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Journal of Experimental and Theoretical Physics

On the Possibility of Preserving Excitation in an Ensemble of Identical Oscillators

Ashat M. Basharov, Andrew I. Trubilko

Published Dec 1, 2021• 3 citations
Publisher

Abstract

Abstract It is shown that an ensemble of Nc independent identical quantum oscillators interacting nonresonantly with a damped oscillator can be effectively described as an ensemble of identical oscillators decaying in the field of a common thermostat. The emission rate of such an ensemble exhibits a peculiar dependence on number Nc of oscillators and can be suppressed completely depending on the number of oscillators in the ensemble for zero thermostat photon number density in a certain frequency range of the spectrum. This feature reflects the non-Wiener nature of the oscillator ensemble dynamics and appears when all antirotating and rapidly varying (with time) terms (in the Dirac pattern) in the oscillator interaction operators, which are usually neglected, are taken into account correctly.

DOI
10.1134/s1063776121120013

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Abstract It is shown that in the local approach to analysis of open oscillator systems, in the presence of a common boson thermostat in an ensemble of identical quantum oscillators, collective emission of radiation by the oscillator ensemble demonstrates features of the non-Wiener dynamics. The intensity of radiation emitted by large number Nc of oscillators in the ensemble decreases with increasing Nc and turns out periodically to be completely suppressed by second-order processes in the constant of coupling of the oscillators with the common thermostat field.
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The spontaneous emission of a quantum particle and superradiation of an ensemble of identical quantum particles in a vacuum electromagnetic field with zero photon density are examined under the conditions of significant Stark particle and field interaction. New fundamental effects are established: suppression of spontaneous emission by the Stark interaction, an additional “decay” shift in energy of the decaying level as a consequence of Stark interaction unrelated to the Lamb and Stark level shifts, excitation conservation phenomena in a sufficiently dense ensemble of identical particles and suppression of superradiaton in the decay of an ensemble of excited quantum particles of a certain density. The main equations describing the emission processes under conditions of significant Stark interaction are obtained in the effective Hamiltonian representation of quantum stochastic differential equations. It is proved that the Stark interaction between a single quantum particle and a broadband electromagnetic field is represented as a quantum Poisson process and the stochastic differential equations are of the non-Wiener (generalized Langevin) type. From the examined case of spontaneous emission of a quantum particle, the main rules are formulated for studying open systems in the effective Hamiltonian representation.
The effective Hamiltonian describing resonant interaction of an ensemble of identical quantum particles with a photon-free vacuum electromagnetic field has been obtained with allowance for the second-order terms over the coupling constant (the Stark interaction) by means of the perturbation theory on the basis of the unitary transformation of the system quantum state. It has been shown that in the Markov approximation the effective Hamiltonian terms of the first-order coupling constant are represented as the quantum Wiener process, whereas the second-order terms are expressed by the quantum Poisson process. In the course of investigation it was established that the Stark interaction played a significant role in the ensemble dynamics, thus influencing the collective spontaneous decay of the ensemble of an appreciably high number of identical particles. New fundamental effects have been discovered, i.e., the excitation conservation in a sufficiently dense ensemble of identical particles and superradiance suppression in the collective decaying process of an excited ensemble with the determined number of particles.