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arXiv:quant-ph/9811007 · Physical Review A

Coherent population transfer beyond the adiabatic limit: Generalized matched pulses and higher-order trapping states

Michael Fleischhauer, Razmik G. Unanyan, Bruce W. Shore, Klaas Bergmann

Published May 1, 1999• 29 citations
arXivHTMLPDF

Abstract

We show that the physical mechanism of population transfer in a three-level system with a closed loop of coherent couplings is not equivalent to an adiabatic rotation of the dark state of the Hamiltonian, but corresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive tool to design pulse sequences for stimulated Raman adiabatic passage, which also give maximum population transfer under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses), there exists a higher-order trapping state, which is an exact constant of motion, and analytic solutions for the atomic dynamics can be derived.

DOI
10.1103/physreva.59.3751

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We show that the physical mechanism of population transfer in a three-level system with a closed loop of coherent couplings is not equivalent to an adiabatic rotation of the dark state of the Hamiltonian, but corresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive tool to design pulse sequences for stimulated Raman adiabatic passage, which also give maximum population transfer under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses), there exists a higher-order trapping state, which is an exact constant of motion, and analytic solutions for the atomic dynamics can be derived.
We investigate several configurations for complete population transfer on the basis of the dressed state picture in a three-level system. This picture allows us not only to confirm an atom staying in the only dark state all the time under the well-known stimulated Raman adiabatic passage but also to find the considerably different dynamics from the conventional adiabatic process in cases where the pulses are significantly overlapped or concurrent (optimal detuning method). We expand the concept of the adiabatic process in order to explain all these cases.
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.
Abstract We consider coherent population transfer in multilevel quantum systems driven by time-delayed pulse trains. We show how to choose the parameters of the trains so that the population dynamics tracks the behavior of a Λ-type three-level system under stimulated Raman adiabatic passage (STIRAP). Efficient population transfer can be achieved regardless of the order and with or without overlap of the pump and the Stokes sub-pulses of the trains. Generalized STIRAP schemes of population transfer in N -level system with sequential couplings are also examined. The mechanism of the population transfer and the robustness of the proposed schemes are discussed.
This paper analyzes the extension of the three-state process of stimulated Raman adiabatic passage to chainwise-connected multistate systems. A necessary condition for such a process is the existence of an adiabatic-transfer state, which connects adiabatically the initial state of the chain to its final state. Various counterintuitive pulse sequences are examined, in all of which the pulse that drives the last transition of the chain precedes the pulse driving the first transition, while the pulses driving the intermediate transitions may have different timings. The paper demonstrates some important qualitative differences and similarities between the systems with odd and even number of states. In the on-resonance case, an adiabatic-transfer state always exists for an odd number of states while it never exists for an even number of states. In the off-resonance case, however, the two types of systems behave in a very similar manner and the condition for existence of an adiabatic-transfer state is essentially the same. This condition, which imposes certain limitations on the laser parameters, is derived in a simple and compact form. It is also shown analytically that, besides by large detunings, the populations of the intermediate states (which are generally nonzero during the transfer) can be damped by large intermediate couplings. It is concluded that for an odd number of states, the optimal case is the on-resonance one, with equal and large intermediate couplings. For an even number of states, the optimal (off-resonance) case is when the intermediate couplings and the detunings have similar values. Various numerical examples of success and failure of multistate population transfer confirm the analytic conclusions.
We have studied the population transfer in a three-state system driven by laser beams in terms of the theory of Lewis–Riesenfeld Hermitian invariants for explicitly time-dependent Hamiltonian. The exact solutions obtained allow us to recover two existing schemes producing complete population transfer in the literature, i.e. the π-pulse and stimulated Raman adiabatic passage methods in our unified description. We present a strict formulation of adiabatic conditions and a more accurate expression of the π-pulse method according to the exact time-evolution of state vector.
By generalizing the definition of fidelity for the nonlinear system, we investigate the dynamics and adiabaticity of the population transfer for atom-molecule three-level $\ensuremath{\Lambda}$ system on a stimulated Raman adiabatic passage (STIRAP). We find that the adiabatic fidelity for the coherent population trapping state or dark state, as the function of the adiabatic parameter, approaches to unit in a power law. The power exponent, however, is much less than the prediction of the linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of the STIRAP.