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Journal of Experimental and Theoretical Physics

Second-Order Processes in Emission of Radiation by an Ensemble of Quantum Oscillators

Ashat M. Basharov, Andrew I. Trubilko

Published Oct 1, 2021• 4 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776121100010

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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 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.
The problems of phase synchronization in an ensemble of oscillators or dipoles, and the mechanisms of coherent field generation in superradiance mode, are discussed. It is shown that an increase in the spread of the initial amplitudes of an ensemble of oscillators suppresses their phase synchronization and reduces the efficiency of field generation. The influence of noise is discussed; it is shown that, below the generation threshold, even an external initiating field cannot synchronize the phases of an ensemble of particles. When the generation threshold is exceeded, the initiating field may not be required. It is shown that the convergence of the oscillator phases with the field phases at the locations of moving oscillators is noticeable only near their exit from the system. At the same time, a complete coincidence of the phases of synchronized oscillators and the field phases in the region of their localization is not observed. Nevertheless, the intensity of the generation field in the superradiance mode significantly exceeds the spontaneous level, which allows us to speak about the signs of induced radiation. The features of the development of the quantum process of superradiance of an ensemble of dipoles are discussed, and a system of equations for its description is given. The features of the quantum analog of superradiance are qualitatively modeled, and the role of the Rabi frequency determining the dynamics of the population inversion is noted. The nutation of the population inversion in the region occupied by the field affect the field intensity not only in this local zone, but also in subsequent regions of the active zone. This explains the unusual nature of the generation development: the field growth in a certain region of the active zone first stabilizes and then decreases significantly. This decrease in intensity also occurs in the direction of radiation in the peripheral regions of the active zone, despite the large energy reserve in them in the form of unperturbed population inversion.
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.