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Известия Российской академии наук Серия физическая / Bulletin of the Russian Academy of Sciences Physics

Transfer of the state of a broadband single-photon packet in non-resonant interaction with isolated systems of different physical nature: General approach

A. M. Basharov, Andrew I. Trubilko

Published Jan 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.7868/s3034646025120016

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•Aug 17, 2016•1 citation
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 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.
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.
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.
We demonstrate that a highly excited quantum electromagnetic mode strongly interacting with a single qubit exhibits several distinct resonances in addition to the Bloch-Siegert resonance condition that arises in the interaction with classical radiation. The resonance phenomena are associated with non-classical effects: Collapse of Rabi oscillations, splitting of the photon wave packet, and field-qubit entanglement. The analysis is based on a semiclassical phase-space flow of 2-by-2 matrices and becomes exact when the photon number tends to infinity. The flow equations are solved perturbatively and numerically, showing that the resonant detuning of the field and qubit frequencies lie on two branches in the leading order, that further split into distinct curves in higher orders. 1