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arXiv:1901.04958

Superradiance in an external classical nonresonant field under the Stark interaction with a vacuum field

Ashat M. Basharov, Andrew I. Trubilko

Published Jan 15, 2019• 0 citations
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Abstract

Generalized with respect to the Stark interaction of atoms with a vacuum field of zero photon density, Dicke's model is used to describe the Raman superradiance of a localized ensemble of identical atoms in a coherent non-resonant light wave. It is shown that at a certain critical number of atoms in the ensemble the stabilization effect of the excited state of the ensemble relative to collective atomic decay is possible, with superradiance of the atomic ensemble being suppressed. When the number of atoms is close to the critical value, superradiance exhibits features that are opposite to the effects of the conventional superradiance in the pulse delay time. The identified features depend on the intensity of an external coherent field as well as make it possible to assess whether the Stark interaction of an ensemble with a photon-free vacuum electromagnetic field is significant or not.

DOI
10.48550/arxiv.1901.04958

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Generalized with respect to the Stark interaction of atoms with a vacuum field of zero photon density, Dicke's model is used to describe the Raman superradiance of a localized ensemble of identical atoms in a coherent non-resonant light wave. It is shown that at a certain critical number of atoms in the ensemble the stabilization effect of the excited state of the ensemble relative to collective atomic decay is possible, with superradiance of the atomic ensemble being suppressed. When the number of atoms is close to the critical value, superradiance exhibits features that are opposite to the effects of the conventional superradiance in the pulse delay time. The identified features depend on the intensity of an external coherent field as well as make it possible to assess whether the Stark interaction of an ensemble with a photon-free vacuum electromagnetic field is significant or not.
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.
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 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 spontaneous emission from an atomic ensemble localized in a microcavity with the participation of microcavity photons and an external broadband quantized electromagnetic field at the Raman resonance of photons with an optically forbidden (two-photon) atomic transition has been studied. The average spontaneous decay intensity has been calculated for simple cases. It is shown that the dynamics of spontaneous emission from this atomic ensemble differs generally from the conventional superradiance (spontaneous emission of an atomic ensemble at a one-photon optically allowed transition from excited to the ground state. When the atomic ensemble is strongly excited, the delay times and the emission pulse shape differ significantly. The parameter ranges where the spontaneous emission from the atomic ensemble under consideration at a two-photon Raman transition can be described as conventional superradiance with renormalized parameters are found. In the case of single excitation the photon emission probability depends on the number of photons and atoms in the microcavity.