequency, u(t) is a step function, is the principle value of Cauchy and φ(ω ) is arbitrarily set to. The first term in eq. 1 represents the resonant absorption, which rises at t = and remains constant at t >. The second term integrates over the nonresonant components of the excitation pulse, resulting in a transient amplitude coefficient during the action of the exciting pulse at long times the nonresonant coefficient vanishes due to the oscillatory e i(ω ω)t term. For an exciting pulse with a symmetric spectral content and phase about the resonant frequency, the nonresonant term vanishes for short times as well, since the blue shifted components cancel the contribution of the red shifted components. As the nonresonant term depends strongly on the symmetry of the exciting pulse, coherent manipulation of the spectral phase can alter or control the transient amplitude, as was demonstrated by using various pulse shaping schemes in the infrared regime [4 7, 21]. One of the techniques for spectral phase manipulation is the propagation of a pulse through a resonant filter medium with one or more absorption resonances [4]. The result of the propagation can be described by a refractive index n(ω) = 1 + c [ 2L Γ ω 2 ω2 iωγ ] (2) where c is the speed of light, L is the attenuation length at the resonant frequency, and Γ is the frequency width of the absorption resonance. The electric field of the EUV pulse, E i (ω)e φi(ω), will therefore be shaped by the transmission through the He gas E(ω)e iφ(ω) = E i (ω)e iφi(ω) e in(ω)ωαl/c (3) where α is the optical thickness of the resonant medium, such that for α = 1 the transmission on resonance is e 1. For example, Fig. 3 shows the spectral content and phase of the EUV pulse around the He(1s3p) resonance after it propagates through an optical density of α = 1. The 15th harmonic spectral bandwidth 1 cm 1 [2] is much wider than the 3 cm 1 region of interest shown in the figure, such that the magnitude of the spectrum (full line) appears to be nearly flat with a narrow dip at the Doppler broadened resonant frequency. The red and blue shifted nonresonant parts of the spectrum acquire opposite phase due to the dispersion close to the resonance according to eqs. 2 and 3. The initial chirp of the harmonic pulse, demonstrated by [22, 23], would contribute to a phase change of less than.1 radians over the spectral region shown in Fig. 3 and can be therefore neglected. Assuming that the spectral range of the 15th E(ω) magnitude (a.u.) 2 1.5 1.5.5 1 1.5 2 1.861 1.862 1.863 ω ( 1 5 cm 1 ) FIG. 3: The phase and magnitude of the EUV spectrum in the region around the He(1s3p) resonance, after it has propagated through an α = 1 He optical thickness. The full line shows the magnitude of the electric field in arbitrary units while the dotted line shows the phase in radians. harmonic is much wider than the spectral region of interest and neglecting the initial spectral phase compared to the phase acquired by the interaction with the absorption resonance (i.e. E i (ω) = E i and φ i (ω) = ), the integral in eq. 1 can be solved analytically. It is interesting to note that this solution was derived first to describe the propagation of Gamma-rays in resonance with a nuclear absorption line [24] where it was used to describe recurrences, on the µs scale, in multiple nuclear scattering. Later it was derived again [25] to describe the propagation of short weak pulses through resonant matter and used to enhance transient absorption in the infrared [4]. For the case of the He(1s 2 ) interaction with the 15th high harmonic pulse, we can describe the temporal evolution of the transient He(1s3p) population by 2 15 1 5 5 1 15 2 a e (t) 2 e Γt J o ( 4αΓt) 2, (4) where J is a Bessel function of the first kind. Figs. 4(a-e) show the spectral phase shaping effect on the transient He(1s3p) population amplitudes by increasing He optical thickness with increasing partial He pressure in the grating chamber. The measured pump-probe signal as a function of delay time at different pressures shown by the filled circles is compared to the temporal profile of eq. 4 shown with the full line, which was convoluted with a 32 fs Gaussian to account for the pulse front tilt broadening of the EUV pulse as well as the 8 fs width of the 4 nm pulse. The width of the resonance was set to Γ = 18 MHz, corresponding to the Doppler broadened line width of the He(1s3p) line at room temperature, and the modeled optical thickness was varied spectral phase (rad) 3

4 photoelectrons (counts) 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 (a) 5 1 15 2 25 (b) 5 1 15 2 25 (c) 5 1 15 2 25 (d) 5 1 15 2 25 (e) 5 1 15 2 25 time (ps) temporal shape of the exciting spectral components of the EUV pulse since we observe features on the 1 fs time scale, it includes contributions from the 3 cm 1 region, shown in Fig. 3. We have demonstrated control of coherent transients in the He atom by propagation of ultra-short EUV pulses in atomic He gas that shapes the spectral phase of the EUV pulse with only a narrow band of attenuated frequencies on the atomic absorption line. The dispersion near the absorption resonance adds positive or negative chirp to the frequencies, respectively, below and above the resonance. The amount of chirp can be continuously controlled by the density of gas along the propagation path, thus manipulating the pulse shape, and time-resolved photoionization of the transient population serves as a sensitive probe of the acquired spectral phase. Coherent control of transient excitation in more complex systems that are accessible with EUV light, such as autoionizing doubly-excited states or predissociating molecular Rydberg states can provide insight on the role of quantum phase in the dynamics of those systems. The authors gratefully acknowledge funding from the Air Force Office of Scientific Research grants #FA955-4-1-83 and #FA955-4-1-242, with additional equipment and support from the Department of energy under contract #DEAC3-76SF98 and the National Science Foundation Extreme Ultraviolet Center, EEC-31717. T. P. acknowledges the support of a Feodor Lynen Fellowship of the Alexander von Humboldt-Foundation. FIG. 4: Photoelectron yield as a function of the pump-probe delay time for different partial He pressures in the grating chamber: (a) 12 1 4 Pa, (b) 52 1 4 Pa, (c) 68 1 4 Pa, (d) 23 1 4 Pa, (e) 524 1 4, all ±4 1 4 Pa. Data are shown by the points and compared to a model calculation shown by the full line. The modeled He optical thickness scales approximately linearly with the measured chamber pressure. The extracted optical thicknesses are: α = 8, 5, 7, 225, 57, respectively. from α = 8 to α = 57, scaling approximately linearly with the He pressure in the grating chamber, which is increased from 12 1 4 Pa to 524 1 4 Pa. The measured data are found to be in good agreement with the analytical model: the time dependent population of the He(1s3p) state exhibits the expected amplitude maxima that are due to the opposite chirp acquired by the red and blue sides of the EUV pulse. The maxima occur at times that scale quadratically with the maxima number and inversely depend on the He optical thickness before the interaction region, while the overall amplitudes of all the maxima decay on the same time scale, which is inversely proportional to the width of the absorption line. Essentially, the measured transient population mimics the [1] M. Shapiro, and P. Brumer, Rep. Prog. Phys. 3, 165 (25) [2] T. Brixner, and G. Gerber, ChemPhysChem 4, 418 (23) [3] S. A. Rice, and M. Zhao, Optical Control of Molecular Dynamics, Wiley, New York (2) [4] N. Dudovich, D. Oron, and Y. Silberberg, Pys. Rev. Lett. 88, 1234 (22) [5] J. B. Ballard, H. U. Stauffer, E. Mirowski and S. R. Leone, Phys. Rev. A. 66, 4342 (22) [6] N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (21). [7] D. Meshulach and Y. Silberberg, Nature (London)396, 239 (1998) [8] P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993) [9] R. W. Schoenlein et al. Science 287, 2237 (2) [1] J. J. Rocca et al. Phys. Rev. Lett. 73, 2191 (1994) [11] V. Ayvazyan et al. Phys. Rev. Lett. 88, 1482 (22) [12] A. Johansson et al. Eur. Phys. J. D 22,3 (23) [13] M. Gisselbrecht et al. Phys. Rev. Lett. 82, 467 (1999). [14] L. Nugent-Glandorf et al. Phys. Rev. Lett. 87, 1932 (21) [15] S. L. Sorensen et al. J. Chem. Phys. 112, 838 (2) [16] P. Cacciani et al. Eur. Phys. J. D 15, 47 (21) [17] W. Ubachs et al. Chem. Phys. 27, 215 (21)

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