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arXiv:0803.0791 · Physical Review A

Stimulated Raman adiabatic passage in a multilevel atom

A. David. Boozer

Published Feb 11, 2008• 9 citations
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Abstract

We present a general formalism for describing stimulated Raman adiabatic passage in a multilevel atom. The atom is assumed to have two ground state manifolds $a$ and $b$ and an excited state manifold $e$, and the adiabatic passage is carried out by resonantly driving the $a\text{\ensuremath{-}}e$ and $b\text{\ensuremath{-}}e$ transitions with time-dependent fields. Our formalism gives a complete description of the adiabatic passage process and can be applied to systems with arbitrary numbers of degenerate states in each manifold and arbitrary couplings of the $a\text{\ensuremath{-}}e$ and $b\text{\ensuremath{-}}e$ transitions. We illustrate the formalism by applying it to both a simple toy model and to adiabatic passage in the cesium atom.

DOI
10.1103/physreva.77.023411

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We present a general formalism for describing stimulated Raman adiabatic passage in a multilevel atom. The atom is assumed to have two ground state manifolds aaa and bbb and an excited state manifold eee, and the adiabatic passage is carried out by resonantly driving the a\ensuremath-ea\text{\ensuremath{-}}ea\ensuremath-e and b\ensuremath-eb\text{\ensuremath{-}}eb\ensuremath-e transitions with time-dependent fields. Our formalism gives a complete description of the adiabatic passage process and can be applied to systems with arbitrary numbers of degenerate states in each manifold and arbitrary couplings of the a\ensuremath-ea\text{\ensuremath{-}}ea\ensuremath-e and b\ensuremath-eb\text{\ensuremath{-}}eb\ensuremath-e transitions. We illustrate the formalism by applying it to both a simple toy model and to adiabatic passage in the cesium atom.
We generalize Stark-chirped rapid adiabatic passage to the case of a multilevel atom.The atom is assumed to have two ground state levels g and f and an excited level e.The adiabatic passage is carried out by resonantly driving the g-e and f -e transitions with time-dependent pump and Stokes fields in the presence of strong far-off-resonant Stark field.Our formalism determines the states that participate in population transfer and is applicable to systems with arbitrary numbers of degenerate states in each level and arbitrary couplings of the g-e and f -e transitions.We give an application to adiabatic passage in Rb atom.
Coherent population transfer and superposition of atomic states via a technique of stimulated Raman adiabatic passage in an excited-doublet four-level atomic system have been analyzed. It is shown that the behavior of adiabatic passage in this system depends crucially on the detunings between the laser frequencies and the corresponding atomic transition frequencies. Particularly, if both the fields are tuned to the center of the two upper levels, the four-level system has two degenerate dark states, although one of them contains the contribution from the excited atomic states. The nonadiabatic coupling of the two degenerate dark states is intrinsic, it originates from the energy difference of the two upper levels. An arbitrary superposition of atomic states can be prepared due to such nonadiabatic coupling effect.
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.
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 propose a scheme for creating atomic coherent superposition states via the technique of stimulated Raman adiabatic passage in a $\ensuremath{\Lambda}$-type system where the final state has twofold levels. With the application of a control field, it is found that the presence of double dark states leads to two arbitrary coherent superposition states with equal amplitude but inverse relative phases, even though the condition of multiphoton resonance is not met. In particular, two orthogonal maximal coherent superposition states are created when the control field is resonant with the transition of the twofold levels. This scheme can also be extended to manifold $\ensuremath{\Lambda}$-type systems.
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.