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Physical Review A

Irreversibility of energy-conservative dipole dephasing in a simple model

J. J. Yeh, Joseph H. Eberly

Published Sep 1, 1980• 19 citations
Publisher

Abstract

Abrupt radiative excitation into a one-electron atomic continuum of distinct zero-width energy levels is investigated in a simple energy-conservative atomic model. Induced off-diagonal coherence is shown to decay irreversibly. That is, it is shown that one cannot recover off-diagonal coherence by the application of subsequent radiative pulses, ruling out the occurrence of long-time or repetitive coherent transients such as photon echoes in this model of continuum transitions. A brief comparison with the case of transitions in a Doppler-broadened continuum, where coherent transients are commonly observed, is made.

DOI
10.1103/physreva.22.1124

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Abrupt radiative excitation into a one-electron atomic continuum of distinct zero-width energy levels is investigated in a simple energy-conservative atomic model. Induced off-diagonal coherence is shown to decay irreversibly. That is, it is shown that one cannot recover off-diagonal coherence by the application of subsequent radiative pulses, ruling out the occurrence of long-time or repetitive coherent transients such as photon echoes in this model of continuum transitions. A brief comparison with the case of transitions in a Doppler-broadened continuum, where coherent transients are commonly observed, is made.
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The response of an arbitrary closed quantum system to a partially coherent electric field is investigated, with a focus on the transient coherences in the system. As a model we examine, both perturbatively and numerically, the coherences induced in a three level V system. Both rapid turn-on and pulsed turn-on effects are investigated. The effect of a long and incoherent pulse is also considered, demonstrating that during the pulse the system shows a coherent response which reduces after the pulse is over. Both the pulsed scenario and the thermally broadened CW case approach a mixed state in the long time limit, with rates dictated by the adjacent level spacings and the coherence time of the light, and via a mechanism that is distinctly different from traditional decoherence. These two excitation scenarios are also explored for a minimal "toy" model of the electronic levels in pigment protein complex PC645 by both a collisionally broadened CW laser and by a noisy pulse, where unexpectedly long transient coherence times are observed and explained. The significance of environmentally induced decoherence is noted.
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A simple application of the Stark-pulse technique, developed by Brewer and Shoemaker, demonstrates optical free induction decay-the optical analog of free induction decay in NMR. A molecular sample which is coherently prepared by a cw laser beam exhibits such a decay when it is suddenly switched out of resonance by a Stark field. Observations are presented for a nondegenerate Doppler-broadened infrared transition of NH2{\mathrm{H}}_{2}H2​D, where the sample is optically thin, and the decay behavior can be compared quantitatively with a solution of the Bloch equations. When the molecular sample is prepared under steady-state conditions, the solutions are analytic; for pulse excitation, a numerical solution is required. The treatment invokes a hard-collision relaxation model. Such characteristics as the abrupt termination of the decay and the related edge echo, which result from Doppler dephasing, can be examined for Stark pulses of finite extent.
Each of three basic coherent transient phenomena (optical nutation, free polarization decay photon echo) can be generated by sufficiently abrupt modulation of the interaction between the matter and radiation. This can be performed by rapid commutation of either radiation parameters, or the parameters of the matter. I present here comparative analysis of these two approaches (the first one, using electro-optical switching of the resonant laser power to create the pulses for the gas excitation and the second one, based on the Stark switching of vibro-rotational levels in a gas, excited by CW laser radiation), used in our experiments in molecular gases, from the point of view of both their capability to generate various coherent transients and their sensitivity to the intensity of laser radiation.
We describe the temporal behavior of the dynamic elements of an exactly soluble quantum model. The model consists of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation. We give new long-time numerical and closed-form approximate analytic solutions for the expectation values of the atomic dipole moment and the difference in population of the two atomic levels in the rotating wave approximation. The atomic dipole-dipole correlation function is calculated. All of the results are obtained without semiclassical or decorrelation approximations. Unusual features found in the temporal behavior of this lossless model problem are "collapse," i.e., episodic nonexponential damping of both the atomic inversion and dipole moment, and two kinds of "revival" or partial recorrelation, in the dynamic evolution, during which the initial state is nearly recovered. We give analytic formulas for the collapse function, for both of the revival times, and for the envelope of the revival maxima. Some remarks are made about the nature of irreversibility in this exactly soluble and loss-free model.