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The Journal of Physical Chemistry A

Population Transfer to a Predissociating Target State Using Pulsed Coherent Excitation: Sensitivity to Coupling to Background States

Vandana Kurkal, Stuart A. Rice

Published Aug 16, 2002• 10 citations
Publisher

Abstract

We have examined the sensitivity to the presence of background states of population transfer to a predissociating molecular state generated by coherent two-pulse excitation. The system studied is intended to model optical control of the formation of a product in a photofragmentation reaction. The model spectrum of states is a generalization of the three-state spectrum considered in the conventional STIRAP method in three respects: the target state is a resonance in the continuum, the spectrum includes both unoccupied background states that have finite lifetimes and some unoccupied pairs of background states that are in resonance with the excitation pulses, and nonadiabatic population transfer is allowed. We examine the variation of the population transfer to the target state with respect to its lifetime, as well as the robustness of the population transfer with respect to variation of the area of overlap of the two excitation pulses and with respect to the presence of background states (some of which have finite lifetimes). Our results show that there is a broad range of conditions under which it is possible to transfer population efficiently from an initial state to a target predissociating state using coherent two-pulse excitation, although that population transfer is not always adiabatic.

DOI
10.1021/jp0202643

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We have examined the sensitivity to the presence of background states of population transfer to a predissociating molecular state generated by coherent two-pulse excitation. The system studied is intended to model optical control of the formation of a product in a photofragmentation reaction. The model spectrum of states is a generalization of the three-state spectrum considered in the conventional STIRAP method in three respects: the target state is a resonance in the continuum, the spectrum includes both unoccupied background states that have finite lifetimes and some unoccupied pairs of background states that are in resonance with the excitation pulses, and nonadiabatic population transfer is allowed. We examine the variation of the population transfer to the target state with respect to its lifetime, as well as the robustness of the population transfer with respect to variation of the area of overlap of the two excitation pulses and with respect to the presence of background states (some of which have finite lifetimes). Our results show that there is a broad range of conditions under which it is possible to transfer population efficiently from an initial state to a target predissociating state using coherent two-pulse excitation, although that population transfer is not always adiabatic.
This paper presents a systematic numerical investigation of background state participation in STIRAP (stimulated Raman-adiabatic passage) population transfer among vibrational states, focusing on the consequences for the robustness of the method. The simulations, which are performed over extended grids in the parameter space of the Stokes- and pump pulses (frequencies, field strengths, and pulse lengths), involve hierarchies of (3 + N)-level systems of increasing complexity, ranging from the standard three-level STIRAP setup, (N = 0) in Λ-configuration, up to N = 446. A strongly coupled three-level core system is selected from the full Hamiltonian of the double-well HCN∕HNC system, and the couplings connecting this core system to the remaining states are (re-) parameterized in different ways, from very weak to very strong. The systems so obtained represent a three-level system embedded in various ways in webs of cross-linked vibrational background states and incorporate typical molecular properties. We first summarize essential properties of population transfer in the standard three-level system and quantify the robustness of the method and its dependence on the pulse parameters. Against these reference results, we present results obtained for four (3 + 446)-level systems and several subsystems. For pulse lengths of at most few picoseconds the intrinsic robustness of STIRAP with respect to variations in the field strength disappears as soon as the largest core-background couplings exceed about one tenth of the STIRAP couplings. In such cases robustness with respect to variations in the field strength is entirely lost, since at higher field strengths, except for irregularly spaced narrow frequency ranges, transfer probabilities are strongly reduced. STIRAP-like population transfer is maintained, with some restrictions, at low field strengths near the onset of adiabatic transfer. The suppression of STIRAP is traced back to different mechanisms based on a plentitude of single- and multiphoton transitions to background states, which at the high field strengths characteristic for STIRAP proceed readily even along weakly coupled pathways.
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 report studies of state-to-state vibrational energy transfer in an isolated polyatomic molecule driven by combined stimulated Raman adiabatic passage (STIRAP) and counter-diabatic fields (CDFs). The goal of these studies is development of a method for improving the efficiency of level-to-level population transfer under conditions that degrade the efficiency of conventional STIRAP-generated population transfer. The vehicles for our studies are selective population of one of a pair of near-degenerate states in nonrotating SCCl 2 and enhancing the yield of nonrotating HNC in the HCN → HNC isomerization reaction. The efficiency of the population transfer within a subset of states embedded in a manifold of states is examined for the cases in which the transition dipole moments between the initial and target states are much smaller than and comparable to the transition dipole moments between background states and for the case in which the subset states have large transition dipole moments with the background states. We show that, in a subset of states that is coupled to background states, a combination of STIRAP fields and CDFs that do not individually generate processes that are competitive with the desired population transfer can generate population transfer efficiency greater than can ordinary STIRAP with field strength and/or pulse duration similarly restricted and that the exact CDF for an isolated three-level system is a useful approximation to the exact CDF for three- and five-state systems embedded in background states. We report a study of the stability of the STIRAP and approximate CDF control protocol to variation of the CDF intensity, the relative phase between the STIRAP and CDFs, and the pulse duration.
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 report studies of state-to-state vibrational energy transfer in an isolated polyatomic molecule driven by combined stimulated Raman adiabatic passage (STIRAP) and counter-diabatic fields (CDF), using as vehicles selective population of one of a pair of near degenerate states in SCCl2_22​ and enhancing the yield of HNC in the HCN/HNC isomerization reaction. The efficiency of the population transfer within a subset of states embedded in a dense manifold of states is examined for the cases that the transition dipole moments between the initial and target states are much smaller than and comparable to the transition dipole moments between background states, and for the case that the subset states have large transition dipole moments with the background states. We show that, in a subset of states that is coupled to background states, a combination of STIRAP fields and CDFs 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 field strength and/or pulse duration similarly restricted. We also show that the exact CDF for an isolated three level system is a useful approximation to the exact CDF for three and five state systems embedded in background states, and we report a study of the stability of the STIRAP + approximate CDF control protocol to variation of the CDF.
The technique of stimulated Raman adiabatic passage (STIRAP) is used to transfer potassium atoms from the 22p state to the 21p Rydberg state through the intermediate state 22s. The results show that complete population transfer is related to pulse duration and overlap, and occurs when the pulse duration and overlap have adequate values. At the same time, population trapping is also formed. Complete population transfer can also occurs when the two-photon resonance condition ( Δ s = Δ p ) is met.