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The Journal of Physical Chemistry A

Controlling Non-Franck−Condon Transitions: Counterintuitive Schemes of Population Transfer in the Adiabatic and Strong Adiabatic Regimes

Vladimir S. Malinovsky, Jesús Santamarı́a, Ignacio R. Solá

Published Jul 23, 2003• 24 citations
Publisher

Abstract

Vibrationally selective population transfer in electronic transitions involving small Franck−Condon factors is studied by means of two-photon excitation with pulse sequences applied in counterintutive order. Depending on the intensity of the pulses, two schemes allow ultrafast adiabatic passage. Both schemes, called STIRAP and APLIP, are analyzed as a function of the geometry of the electronic states and of the time duration and intensity of the pulses that drive the transitions. Although both schemes imply adiabatic following, the APLIP scheme requires pulses of considerably larger intensity than STIRAP, hence operating in a strong adiabatic regime. Simple adiabatic criteria for high-quality transfer are proposed, and analytic proofs are provided that show under which conditions STIRAP and APLIP converge. The results of this paper are illustrated with numerical simulations for two different electronic transitions in the Na 2 molecule.

DOI
10.1021/jp0226477

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Vibrationally selective population transfer in electronic transitions involving small Franck−Condon factors is studied by means of two-photon excitation with pulse sequences applied in counterintutive order. Depending on the intensity of the pulses, two schemes allow ultrafast adiabatic passage. Both schemes, called STIRAP and APLIP, are analyzed as a function of the geometry of the electronic states and of the time duration and intensity of the pulses that drive the transitions. Although both schemes imply adiabatic following, the APLIP scheme requires pulses of considerably larger intensity than STIRAP, hence operating in a strong adiabatic regime. Simple adiabatic criteria for high-quality transfer are proposed, and analytic proofs are provided that show under which conditions STIRAP and APLIP converge. The results of this paper are illustrated with numerical simulations for two different electronic transitions in the Na 2 molecule.
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)].
We consider combined stimulated Raman adiabatic passage (STIRAP) and fast-forward field (FFF) control of selective vibrational population transfer in a polyatomic molecule. The motivation for using this combination control scheme is 2-fold: (i) to overcome transfer inefficiency that occurs when the STIRAP fields and pulse durations must be restricted to avoid excitation of population transfers that compete with the targeted transfer and (ii) to overcome transfer inefficiency resulting from embedding of the actively driven subset of states in a large manifold of states. We show that, in a subset of states that is coupled to background states, a combination of STIRAP and FFFs that do not individually generate processes that are competitive with the desired population transfer can generate greater population transfer efficiency than can ordinary STIRAP with similar field strength and/or pulse duration.
Ongoing work aimed at developing highly efficient methods of populating a chosen sublevel of an energy level highlights the need to understand off-resonant effects in coherent excitation. This motivated us to re-examine some aspects of the theory of coherent excitation in a three-state system with a view to obtaining algebraic expressions for off-resonant eigenvalues and eigenvectors. Earlier work gives simple closed-form expressions for the eigenvalues this system, expressions applying even when the system is not on two-photon resonance. We present here expressions of similar simplicity for the components of the normalised eigenvectors. The analytic properties of these components explain the observed sensitivity of the stimulated-Raman-adiabatic-passage process (STIRAP) to the condition of two-photon resonance. None of the eigenstates is ‘trapped’ or ‘dark’ unless the system is on two-photon resonance; off resonance, all states have nonzero projections on the unperturbed intermediate state. A simple argument shows that no dressed state can be adiabatically connected to both the unperturbed initial and final states when the system is off two-photon resonance. That is, adiabatic transfer from initial to final state requires that these be degenerate before and after the STIRAP pulse sequence, and this implies zero two-photon detuning. However, substantial transfer probabilities are observed experimentally for very small two-photon detunings. We show that such systems are characterised by very sharp avoided crossings of two eigenvalues, and that the observed population transfer can be understood as an effect of non adiabatic transitions occurring at the avoided crossings.
We show that the technique of Stark-chirped rapid adiabatic passage (SCRAP), hitherto used for complete population transfer between two quantum states, offers a simple and robust method for complete population transfer amongst three states in atoms and molecules. In this case SCRAP uses three laser pulses: a strong far-off-resonant pulse modifies the transition frequencies by inducing dynamic Stark shifts and thereby creating time-dependent level crossings amongst the three diabatic states, while near-resonant and moderately strong pump and Stokes pulses, appropriately offset in time, drive the population between the initial and final states via adiabatic passage. The population transfer efficiency is robust to variations in the intensities of the lasers, as long as these intensities are sufficiently large to enforce adiabatic evolution. With suitable pulse timings the population in the (possibly decaying) intermediate state can be minimized, as with stimulated Raman adiabatic passage (STIRAP). This technique applies to one-photon as well as multiphoton transitions and it is also applicable to media exhibiting inhomogeneous broadening; these features represent clear advantages over STIRAP by overcoming the inevitable dynamical Stark shifts that accompany multiphoton transitions as well as unwanted detunings, e.g., induced by Doppler shifts.
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.