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Известия Российской академии наук Серия физическая

The non-Wiener dynamics of an ensemble of identical anharmonic oscillators

M. K. Aleksashin, Ashat M. Basharov, Andrew I. Trubilko

Published Nov 1, 2023• 0 citations
Publisher

Abstract

The model of an ensemble of anharmonic oscillators in the field of a common broadband photon-free thermostat is reduced to a model of an ensemble of identical N-level particles in terms of the algebraic perturbation theory. In one region the model describes the Dicke superadiance, and in the other one—oscillating dependence of the collective radiation intensity on the number of the ensemble oscillator. The collective radiation proves to be suppressed with a certain number of oscillators.

DOI
10.31857/s0367676523702848

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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.
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.
Abstract It is shown that when nonresonant interactions between atoms and a vacuum electromagnetic field are included in analysis of emission of a localized ensemble of identical atoms, a delay must appear in the cooperative radiation pulse emitted by the atomic ensemble that is initially in a half-excited state. At the same time, the emission of cooperative radiation from a completely excited ensemble for certain parameters must begin without any delay. This contradicts the familiar facts of the conventional Dicke superradiance, in the theory of which nonresonant interactions are disregarded. The model taking into account nonresonant interactions along with other factors of the Dicke model is called the generalized Dicke model.
Abstract We propose a collective decay model for a localized ensemble of identical atoms in a vacuum broadband electromagnetic field with a nonzero photon number density considering second-order terms in the atom–field interaction constant. The model is based on the stochastic differential equation for the evolution operator for the atomic ensemble and surroundings, which is controlled by the main quantum random processes and independent classical Wiener processes. It is shown that in some cases, nonzero photon number density does not influence the suppression of collective emission of atoms, and its existence is manifested as an additional mechanism of redistribution of atoms over collective sublevels.