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The Journal of Chemical Physics

Theory of stimulated Raman adiabatic passage in a degenerated reaction system: Application to control of molecular handedness

Y. Ohta, Kunihito Hoki, Yuichi Fujimura

Published May 1, 2002• 36 citations
Publisher

Abstract

We have developed a new type of stimulated Raman adiabatic passage (STIRAP) that is applicable to a degenerated reaction system. The direction of the photon polarization vector is the adiabatic parameter in the STIRAP. The molecular handedness of H2POSH, a preoriented phosphinotioic acid that has two stable configurations, L and R enantiomers, is used as a model system. The control of molecular handedness in both pure and mixed state cases are considered. In the case of a pure state, a STIRAP with a linearly polarized single laser allows an almost complete transfer from an L (R) enantiomer to the other by adiabatically changing its polarization direction. The adiabatic criterion for changing the polarization direction is clarified. In the case of a mixed state, a STIRAP with two linearly polarized laser pulses allows a selective preparation of pure enantiomers from its racemic mixture. In the low temperature limit, a five-level model reduces a three-level model by setting the direction of the polarization of the pump and Stokes pulses in such a way that only the forward transfer is allowed, while the reverse is forbidden. Furthermore, in the case of mixed state, relaxation effects originating from vibrational mode couplings are taken into account, and the influence of the population decay from intermediate states on the STIRAP is compared with that by a π-pulse approach.

DOI
10.1063/1.1467054

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We have developed a new type of stimulated Raman adiabatic passage (STIRAP) that is applicable to a degenerated reaction system. The direction of the photon polarization vector is the adiabatic parameter in the STIRAP. The molecular handedness of H2POSH, a preoriented phosphinotioic acid that has two stable configurations, L and R enantiomers, is used as a model system. The control of molecular handedness in both pure and mixed state cases are considered. In the case of a pure state, a STIRAP with a linearly polarized single laser allows an almost complete transfer from an L (R) enantiomer to the other by adiabatically changing its polarization direction. The adiabatic criterion for changing the polarization direction is clarified. In the case of a mixed state, a STIRAP with two linearly polarized laser pulses allows a selective preparation of pure enantiomers from its racemic mixture. In the low temperature limit, a five-level model reduces a three-level model by setting the direction of the polarization of the pump and Stokes pulses in such a way that only the forward transfer is allowed, while the reverse is forbidden. Furthermore, in the case of mixed state, relaxation effects originating from vibrational mode couplings are taken into account, and the influence of the population decay from intermediate states on the STIRAP is compared with that by a π-pulse approach.
In this paper we extend the existing theory of stimulated Raman adiabatic passage (StiRAP) in three-level systems to examine the nature of selective photoexcitation using counterintuitively ordered pulses. Our goal is to develop a version of StiRAP that permits control of product selectivity in a chemical reaction. We analyze the case of selective excitation to one state in a pair of degenerate target states in a four-level system, and find that one cannot control the ratio of the populations in the two states in a resonant two-photon process. However, the extension of the system to include a fifth state and a third laser field makes selective excitation to one of the degenerate states possible. It is found that, subject to reasonable restrictions, one may accomplish complete population transfer to a single target state of a degenerate pair of states in a five-level system.
We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (ground ggg, excited eee, and final fff) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction $(g\text{\ensuremath{-}}e)$ and to the Stokes-pulse interaction $(e\text{\ensuremath{-}}f)$. We show that in general a sufficient condition for complete population removal from the ggg set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence ggg, eee, and fff. Using a sequence of unitary transformations we demonstrate that when this condition holds it is possible to achieve the degenerate counterpart of conventional STIRAP, whereby adiabatic passage produces complete population transfer. Indeed, the system is equivalent to a set of independent three-state systems, in each of which a STIRAP procedure can be implemented. We also examine the cases when this degeneracy constraint does not hold and show what can be accomplished in those cases. For example, for angular momentum states when the degeneracy of the ggg and fff levels is less than that of the eee level we show how a special choice for the pulse polarizations and phases can produce complete removal of population from the ggg set. Our scheme can be a powerful tool for coherent control in degenerate systems, because of its robustness, when selective addressing of the states is not required or impossible. We illustrate the analysis with several analytically solvable examples, in which the degeneracies originate from angular momentum orientation, as expressed by magnetic sublevels.
We explore theoretically the rovibrational dynamics of stimulated Raman adiabatic passage (STIRAP) in molecular electronic states including both the rotational and the vibrational degrees of freedom, with the LiH molecule as an example. By using a pure rovibrational state as initial state, we find that, under the condition of two-photon resonance, an efficient rovibrational population transfer can be achieved via STIRAP in molecular electronic states and the desired target state can be selected by adjusting laser-pulse parameters. Besides the interested rovibrational states, however, some unwanted rovibrational states may affect population transfer process, especially while the two-photon detuning is taken into account. By inspecting the evolution process of wave packet, we can easily search these unwanted rovibrational states and study their influences. Moreover, the effect of rotational temperature on the population transfer process is discussed using thermal mixed state as initial state.
We have considered a coherent population transfer to a higher excited singlet state ( S2 ) of molecules with anomalous fluorescence in molecular assemblies (e.g., a dense medium). A direct excitation to S2 requires light in the UV region. Because of this, the transition is conveniently realized by a two-step (two-photon) process: S0→S1→S2 , where transitions S0→S1 and S1→S2 correspond to the optical region. We have shown that efficient stimulated Raman adiabatic passage (STIRAP) in the ladder configuration can be realized in this case, using suitably chirped pulses, to compensate a change of the two-photon transition frequency in time, induced by the pulses themselves, due to near dipole-dipole interactions. We have provided a reduced state formulation of the optical control process. Chirping the “pump” pulse that excites transition S0→S1 is nonequivalent to chirping the “Stokes” pulse that excites transition S1→S2 , with respect to the population of the intermediate state ( S1 ) in the pulse nonadiabatic regime. We have also shown that with suitably chirped pulses, efficient STIRAP still persists even for a rather large decay of the intermediate state.
We use a 28-level system consisting of the vibrational bend states of the HCN/HNC system as a model system for the investigation of population transfer across the isomerization barrier using counterintuitively ordered multiphoton (MP) laser pulses. This (m+n)-STIRAP (stimulated Raman-adiabatic passage) arrangement with m pump- and n Stokes-photons is found to be capable of driving HCN→HNC transition states selectively and in a robust manner, despite the presence of near-degenerate parallel processes of different photonicities. Employing Gaussian pulses with widths of 80 ps, the process of highest photonicity we demonstrate is (4+6)-STIRAP, and we investigate systematically the robustness against variations in pulse amplitudes and frequencies for all parallel processes with m=2 and 3, and n=1–6. We discuss the conditions under which selective population transfer is obtained. We also compare with (1+1)-STIRAP using overtone transitions to drive the same state-specific processes and conclude that the few-step sequential MP-STIRAP isomerization is a feasible alternative to the sequential (1+1)-STIRAP based method proposed by Kurkal and Rice [J. Phys. Chem. B 105, 6488 (2001)].
Stimulated Raman scattering involving adiabatic passage (STIRAP) is a proven technique for population transfer in three-level systems with strong oscillator strengths. We show that the STIRAP process should also yield high transfer efficiencies when the densities of states near the intermediate and final levels are high, provided certain criteria for the experimentally controllable parameters are met. We also show that high transfer efficiencies may even be possible when the pump and Stokes lasers can access levels outside of the three-level system. The criteria are derived with an approach that emphasizes the adiabatic nature of the transfer process in an eigenvector of the interaction Hamiltonian that resembles a trapped state. The results are compared to density matrix calculations.