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

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 sequentially-encountered modes of the same frequency, each of which it interacts with through a beam splitter. We then analyze the dependence of the asymptotic state of this mode on the assumed stationary common initial state $\sigma$ of the reservoir modes and on the transmittance $\tau =\cos \lambda$ of the beam splitters. These results allow us to establish that at small $\lambda$ such a mode will, starting from an arbitrary initial system state $\rho$, 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.

References in corpus (10)

• Quantum collision models: open system dynamics from repeated interactions
• Another Return of 'Return to Equilibrium'
• Theory of Non-Equilibrium Sationary States as a Theory of Resonances
• Dynamics of Open Quantum Systems II, Markovian Approximation
• Random repeated interaction quantum systems
• Entropy growth during free expansion of an ideal gas
• Decoherence and nonclassicality of photon-added/subtracted multi-mode Gaussian states
• Measuring the quadrature coherence scale on a cloud quantum computer
• Boltzmann entropy of a freely expanding quantum ideal gas
• Interferometric measurement of the quadrature coherence scale using two replicas of a quantum optical state