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Journal of Experimental and Theoretical Physics Letters

Effects of the Stark Interaction in the Dynamics of an Atomic System in a Broadband Squeezed Electromagnetic Field

Andrew I. Trubilko, Ashat M. Basharov

Published Jul 1, 2025• 5 citations
Publisher

Abstract

The effects of the Stark interaction in the collective radiation of an ensemble of atoms in the field of a broadband electromagnetic field in a squeezed quantum state have been considered. It has been shown that the inclusion of the conditions for the formation of the squeezed field allows one to describe the dynamics of atoms in terms of random quantum creating, annihilating, and counting processes. The latter process is the Stark interaction of atoms and the field and manifests itself in the form of a trigger superradiance pulse generated by an ensemble of identical atoms excited by a quantized resonant squeezed electromagnetic field. The description is based on the kinetic equation derived for an open localized quantum system in a broadband squeezed quantized electromagnetic field. The resulting equation differs from the known ones, but agrees with them in particular and limiting cases.

DOI
10.1134/s002136402560675x

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The effects of the Stark interaction in the collective radiation of an ensemble of atoms in the field of a broadband electromagnetic field in a squeezed quantum state have been considered. It has been shown that the inclusion of the conditions for the formation of the squeezed field allows one to describe the dynamics of atoms in terms of random quantum creating, annihilating, and counting processes. The latter process is the Stark interaction of atoms and the field and manifests itself in the form of a trigger superradiance pulse generated by an ensemble of identical atoms excited by a quantized resonant squeezed electromagnetic field. The description is based on the kinetic equation derived for an open localized quantum system in a broadband squeezed quantized electromagnetic field. The resulting equation differs from the known ones, but agrees with them in particular and limiting cases.
The Markov model of spontaneous emission of an atom localized in a spatial region with a broadband electromagnetic field with zero photon density is considered in the conditions of coupling of the electromagnetic field with the broadband field of a neighboring space. The evolution operator of the system and the kinetic equation for the atom are obtained. It is shown that the field coupling constant affects the rate of spontaneous emission of the atom, but is not manifested in the atomic frequency shift. The analytic expression for the radiative decay constant for the atom is found to be analogous in a certain sense to the expression for the decay constant for a singly excited localized ensemble of identical atoms in the conditions when the effect of stabilization of its excited state by the Stark interaction with the vacuum broadband electromagnetic field is manifested. The model is formulated based on quantum stochastic differential equations of the non- Wiener type and the generalized algebra of the Ito differential of quantum random processes.
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 terms of second order in 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 first order in the coupling constant are represented by the quantum Wiener process, whereas terms of second order are expressed by the quantum Poisson process. During the course of the 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. 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 a determined number of particles.
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.
The radiation of a quantum particle in a thermostatic electromagnetic field with a nonzero photon density in the presence of a strong Stark interaction between the particle and field is considered. New fundamental effects—the suppression of radiation by the Stark interaction in an intense broadband field and an additional “decay” shift in the energy of the decaying level, which is different from the Lamb and Stark level shifts—have been established. A new effect of the suppression of radiation is complementary to the effect of suppression of the polarization relaxation of the quantum particle in a squeezed field, which is discovered earlier by Gardiner. The new effect can occur independently of the effect established by Gardiner.
A new kinetic master equation for the generalized Langevin dynamics of a mechanical system undergoing radiative interaction with a broadband electromagnetic field in a squeezed state has been derived from a quantum stochastic differential equation constructed using the algebra of generators of two-quantum stochastic processes. The latter express the Hamiltonian of the radiative interaction in terms of the Ito increments of these processes. The motion of a harmonic oscillator and a free particle has been analyzed using the equation for the Wigner quasiprobability, which is next in the harmonic approximation of the original equation for an open system. Features of the system dynamics in a broadband squeezed field and a broadband field in a classical state have been revealed.