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Physical Review A

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

Z. Kis, Stig Stenholm

Published Nov 15, 2001• 39 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.64.063406

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In this paper we consider a generalization of the three-level stimulated Raman adiabatic-passage process (STIRAP). In our scheme, there are N\ensuremath−1N\ensuremath{-}1N\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.
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.
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 $N\ensuremath{-}1$ 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.
Coherent manipulation of quantum states is of crucial importance in accurate control of a quantum system. A fundamental goal is coherently transferring the population of a desired state with near-unit fidelity. For this purpose, we theoretically demonstrate a novel coherent double-stimulated Raman adiabatic passage (STIRAP) in a three-level Λ-type system for realizing the switch of unequal initial preparations on two ground states. This operation uses a single optical pulse sequence accomplishing both bright-STIRAP and dark-STIRAP processes, in which the intermediate-level detuning and the pulse delay must be given an optimal adjustment. Besides, owing to the imperfection of double-STIRAP transition, the sensitivity of the switch fidelity with respect to the spontaneous loss from the intermediate state, to the pulse amplitude and to the population difference, is also discussed. This work suggests a simple and experimentally feasible all-optical approach to switch a superposition quantum state, serving as one-step closer to the goal of coherent manipulation of quantum systems.
Coherent stimulated Raman adiabatic passages (STIRAP) based on a dark state have many applications in diverse quantum systems. In the case of large single-photon detuning in three-level $\ensuremath{\Lambda}$ systems, one of the bright states almost does not involve the excited state and then acts as the dark state. In this paper, we report the experimental observation of STIRAP based on the dark state, as well as b-STIRAP based on the above bright state, with the same transfer efficiency in a three-level $\ensuremath{\Lambda}$ cold atomic ensemble. Moreover, both STIRAP and b-STIRAP are found to be immune to the time-varying ac Stark shift. As for a typical example to manipulate a superposition state, we realize an inverse operation on an initial superposition state, which cannot be achieved efficiently for STIRAP based on only the dark state. Our observed double STIRAP thus provides a feasible and robust manner to manipulate quantum states.
Adiabatic techniques using multilevel systems have recently been generalized from the optical case to settings in atom optics, solid state physics, and even classical electrodynamics. The most well known example of these is the so-called stimulated Raman adiabatic passage (STIRAP) process, which allows transfer of a particle between different states with large fidelity. Here we generalize and examine this process for an atomic center-of-mass state with a nontrivial phase distribution and show that even though dark state dynamics can be achieved for the atomic density, the phase dynamics will still have to be considered as a dynamical process. In particular we show that the combination of adiabatic and nonadiabatic behavior can be used to engineer phase superposition states.
In this paper we consider the adiabatic transfer in three-level systems using the counterintuitive pulse sequence, the stimulated Raman process (STIRAP). We consider explicitly the nonadiabatic corrections to the ideal case. The problem simplifies when we use certain pulse types extending to infinity, ramp pulses. In this case we find models which are analytically solvable. In the smooth pulse case, we find simple exponential corrections to adiabatic behavior. For a resonant intermediate level, the problem is equivalent to a two-level problem, where adiabatic corrections have been investigated extensively. We utilize these results to interpret the behavior of the three-level system exposed to the counterintuitive pulse case. When the pulse separation is in a certain range, exponential adiabatic behavior is found, and the numerical data can be explained by the analytic theory taken from the two-level work. We cannot explain all results analytically, but the computations suggest that this description of the three-level system gives a good understanding of the STIRAP. \textcopyright{} 1996 The American Physical Society.