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Physical Review A

Population transfer through coupled continua

Andrzej Raczyński, A. Rezmerska, Jarosław Zaremba

Published Jan 11, 2001• 8 citations
Publisher

Abstract

The population transfer in a $\ensuremath{\Lambda}$-like system, with intermediate states belonging to the continuous spectrum, is investigated in the case in which continuum-continuum and nonresonant transitions must be taken into account. The two phenomena are shown to essentially influence the dynamics of the system, in particular the final populations of the discrete states. The transfer probability can be increased if the two components of the pulse are shifted in time in a counterintuitive way, but unlike in the typical case of STIRAP, it is an oscillating function of the time delay.

DOI
10.1103/physreva.63.025402

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The population transfer in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-like system, with intermediate states belonging to the continuous spectrum, is investigated in the case in which continuum-continuum and nonresonant transitions must be taken into account. The two phenomena are shown to essentially influence the dynamics of the system, in particular the final populations of the discrete states. The transfer probability can be increased if the two components of the pulse are shifted in time in a counterintuitive way, but unlike in the typical case of STIRAP, it is an oscillating function of the time delay.
We present a remarkable analytic result which suggests that a continuum can be used as an intermediary for a significant transfer of population from one discrete state to another discrete state in a stimulated Raman transition. The population transfer is accomplished by employing two laser pulses that overlap in time, arranged in the so-called counterintuitive order. That a continuum can be used for population transfer is shown here for the first time. It promises to open up more channels for selective coherent excitation of atoms or molecules.
We study the ir excitation of HeH+{\mathrm{HeH}}^{+}HeH+ using the counterintuitive arrangement of two pulsed lasers with the continuum as the intermediate state. The time-dependent Schr\"odinger equation describing the system is integrated numerically using the split-operator technique. We examine the maximum population transfer as a function of the pulse separation, pulse width, relative pulse strength, two-photon detuning, and relative position of the intermediate continuum state. The largest population transfer found is 63%.
We propose a technique which produces nearly complete ionization of the population of a discrete state coupled to a continuum by a two-photon transition via a lossy intermediate state whose lifetime is much shorter than the interaction duration. We show that using counterintuitively ordered pulses, as in stimulated Raman adiabatic passage (STIRAP), wherein the pulse coupling the intermediate state to the continuum precedes and partly overlaps the pulse coupling the initial and intermediate states, greatly increases the ionization signal and strongly reduces the population loss due to spontaneous emission through the lossy state. For strong spontaneous emission from that state, however, the ionization is never complete because the dark state required for STIRAP does not exist. We demonstrate that this drawback can be eliminated almost completely by creating a laser-induced continuum structure (LICS) by embedding a third discrete state into the continuum with a third control laser. This LICS introduces some coherence into the continuum, which enables a STIRAP-like population transfer into the continuum. A highly accurate analytic description is developed and numerical results are presented for Gaussian pulse shapes.
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 consider the problem of coherent population trapping in a model quantum system consisting of two (and briefly three) coupled continua of energy levels. While an earlier study [Z. Deng and J. H. Eberly, Phys. Rev. A 34, 2492 (1986)] has demonstrated population trapping in a closely related system, it has done so only for the case of a broad featureless continuum. We will demonstrate, on the other hand, that the time evolution of the continuum is qualitatively very different when different types of continua are allowed, and that population trapping is not likely to occur except in the broad featureless continuum. We do show, however, that in some cases other counterintuitive results surface.