Coherent population transfer and dark resonances in SO 2

Transcription

1 Coherent population transfer and dark resonances in SO 2 T. Halfmann and K. Bergmann Fachbereich Physik der Universität, Kaiserslautern, Germany Received 12 February 1996; accepted 20 February 1996 Highly efficient population transfer between the 0,0,0 and the 9,1,0 vibrational levels of the electronic ground state X 1 A 1 of SO 2 is demonstrated. The process relies on stimulated Raman scattering with adiabatic passage induced by two suitably delayed ultraviolet laser pulses with nearly transform-limited bandwidth. A transfer efficiency of 100% is achieved. The associated dark resonance is observed. Properties of the latter are compared for delayed and fully overlapping pulses American Institute of Physics. S INTRODUCTION The collision dynamics and spectroscopy of highly vibrationally excited molecules are themes of great current interest. 1 In thermal equilibrium such levels are not populated but methods to access them have recently been developed. These methods differ in the degree of flexibility, efficiency, selectivity, and experimental complexity. A successful and widely used technique to transfer population relies on stimulated emission pumping SEP. 1,2 A pump laser transfers population to a suitable level in an electronically excited state, followed by a dump laser, which transfers part of that population to the targeted vibrational level of the electronic ground state. When the fluence of the laser pulses is high enough, as much as one-third of the population can be transferred from the initial to the final level. Some population will remain in the electronically excited state, and from there it reaches other vibrational levels by spontaneous emission. It is straightforward to implement the SEP method with pulsed multimode lasers because coherence properties of the radiation are not important. Coherence may even be detrimental to an experimentally robust transfer process, because Rabi oscillations 3 will be induced. The coherence of the radiation needs to be invoked to achieve a significantly higher transfer efficiency from the initial to the final level. In fact, chirped pulse multiphoton excitation schemes, such as those recently proposed 4 can transfer a substantial fraction of the thermal population of low lying levels to high lying ones. The technique of coherent population transfer with delayed pulses, proposed some time ago 5 and experimentally demonstrated later, 6 is a method capable of achieving a transfer efficiency of unity, which implies perfect selectivity. This method relies on stimulated Raman scattering with adiabatic passage STIRAP. The STIRAP method is now well established for diatomic molecules. It has been successfully implemented with cw lasers in the visible 6,7 and in the infrared 8 using molecular beams, where the particles fly through the spatially displaced laser beams. The technique has been used in crossed beams collision experiments. 7 It has also been implemented for multilevel systems 9 and in the context of atomic interferometry and laser cooling. 10 Pulsed laser work dealing with atoms 11 or molecules 12 has been reported as well. A necessary condition for the success of the transfer process is a counterintuitive sequence of the laser pulses, with the Stokes laser pulse, coupling the intermediate and final level, arriving before the pump laser pulse, which couples the initial and the intermediate level. It is straightforward to rationalize the striking features of STIRAP by using the dressed state picture. When the two laser frequencies involved are tuned to the two-photon resonance with the initial and final level, then one of the eigenstates of the strongly coupled system comprising initial, intermediate, and final bare states 1, 2, and 3, respectively reads 6,13 a 0 cos 1 sin 3 with tan P / S where P and S are the Rabi frequencies related to the pump laser and the Stokes laser, respectively. The Rabi frequency is given by P,S E P,S / where is the dipole moment of the respective transition and E P,S the electric field of the radiation. Since we are dealing with delayed laser pulses, the Rabi frequencies and their ratio is time dependent. Therefore the mixing angle varies with time. Important properties of the STIRAP transfer process can be seen from Eq. 1. Unlike the other two dressed states a and a of a three states system, 6 the dressed state a 0 has no component of the radiatively decaying bare state 2. Radiative decay will not occur as long as the system is in a 0. In a geometrical picture we visualize a three dimensional Hilbert space spanned by the state vectors of the bare states 1, 2, and 3. The molecule is initially in the bare state 1. At early times when only the Stokes laser is present, we have cos 1. The state vector, which describes the population distribution among the bare states, as well as the dressed-state vector a 0, are both lined up parallel to 1. When the Stokes laser pulse gives way to the pump laser pulse, the mixing angle increases from 0 to 90, i.e., a 0 rotates and eventually lines up antiparallel to 3 at late times. Efficient population transfer occurs if the state vector remains aligned with a 0, i.e., if it follows the rotation of the latter. Adiabatic following requires sufficiently strong coupling of the bare states, so that the consequent Stark splitting separates the eigenvalues of the dressed states. 6,13 In a three-state system, adiabatic following occurs when J. Chem. Phys. 104 (18), 8 May /96/104(18)/7068/5/$ American Institute of Physics

2 T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO , 2 where is the width of the laser pulses, assuming that the pump and Stokes laser Rabi frequencies are about equal. 6 The adiabatic following condition needs to be modified when phase fluctuations of the laser pulses are appreciable on the time scale of the interaction. Phase fluctuations that lead to a substantial increase of the laser bandwidth are detrimental to the success of the transfer process. 14 When the transfer in a multistate system is considered, crossings of dressed-state eigenvalues may occur and a more detailed analysis is required. Such complications may result from Zeeman splittings 9 or fine and hyperfine interactions 15 or from a high density of states. In particular, they may be detrimental when nearby levels are radiatively coupled to intermediate states, but are separated in energy from the considered levels by less than the Rabi frequency. For the experiments on SO 2 discussed in this paper, the three-state picture is adequate. Hyperfine splitting does not occur because the nuclear spins are zero for the most abundant isotopes of sulphur and oxygen. The density of states near the final level is low enough to allow full resolution of individual eigenstates. Although the states involved have a nonzero angular momentum, the m-level degeneracy causes no problems, since the lasers are linearly polarized parallel to each other and only m 0 transitions are involved. Therefore, the population transfer occurs within several unrelated three-state systems in parallel, each one labeled by a different magnetic quantum number. 16 EXPERIMENT Our experiment is as follows. A pulsed beam of SO 2 molecules, seeded in argon with a concentration of 2%, expands from a stagnation pressure of 300 mbar through a 0.8 mm diam. nozzle into a vacuum chamber. The beam is collimated by a 0.8 mm diam. skimmer placed 20 mm downstream of the nozzle. The residual transverse Doppler width, for excitation with a laser which crosses the molecular beam axis at right angle, is 230 MHz. The pump laser at 227 nm and the Stokes laser at 300 nm couple the 0,0,0 vibration ground level of SO 2 in the X 1 A 1 electronic state 17,18 to the vibrational level 9,1,0 of the X 1 A 1 state via the 1,1,0 level of the electronic C 1 B 2 state; 19 see Fig. 1. The sequence of rotational levels is 2 02,3 03,2 02. The radiation from two cw single-mode dye lasers at 600 nm and 579 nm is amplified in pulsed dye amplifiers, pumped by the second harmonic of an injection-seeded Nd:YAG laser. The amplified radiation at 600 nm is frequency doubled in KD*P crystal and provides the Stokes laser radiation with a typical pulse energy of 200 J. The width of this pulse half-width at 1/e of E(t) is 3.1 ns as measured with a high speed 2 GHz analog-bandwidth digital oscilloscope. The radiation from the other amplifier at 579 nm is first frequency doubled and then mixed with the fundamental frequency of the Nd:YAG laser to yield typically 500 J of pump laser radiation. The width of this pulse is 2.7 ns. The pump radiation is mildly focused to a diameter of 0.8 FIG. 1. SO 2 energy levels and the pump, Stokes and probe laser transitions. Relevant wavelengths are given in nm. The bandwidth of the former two pulses is nearly transform limited. A multimode dye laser provides the probe laser pulse. mm and the Stokes beam has a diameter of 2.5 mm near the axis of the molecular beam. The resulting Rabi frequencies are about s 1 for pump and Stokes pulse, which yields 20. The time delay of the pulses at the molecular beam axis is controlled by sending the pump pulse through an adjustable folded optical delay line. The population transferred to the 9,1,0 level is probed by fluorescence from the 1,2,0 level of the C 1 B 2 state induced by a multimode excimer pumped dye laser which is delayed by 300 ns relative to the pulses for the STIRAP process. TRANSFER EFFICIENCY: RESULTS AND DISCUSSION Figure 2 shows fluorescence induced by the probe laser. The signal is proportional to the population of the final 9,1,0 level. The lower trace shows the signal S FCP obtained when the Stokes laser is blocked and population in the final level is established by spontaneous emission from the intermediate level Franck Condon pumping of population. The upper trace shows the signal S STIRAP when the Stokes laser pulse participates in the transfer process. The signal S FCP has been multiplied by a factor of 10 to be visible on the same scale. If this particular case, the STIRAP process enhances the population in the final level by more than two orders of magnitude. The absolute transfer efficiency is derived from the ratio of the two signals S STIRAP and S FCP. This is possible since the spontaneous transition rate from the intermediate to the final level, given by the Franck Condon factor F and the rotational line-strength factor H are known. The value of the Franck Condon factor was taken from dispersed laser induced fluorescence spectra 18 to be F %. The linestrength factor for the rotational transition for an

3 7070 T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO 2 FIG. 3. Variation of the measured transfer efficiency filled squares as the delay t between pump and Stokes pulse is changed. Complete population transfer is achieved for 5 ns t 3 ns STIRAP regime. Results from a density matrix calculation with Rabi frequencies P s 1 and S s 1 are shown in open circles. FIG. 2. Population in the final level X 9,1,0, measured by the probe laser induced fluorescence with and without Stokes laser, as the frequencies are tuned across two-photon resonance. The pump pulse is delayed 3.6 ns relative to the Stokes pulse. The trace obtained when the Stokes laser is off, is shifted downward from zero for better visibility. asymmetric top molecule is calculated to be H However, unlike for Na 2 or Ne* in molecular beams interacting cw with lasers, 6,9 the interaction time of the molecules with the laser fields is short compared to the spontaneous emission lifetime. Therefore the consequences of Rabi oscillations needs to be considered. 15 If the pulse energy would show no shot-to-shot variation, the fraction of the population transferred to the intermediate level at the end of the pump laser pulse would vary between zero and 100%, sensitively dependent on the pulse area. For a pulse area which is sufficiently large equivalent to ten or more Rabi cycles during the interaction with a single pulse, i.e., under conditions of strong saturation and for pulse-to-pulse fluctuations which are sufficiently strong, the predicted excitation probability exhibits also large pulse-to-pulse variations. However, on average, half of the population will reside in the intermediate state at the end of the pump laser pulse. In the present case strong saturation is fulfilled for all magnetic sublevels, including the one with the weakest coupling strength. Therefore, the transfer efficiency T is determined according to the formula T 2FH S STIRIAP G S FCP absorb Doppler. 3 The value of the function G absorb / Doppler depends on the one- or two-photon saturation broadened linewidth and the related Doppler width. Since the STIRAP process involves an absorption and emission process, a partial compensation of the Doppler shift occurs. The velocity components v, perpendicular to the molecular beam axis, of molecules which can participate in the two-photon process, largely exceeds the maximum value of v, determined by the divergence of the collimated molecular beam. We have also confirmed experimentally that the saturation broadened signalphoton absorption linewidth for a pulse energy 10 J exceeds the residual Doppler width of 230 MHz. Therefore, all molecules in the collimated molecular beam participate in the excitation leading to S FCP as well as in the transfer process yielding S STIRAP and we have G( absorb / Doppler 1. From data such as those shown in Fig. 2 we derive S STIRAP /S FCP in very good agreement with S STIRAP /S FCP 246 expected for 100% transfer efficiency (T 1 from Eq. 3. Additional independent evidence for complete population transfer is derived from the data of Fig. 3, which shows the characteristic variation of the transfer efficiency T with the delay t of the Stokes laser pulse relative to the pump laser. The overall agreement with numerical calculations based on the Liouville equation 16 open circles in Fig. 3 is excellent. The simulation study uses the measured temporal profile of the pulses and includes an average over the measured pulse-to-pulse energy fluctuations of 14%. For negative delay the STIRAP configuration, where the Stokes laser pulse preceeds the pump laser pulse a transfer efficiency of 100%, within the given errors bars, is observed for the range 3 ns t 5 ns.the plateau of T( t) is clear qualitative evidence for a transfer efficiency of nearly unity, even in a case when quantitative analysis according to Eq. 3 is unreliable because of the uncertainty of the value of some of the factors involved. The plateau is characteristic of the adiabatic following process. It develops when the adiabaticity criterion, such as the one given in Eq. 2, is well fulfilled. In that case a small deviation from the optimal configuration pulse energies, pulse delay is not detrimental. DARK RESONANCE: RESULTS AND DISCUSSION When complete population transfer occurs through the state a 0 we expect, according to Eq. 1, the fluorescence

4 T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO FIG. 4. Dark resonances of the fluorescence induced by the pump laser, as the Stokes laser frequency is tuned across the two-photon resonance. The data shown in the panel to the left are obtained with delayed pulses STIRAP configuration, while the Raman configuration delay t 0 leads to the results shown in the panel to the right. Although the maximum value of P is reduced by a factor of 10 in the latter case, the residual fluorescence of the dark resonance is negligibly small. from the intermediate level will vanish, provided the pump and Stokes laser frequencies are tuned to the two-photon resonance between the initial and final level. Figure 4 shows this dark resonance for the STIRAP configuration Stokes laser pulse proceeds the pump laser pulse and for the Raman configuration the two laser pulses coincide, which was recently applied to coherent fluorescence-dip or ion-dip spectroscopy by Neusser and co-workers. 21 At first glance it is surprising that the residual fluorescence from the intermediate level at two-photon resonance is no more than a few percent in the latter case, despite the reduction of the pump laser Rabi frequency by a factor of ten, while it is about 20% in the former case. The explanation is as follows. The adiabaticity criterion in its simplest form, Eq. 2, can be rewritten as 6, i.e., the rate of change of the mixing angle during the interaction must be small compared to the separation from the nearest nonzero dressed-state eigenvalue. Violation of the condition imposed by Eq. 4 results in diabatic coupling the other dressed states, which include a component of the radiatively decaying bare states. Thus, if S P at early times and the state a 0 is initially exclusively populated, the residual fluorescence at two-photon resonance is a measure of 4 the degree of diabatic coupling. The consequences of Eq. 4 are best seen in the geometrical picture briefly discussed in the Introduction. When the objective is population transfer, the state vector must follow the 90 rotation of a 0 from the orientation parallel to 1 into the orientation antiparallel to 3. Therefore the mean value of the lhs of Eq. 4, averaged over the interaction time of pulse overlap 0, is STIRAP /(2 0 ). When the objective of dark resonance spectroscopy with overlapping laser pulses, and provided the pulse shape and width of both pulses are identical, the mixing angle does not change, Raman 0 and Eq. 4 is trivially fulfilled. However, in this case we do not have cos 1 initially, and radiatively decaying states are also populated, which excludes the observation of a pronounced dark resonance. A deep dark resonance can be recovered in the Raman configuration if the width P of the pump laser pulse is smaller than the width S of the Stokes laser pulse, as realized in the experiments by Neusser and co-workers, 21 and in this work. For P S and t 0 we have P / S 1 at the beginning and at the end of the interaction. The mixing angle reaches a maximum value of arctan( P / S ) 1 for max P max S before returning to zero. The lhs, averaged over the interaction time, is Raman (1/ P )arctan( P / S ). Raman decreases with decreasing P and increasing S, while the residual fluorescence in the STIRAP configuration decreases with further increasing Rabi frequencies P and S. Obviously, it is easier to prevent diabatic coupling in the Raman configuration, and dark resonances with less residual fluorescence at two-photon resonance are to be expected, as observed in the experiment see Fig. 4. This observation is closely related to the phenomenon of electromagnetically induced transparency, 22 where an alternative picture is used to describe the process. When a strong Stokes laser causes dynamic Stark splittings of the upper level, the absorption of a weak pump laser, tuned to the one-photon resonance, is zero due to destructive interference of the contributions from the two Stark components. A detailed numerical and experimental study of the diabatic coupling processes will be the subject of a future publication. CONCLUSION We have shown that the technique of coherent population transfer can be applied to populate very high-lying vibrational levels of a polyatomic molecule. An efficiency of 100% for transfer from the vibrational ground level to the 9,1,0 vibrational level of SO 2 in the electronic ground state has been achieved. This demonstrates that experiments involving polyatomic molecules in selectively excited high lying vibrational levels are possible. We also demonstrate that, and explain why, the amount of residual fluorescence at the center of the dark resonance is different for the delayed pulse configuration on one hand and the Raman configuration with overlapping pulses on the other hand.

5 7072 T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO 2 ACKNOWLEDGMENTS E. Tiemann Hannover and K. Yamanouchi Tokyo kindly provided us with spectroscopic data of SO 2 from their unpublished work. This work was supported by the Deutsche Forschungsgemeinschaft and by the Stiftung für Innovation Rheinland Pfalz through the Lasercenter in Kaiserslautern. Partial support through the EU network Laser Controlled Dynamics of Molecular Processes and Applications, 4050PL , is also acknowledged. We thank B. W. Shore for valuable comments on the manuscript. 1 Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping, edited by H. L. Dai and R. W. Field World Scientific, Singapore, C. H. Hamilton, J. L. Kinsey, and R. W. Field, Annu. Rev. Phys. Chem. 37, ; X. Yang, J. M. Price, and A. Wodke, J. Phys. Chem. 97, ; J. M. Price, C. A. Rogaski, X. Yang, and A. Wodke, Chem. Phys. 175, ; R. Tuomi, J. A. Mack, and A. M. Wodtke, Science 265, B. W. Shore, The Theory of Coherent Atomic Excitation Wiley, New York, 1990, Sec S. Chelkowski and G. N. Gibson, Phys. Rev. 52, J. Oreg, F. T. Hioe, and J. H. Eberly, Phys. Rev. A 29, U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, ; H. G. Rubahn, E. Konz, S. Schiemann, and K. Bergmann, Z. Phys. D 22, P. Dittmann, J. Martin, G. Coulston, H. Z. He, and K. Bergmann, J. Chem. Phys. 97, ; P. Dittmann, Ph.D. thesis, Universität Kaiserslautern, Kaiserslautern, 1993; M. Külz, A. Kortyna, M. Keil, B. Schellhaa, J. Hauck, K. Bergmann, W. Meyer, and D. Weyh, Phys. Rev. A to be published. 8 C. Liedenbaum, S. Stolte, and J. Reuss, Phys. Rep. 178, ; J. Reuss and N. Dam, in Applied Laser Spectroscopy, edited by M. Inguscio and W. Demtröder Plenum, New York, 1990 ; N. Dam, L. Oudejans, and J. Reuss, Chem. Phys. 140, B. W. Shore, J. Martin, M. Fewell, and K. Bergmann, Phys. Rev. A 52, ; J. Martin, B. W. Shore, and K. Bergmann, ibid. 52, ; Phys. Rev. A submitted ; K. Bergmann, J. Martin, and B. W. Shore, in Proc. of the Conference on Coherence and Quantum Optics VII, edited by J. Eberly, L. Mandel, and E. Wolf Plenum, New York, P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, R ; P. Pillet, C. Valentin, R. L. Yuan, and J. Yu. ibid. 48, ; L.S. Goldner, C. Gerz, R. J. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, ibid. 72, ; J. Lawall and M. Prentiss, Phys. Rev. Lett. 72, ; M. Weitz, B. C. Young, and S. Chu, ibid. 73, ; L. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, and C. Cohen-Tannoudji, in Proc. of the 4th International Workshop on Laser Physics Moscow, 1995, Laser Physics 6, B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Phys. Rev. Lett. 69, S. Schiemann, A. Kuhn, S. Steuerwald, and K. Bergmann, Phys. Rev. Lett. 71, J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, Phys. Rev. A 40, ; K. Bergmann and B. W. Shore, Sec. 9 in Ref A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, W. S. Warren, and K. Bergmann, J. Chem. Phys. 96, A. Kuhn, Ph.D. thesis, Universität Kaiserslautern, Kaiserslautern, B. W. Shore, Sec. 6 in Ref F. J. Lovas, J. Phys. Chem. Ref. Data 14, ; K. Yamanouchi, H. Yamada, and S. Tsuchiya, J. Chem. Phys. 88, ; Y. Morina, M. Tanimoto, and S. Saito, Acta Chem. Scand. A 42, K. Yamanouchi, S. Takeuchi, and S. Tsuchiya, J. Chem. Phys. 92, J. C. D. Brand, P. H. Chiu, A. R. Hoy, and H. D. Bist. J. Mol. Spec. 60, ; A. R. Hoy and J. C. D. Brand, Mol. Phys. 36, ; S. Becker, C. Braatz, J. Lindner, and E. Tiemann, Chem. Phys. Lett. 208, ; J. E. Szankowski, Diplomarbeit, Universität Hannover, Hannover, 1994; K. Yamanouchi, M. Okunishi, Y. Endo, and S. Tsuchiya, J. Mol. Struc. 352, P. C. Cross, R. M. Hainer, and G. W. King, J. Chem. Phys. 12, ; D. Papousek and M. R. Aliev, Molecular Vibrational-Rotational Spectra Elsevier, Amsterdam, R. Sussmann, R. Neuhauser, and H. J. Neusser, J. Chem. Phys. 100, ; R. Sussmann, R. Neuhauser, and H. J. Neusser, J. Chem. Phys. 103, ; R. Neuhauser, R. Sussmann, and H. J. Neusser, Phys. Rev. Lett. 74, K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 67,