Rigorous Results on Approach to Thermal Equilibrium, Entanglement, and Nonclassicality of an Optical Quantum Field Mode Scattering from the Elements of a Non-equilibrium Quantum Reservoir

Author

Stephan De Bièvre
Marco Merkli
Paul Ernest Parris, Missouri University of Science and TechnologyFollow

Abstract

Rigorous Derivations of the Approach of Individual Elements of Large Isolated Systems to a State of Thermal Equilibrium, Starting from Arbitrary Initial States, Are Exceedingly Rare. This is Particularly True for Quantum Mechanical Systems. We Demonstrate Here How, through a Mechanism of Repeated Scattering, an Approach to Equilibrium of This Type Actually Occurs in a Specific Quantum System, One that Can Be Viewed as a Natural Quantum Analog of Several Previously Studied Classical Models. in Particular, We Consider an Optical Mode Passing through a Reservoir Composed of a Large Number of Sequentiallyencountered Modes of the Same Frequency, Each of Which It Interacts with through a Beam Splitter. We First Analyze the Dependence of the Asymptotic State of This Mode on the Assumed Stationary Common Initial State Σ of the Reservoir Modes and on the Transmittance Τ = Cos Λ of the Beam Splitters. This Analysis Allow Us to Establish Our Main Result, Namely that at Small Λ Such a Mode Will, Starting from an Arbitrary Initial System State Ρ, Approach a State of Thermal Equilibrium Even When the Reservoir Modes Are Not Themselves Initially Thermalized. We Show in Addition that, When the Initial States Are Pure, the Asymptotic State of the Optical Mode is Maximally Entangled with the Reservoir and Exhibits Less Nonclassicality Than the State of the Reservoir Modes.

Recommended Citation

S. De Bièvre et al., "Rigorous Results on Approach to Thermal Equilibrium, Entanglement, and Nonclassicality of an Optical Quantum Field Mode Scattering from the Elements of a Non-equilibrium Quantum Reservoir," Quantum, vol. 8, Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, Jan 2024.

The definitive version is available at https://doi.org/10.22331/q-2024-05-23-1360

Department(s)

Physics

Comments

Centre de Recherches Mathématiques, Grant ANR-11-LABX-0007-01

International Standard Serial Number (ISSN)

2521-327X

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 The Authors, All rights reserved.

Creative Commons Licensing

This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Jan 2024