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Journal of Experimental and Theoretical Physics

Kinetic Equation for the Density Matrix of Atoms in the Field of a Broadband One-Photon Packet Taking into Account the Non-Wiener Dynamics

Andrew I. Trubilko, Ashat M. Basharov

Published May 1, 2018• 6 citations
Publisher

Abstract

We have derived the quantum master kinetic equation for the density matrix of an atomic system in the field of a narrow-beam one-photon broadband packet in the conditions when the latter plays the role of a thermostat. This equation takes into account the Stark interaction of atoms with the broadband field of surroundings of the system, which are in the state with zero photon number density, as well as the interaction of broadband fields at the atomic system.

DOI
10.1134/s1063776118050084

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We have derived the quantum master kinetic equation for the density matrix of an atomic system in the field of a narrow-beam one-photon broadband packet in the conditions when the latter plays the role of a thermostat. This equation takes into account the Stark interaction of atoms with the broadband field of surroundings of the system, which are in the state with zero photon number density, as well as the interaction of broadband fields at the atomic system.
Abstract Under the conditions of the Markov approximation, a master kinetic equation is derived that describes the transfer of the state of a single-photon packet to the state of a solitary object, depending on the nature of the latter. A single-photon excitation is a broadband packet with a Gaussian frequency distribution (an information signal) that interacts nonresonantly with a selected high-Q cavity mode (an intermediary). The latter also interacts nonresonantly with an absorber whose natural frequency is resonant to the central frequency of the packet.
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.
Under the conditions of the Markov approximation, a master equation is derived that describes the transfer of the state of a single- photon broadband packet to the state of a solitary object, depending on the nature of the latter. A single- photon excitation is a broadband packet with a Gaussian frequency distribution (an information signal) that interacts non- resonantly with a selected high- quality resonator mode (an intermediary). The latter also interacts non- resonantly (in the dispersion limit) with a working cell whose natural frequency is resonant with the central frequency of the packet. The derivation is based on quantum stochastic differential equations, which naturally follow from the construction of an effective interaction Hamiltonian based on the algebraic theory of resonance interactions.
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.
Abstract The derived master kinetic equation is used to determine the features of the nature of an isolated object, an absorber, on which the state of a broadband single-photon excitation is transferred. In the role of the absorber, a quantum oscillator or a two-level atom is considered. It is shown that, in the case of a nonresonant interaction between the packet and an intermediary, and between the intermediary and the absorber, the transfer of the state of a single-photon packet is possible if the absorber is a quantum oscillator. In the case where the transfer is to a two-level atom, the excitation transfer is only partial.