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Journal of Experimental and Theoretical Physics Letters

Relaxation of a Single Atom in a Broadband Squeezed Light Field

Andrew I. Trubilko, Ashat M. Basharov

Published Nov 1, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364025608589

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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.
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 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.
In this thesis, we investigate the effect of the dynamical Stark shift on the quantum electrodynamics of an atom undergoing two-photon transitions, interacting with a quantized radiation field in an ideal cavity. To begin with, we discuss the dynamics of the electromagnetic field and the atom in the presence of the Stark shift. We derive closed expressions for the second-order coherence function, quadrature variances, atomic population inversion and dipole squeezing under the approximation of a large initial photon number and coherent or squeezed field input. We show that for an atom initially in the ground state, the inclusion of Stark shift reduces the field squeezing as well as the antibunching. Both the population inversion and the dipole squeezing exhibit phase sensitivity in the presence of Stark shift and for a particular choice of the relative phase of the two atomic levels "trapping" occurs in a two-level atom and the dipole is modified in such a way that it is permanently squeezed. We then discuss the effect of the stark shift on the emission spectrum of an atom and the cavity field spectrum. The inclusion of Stark shift results in asymmetric vacuum field Rabi splitting. We also study the dynamics of the combined atom-field wave function in the presence of the Stark shift and show that both the electromagnetic field and the atom periodically evolve to pure states which are radically different from those in the absence of the Stark shift. Finally, we study the nondegenerate two-photon Jaynes-Cummings model (NTPJCM) in the presence of the Stark shift and show that the dynamics of the NTPJCM in the presence of Stark shift is qualitatively different from the case of the absence of the Stark shift and radically different from the case of degenerate two-photon JCM in the presence of Stark shift.
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.
Equations are derived for the atomic density matrix and relaxation operator for a broadband squeezed field in an arbitrary polarization state and resonance atomic energy levels with an arbitrary degree of degeneracy. It is shown that suppression of the relaxation of the quadrature component of the atomic polarization depends strongly on the type of resonance transition and the polarization state of the squeezed and coherent perturbing fields. When the resonance levels are strongly degenerate, the relaxation of the quadrature component of the atomic polarization under conditions of maximum suppression is nonexponential in character. The mathematical apparatus developed here makes it possible to calculate polarization-related aspects of the multifrequency optical behavior of atomic and molecular systems resonantly excited both by coherent light and by broadband squeezed fields.
We show that atoms interacting with a squeezed radiation field reservoir can exhibit phase-dependent population decay and relax into a highly correlated pure state, in striking difference to decay in a heat bath. We use a Heisenberg operator treatment of radiative transitions in a broadband squeezed light field described as a quantum white-noise field with correlated fluctuations to describe the modified decay of a single atom, and of two atoms cooperatively decaying in a squeezed vacuum. We compare this decay with that generated by a broadband thermal field which lacks the essential field-mode correlations characteristic of squeezing.