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Physical Review A

Population transfer with delayed pulses in four-state systems

J. Oreg, Klaas Bergmann, Bruce W. Shore, Salman Rosenwaks

Published Apr 1, 1992• 71 citations
Publisher

Abstract

We present explicit analytic expressions for adiabatic dressed states which, in suitable limits, produce complete population transfer between initial and final states of a four-state excitation chain without ever placing appreciable population into intermediate states. The population-transfer scheme is a generalization of the three-state stimulated Raman adiabatic passage that makes use of counterintuitive pulse sequences. We demonstrate analytically and numerically that the four-state system differs in a very significant qualitative way from previously studied N-state systems with odd N. In particular, we find that the presence of modest detuning from single-photon resonance is critical to the success of population transfer.

DOI
10.1103/physreva.45.4888

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Journal of Physics Conference Series•Mar 14, 2012•1 citation
We present explicit analytic expressions for adiabatic dressed states which, in suitable limits, produce complete population transfer between initial and final states of a four-state excitation chain without ever placing appreciable population into intermediate states. The population-transfer scheme is a generalization of the three-state stimulated Raman adiabatic passage that makes use of counterintuitive pulse sequences. We demonstrate analytically and numerically that the four-state system differs in a very significant qualitative way from previously studied N-state systems with odd N. In particular, we find that the presence of modest detuning from single-photon resonance is critical to the success of population transfer.
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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 demonstrate that various properties of population transfer by delayed pulses in three-level systems on two-photon resonance can be deduced analytically and for general pulse shapes. We use the fact that the three-level system reduces to effective two-level problems at large intermediate-level detuning \ensuremath{\Delta}, on resonance (\ensuremath{\Delta}=0) and for completely overlapping pulses. Special attention is paid to the effect of the pulse order on the population transfer efficiency. We show that on resonance the transfer efficiency depends substantially on the pulse order, while at large \ensuremath{\Delta} it does not. We also find that under some natural restrictions on the symmetry of the problem, the population of the initial level does not depend on the pulse order at any \ensuremath{\Delta}. Furthermore, we demonstrate that the population transfer in the three-level system can be viewed as a level-crossing problem in an equivalent two-level system not only at large \ensuremath{\Delta} (which is known) but also on resonance, \ensuremath{\Delta}=0. The effective on-resonance two-level problem is interesting by itself as it shows that a level crossing and adiabatic evolution do not necessarily lead to complete population inversion. As examples throughout the paper, we present several analytically solvable models.
We analyze the influence of three pulsed laser fields interacting with a four-state atomic system for which there occur two degenerate population-trapping dressed states. We present a simple expression for the geometrical phase acquired by such an atom during a stimulated Raman adiabatic passage (STIRAP) process using a delay between Stokes and pump pulses, during which the two Rabi frequencies adiabatically traverse a closed path in the parameter space. We describe techniques that can produce (geometrical) state-vector phases that are independent of the longitudial velocity with which atoms move across a laser beam, and that are insensitive to radiative decay from the intermediate excited state. The geometrical phase can be changed by changing the relative delay of the pulses. The geometrical phase can be measured by observing the population in atomic states. We show that when the pump and Stokes pulses are properly timed, high population transfer from the initial state to the target state is achieved. In the adiabatic limit the robustness of the population transfer is equivalent to that of STIRAP.
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.