Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Implementation of stimulated Raman adiabatic passage in degenerate systems by dimensionality reduction

G. Bevilacqua, Gernot Schaller, Tobias Brandes, Ferruccio Renzoni

Published Jul 8, 2013• 9 citations
Publisher

Abstract

We consider the problem of the implementation of stimulated Raman adiabatic passage (STIRAP) processes in degenerate systems, with a view to be able to steer the system wave function from an arbitrary initial superposition to an arbitrary target superposition. We examine the case of an $N$-level atomic system consisting of $N\ensuremath{-}1$ ground states coupled to a common excited state by laser pulses. We analyze the general case of initial and final superpositions belonging to the same manifold of states, and we cover also the case in which they are nonorthogonal. We demonstrate that for a given initial and target superposition, it is always possible to choose the laser pulses so that in a transformed basis the system is reduced to an effective three-level $\ensuremath{\Lambda}$ system, and standard STIRAP processes can be implemented. Our treatment leads to a simple strategy, with minimal computational complexity, which allows us to determine the laser-pulse shape required for the wanted adiabatic steering.

DOI
10.1103/physreva.88.013404

Related papers

Stimulated Raman adiabatic passage among degenerate-level manifolds

Z. Kis, A. Karpati, Bruce W. Shore +1 more

We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (ground $g$, excited $e$, and final $f$) 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 $g$ set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence $g$, $e$, and $f$. 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 $g$ and $f$ levels is less than that of the $e$ level we show how a special choice for the pulse polarizations and phases can produce complete removal of population from the $g$ 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.

arXiv:quant-ph/0412086•Physical Review A•Nov 11, 2004•39 citations

Nonadiabatic dynamics in the dark subspace of a multilevel stimulated Raman adiabatic passage process

Z. Kis, Stig Stenholm

In this paper we consider a generalization of the three-level stimulated Raman adiabatic-passage process (STIRAP). In our scheme, there are $N\ensuremath{-}1$ ground levels and one excited level. The ground levels are coupled with laser pulses through the excited level at multiphoton resonance. The ultimate aim of this scheme is to create coherent-superposition states on the ground levels. In a previous paper [J. Mod. Opt. (to be published), special issue on quantum interference] we have considered this problem from the optimal-control point of view. Here we apply a different approach: We reconsider the adiabatic approximation, which is commonly utilized to describing the STIRAP process. It is shown that in our case, in the adiabatic limit, the dark and bright subspaces of the Hamiltonian are decoupled; however, the nonadiabatic corrections influence significantly the dynamics in the dark subspace. An analytic solution is presented for the case of a five-level system. Moreover, we consider some special examples for the pulse sequences that effect prescribed final superposition states. The robustness of the scheme is studied, and the extension of our scheme is also considered.

Physical Review A•Nov 15, 2001•39 citations

Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage

Z. Kis, Nikolay V. Vitanov, A. Karpati +2 more

A technique for creation of well-defined preselected coherent superpositions of multiple quantum states is proposed. It is based on an extension of the technique of stimulated Raman adiabatic passage (STIRAP) to degenerate levels. As an example, the nine-state system composed of the magnetic sublevels of three levels with angular momenta ${J}_{g}=0$, ${J}_{e}=1$, and ${J}_{f}=2$ is studied in detail. Starting from the $\ensuremath{\mid}{J}_{g}=0,{M}_{g}=0⟩$ state, STIRAP can create an arbitrary preselected coherent superposition between the five ${M}_{f}$ sublevels $({M}_{f}=\ensuremath{-}2,\ensuremath{-}1,0,+1,+2)$ of the ${J}_{f}=2$ level with 100% efficiency in the adiabatic limit. The populations and the phases of the ${M}_{f}$ states in this superposition are determined entirely by the polarizations of the two laser fields. It is shown that this technique allows one to create any superposition of the five ${M}_{f}$ states, that is, to reach any point in the Hilbert space of the ${J}_{f}=2$ manifold, and the corresponding recipes for choosing the laser polarizations are presented.

Physical Review A•Sep 9, 2005•30 citations

Optimal control approach for a degenerate STIRAP

Z. Kis, Stig Stenholm

We have looked at the laser-induced excitation of a level manifold coupled through a single excited level. This generalizes the ordinary Λ configuration to many levels. It is the original situation where stimulated Raman adiabatic passage (STIRAP) has been considered. We then apply optimal control theory to determine the pulse sequence which effects a predetermined superposition state with a minimal involvement of the excited state. The program is free to find its optimal pulse sequence, and we find that a generalization of the ordinary counterintuitive situation emerges. In addition to verifying the efficiency of the counterintuitive approach, the work justifies the separation into dark and bright subspaces, where time evolution in the former has to include the dynamical effects of adiabatic corrections.

Journal of Modern Optics•Jan 1, 2002•33 citations

Selective photochemistry via adiabatic passage: An extension of stimulated Raman adiabatic passage for degenerate final states

Mark N. Kobrak, Stuart A. Rice

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.

Physical Review A•Apr 1, 1998•85 citations

Phase evolution of superposition target states in adiabatic population transfer

Eli Morhayim, Michael T. Ziemba, J. Lim +1 more

We consider stimulated Raman adiabatic passage (STIRAP) when the final state is a superposition of two non-degenerate states. The system consists of four states coupled by two light fields. We find the relative phase of the final superposition depends on relative amplitude, width and timing of the adiabatic transfer pulses. We discuss these results in the context of experiments measuring symmetry violation in atomic and molecular systems.

physics.atom-phCross-listedarXiv:2511.21720•Physical Review A•Nov 20, 2025•0 citations
We consider the problem of the implementation of stimulated Raman adiabatic passage (STIRAP) processes in degenerate systems, with a view to be able to steer the system wave function from an arbitrary initial superposition to an arbitrary target superposition. We examine the case of an NNN-level atomic system consisting of N\ensuremath−1N\ensuremath{-}1N\ensuremath−1 ground states coupled to a common excited state by laser pulses. We analyze the general case of initial and final superpositions belonging to the same manifold of states, and we cover also the case in which they are nonorthogonal. We demonstrate that for a given initial and target superposition, it is always possible to choose the laser pulses so that in a transformed basis the system is reduced to an effective three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system, and standard STIRAP processes can be implemented. Our treatment leads to a simple strategy, with minimal computational complexity, which allows us to determine the laser-pulse shape required for the wanted adiabatic steering.
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.
In this paper we consider a generalization of the three-level stimulated Raman adiabatic-passage process (STIRAP). In our scheme, there are $N\ensuremath{-}1$ ground levels and one excited level. The ground levels are coupled with laser pulses through the excited level at multiphoton resonance. The ultimate aim of this scheme is to create coherent-superposition states on the ground levels. In a previous paper [J. Mod. Opt. (to be published), special issue on quantum interference] we have considered this problem from the optimal-control point of view. Here we apply a different approach: We reconsider the adiabatic approximation, which is commonly utilized to describing the STIRAP process. It is shown that in our case, in the adiabatic limit, the dark and bright subspaces of the Hamiltonian are decoupled; however, the nonadiabatic corrections influence significantly the dynamics in the dark subspace. An analytic solution is presented for the case of a five-level system. Moreover, we consider some special examples for the pulse sequences that effect prescribed final superposition states. The robustness of the scheme is studied, and the extension of our scheme is also considered.
A technique for creation of well-defined preselected coherent superpositions of multiple quantum states is proposed. It is based on an extension of the technique of stimulated Raman adiabatic passage (STIRAP) to degenerate levels. As an example, the nine-state system composed of the magnetic sublevels of three levels with angular momenta Jg=0{J}_{g}=0Jg​=0, Je=1{J}_{e}=1Je​=1, and Jf=2{J}_{f}=2Jf​=2 is studied in detail. Starting from the $\ensuremath{\mid}{J}_{g}=0,{M}_{g}=0⟩$ state, STIRAP can create an arbitrary preselected coherent superposition between the five Mf{M}_{f}Mf​ sublevels $({M}_{f}=\ensuremath{-}2,\ensuremath{-}1,0,+1,+2)$ of the Jf=2{J}_{f}=2Jf​=2 level with 100% efficiency in the adiabatic limit. The populations and the phases of the Mf{M}_{f}Mf​ states in this superposition are determined entirely by the polarizations of the two laser fields. It is shown that this technique allows one to create any superposition of the five Mf{M}_{f}Mf​ states, that is, to reach any point in the Hilbert space of the Jf=2{J}_{f}=2Jf​=2 manifold, and the corresponding recipes for choosing the laser polarizations are presented.
We have looked at the laser-induced excitation of a level manifold coupled through a single excited level. This generalizes the ordinary Λ configuration to many levels. It is the original situation where stimulated Raman adiabatic passage (STIRAP) has been considered. We then apply optimal control theory to determine the pulse sequence which effects a predetermined superposition state with a minimal involvement of the excited state. The program is free to find its optimal pulse sequence, and we find that a generalization of the ordinary counterintuitive situation emerges. In addition to verifying the efficiency of the counterintuitive approach, the work justifies the separation into dark and bright subspaces, where time evolution in the former has to include the dynamical effects of adiabatic corrections.
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.