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Journal of Experimental and Theoretical Physics

Nonresonant Processes as a Basis for the Formation of New Relaxation Channels in the Theory of Quantum Optical Systems

Andrew I. Trubilko, Ashat M. Basharov

Published Jan 1, 2020• 5 citations
Publisher

Abstract

Abstract The mechanisms for the pumping and decay of an “isolated” oscillator that can interact only nonresonantly with a neighboring oscillator of different frequency are presented. We show that if this neighboring oscillator is coupled to a broadband heat-bath field, the isolated oscillator begins to interact with this heat-bath field. A new relaxation channel attributable to the quantum interference of the interacting systems that is difficult or impossible to justify in terms of traditional approaches emerges as a result.

DOI
10.1134/s1063776119120100

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Abstract The mechanisms for the pumping and decay of an “isolated” oscillator that can interact only nonresonantly with a neighboring oscillator of different frequency are presented. We show that if this neighboring oscillator is coupled to a broadband heat-bath field, the isolated oscillator begins to interact with this heat-bath field. A new relaxation channel attributable to the quantum interference of the interacting systems that is difficult or impossible to justify in terms of traditional approaches emerges as a result.
Mechanisms of pumping and decay of an “isolated” oscillator which can nonlinearly interact with a neighboring oscillator having a different frequency have been discussed. It has been shown that, if this neighboring oscillator is coupled to a broadband thermostat field, the isolated oscillator begins to interact with this thermostat field. As a result, a new relaxation channel appears because of the quantum interference of interacting systems, which can hardly be explained within traditional approaches.
The paper shows mechanisms of both the pumping and energy decay of an "isolated" oscillator. The oscillator is only non-resonantly coupled with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the "isolated" oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian, with the latter being the Hamiltonian of two oscillators and environment of one of them.
Abstract The paper shows mechanisms of both the pumping and energy decay of an ‘isolated’ oscillator. The oscillator is only coupled non-resonantly with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the ‘isolated’ oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian. The original model is reduced to two ‘independent’ open systems, with each containing original oscillators connected with their effective independent thermal baths, whose parameters are determined. The paper also gives a description of the obtained model in terms of quantum stochastic differential equations.
Abstract Using algebraic perturbation theory, the applicability of the quantum oscillator model within the theory of open quantum systems is demonstrated. The case of resonant and nonresonant interactions between two spatially separated oscillators is considered, where each oscillator interacts with its own thermostat at different temperatures. The possibility of the decay of an isolated oscillator into the thermostat of the oscillator-mediator under conditions of its nonresonant interaction with the latter is demonstrated. In all the cases presented, algebraic perturbation theory does not lead to any nonphysical features or contradictions, such as violations of the second law of thermodynamics or discrepancies in the description of these cases within the frameworks of the global and local approaches.
Vibrational relaxation of a harmonic oscillator nonlinearly coupled to a heat bath is investigated by the Gaussian–Markovian quantum Fokker–Planck equation approach. The system–bath interaction is assumed to be linear in the bath coordinate, but linear plus square in the system coordinate modeling the elastic and inelastic relaxation mechanisms. Interplay of the two relaxation processes induced by the linear–linear and square–linear interactions in Raman or infrared spectra is discussed for various system–bath couplings, temperatures, and correlation times for the bath fluctuations. The one-quantum coherence state created through the interaction with the pump laser pulse relaxes through different pathways in accordance with the mechanisms of the system–bath interactions. Relations between the present theory, Redfield theory, and stochastic theory are also discussed.
Our normal understanding of the dissipative relaxation of a quantum system interacting with a reservoir or heat bath leads us to expect that the final state of the quantum system is a mixed state characteristic of one subsystem in equilibrium with the larger reservoir. We show that the broadband squeezed vacuum has such strong correlations in its quantum noise that, although it represents a true reservoir, the decay of subsystems, such as pairs of atoms or oscillators interacting with a squeezed reservoir, relaxes to a pure state that reflects these strong correlations.