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The European Physical Journal D

Two-laser multiphoton adiabatic passage in the frame of the Floquet theory. Applications to (1+1) and (2+1) STIRAP

S. Guérin, Hans Rudolf Jauslin

Published Jan 1, 1998• 32 citations
Publisher

Abstract

We develop an adiabatic two-mode Floquet theory to analyse multiphoton coherent population transfer in N-level systems by two delayed laser pulses, which is a generalization of the three-state stimulated Raman adiabatic passage (STIRAP). The main point is that, under conditions of non-crossing and adiabaticity, the outcome and feasibility of a STIRAP process can be determined by the analysis of two features: (i) the lifting of degeneracy of dressed states at the beginning and at the end of the laser pulses, and (ii) the connectivity of these degeneracy-lifted branches in the quasienergy diagram. Both features can be determined by stationnary perturbation theory in the Floquet representation. As an illustration, we study the corrections to the RWA of the (1+1) STIRAP in strong fields and for large detunings. We analyse the possible breakdown of connectivity. In strong fields, the complete transfer is achieved, but the intermediate state, unpopulated within the RWA, can become populated during the process. In the (2+1) STIRAP, we show a residual degeneracy in a four-level system, that can be lifted by additional Stark shifts. The complete transfer is achieved under conditions of connectivity.

DOI
10.1007/pl00021564

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Journal of Physics Conference Series•Mar 14, 2012•1 citation
We develop an adiabatic two-mode Floquet theory to analyse multiphoton coherent population transfer in N-level systems by two delayed laser pulses, which is a generalization of the three-state stimulated Raman adiabatic passage (STIRAP). The main point is that, under conditions of non-crossing and adiabaticity, the outcome and feasibility of a STIRAP process can be determined by the analysis of two features: (i) the lifting of degeneracy of dressed states at the beginning and at the end of the laser pulses, and (ii) the connectivity of these degeneracy-lifted branches in the quasienergy diagram. Both features can be determined by stationnary perturbation theory in the Floquet representation. As an illustration, we study the corrections to the RWA of the (1+1) STIRAP in strong fields and for large detunings. We analyse the possible breakdown of connectivity. In strong fields, the complete transfer is achieved, but the intermediate state, unpopulated within the RWA, can become populated during the process. In the (2+1) STIRAP, we show a residual degeneracy in a four-level system, that can be lifted by additional Stark shifts. The complete transfer is achieved under conditions of connectivity.
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.
The technique of stimulated Raman adiabatic passage (STIRAP) is a highly efficient tool for coherent population transfer in a chainwise-connected three-state quantum system. It is widely accepted that the two-photon resonance between the two end states of the chain is a crucial condition for STIRAP. This assumption is indeed correct when the two driving fields, pump and Stokes, produce nearly equal couplings for their respective transitions. We show analytically, supported by numeric examples, that when the pump and Stokes couplings differ significantly, the two-photon population transfer profile is distorted and its center is shifted away from the two-photon resonance; hence, the optimal operation of STIRAP demands a two-photon detuning. We derive simple analytic estimates for the center and the width of the two-photon profile. The results are of potential importance in situations when the pump and Stokes fields are of different physical natures (e.g., laser and cavity fields) or when two-photon resonance is unwanted (e.g., in the presence of residual light).
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.
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 consider a five-level atomic system (M-system) driven by four near-resonant laser pulses and study the possibilities of population transfer via different combinations of Stimulated Raman Adiabatic Passage (STIRAP) and bright-STIRAP (b-STIRAP) processes. We examine these combinations analytically and numerically from the point of view of efficiency of population transfer. It is shown, in particular, that the combination of the processes above enhances the efficiency. Analytical expressions are obtained for the quasienergies of the system in two regimes differing by conditions imposed on resonance detunings. Interaction adiabaticity conditions are analyzed. We also study the necessary successions of turning on and off of pulses which ensure efficient transfer of atomic populations. The obtained analytical results agree well with direct numerical calculations.