Bath-induced correlations in an infinite-dimensional Hilbert space

TL;DR

This paper analytically investigates how a thermal bath induces quantum correlations between two dissipative particles in an infinite-dimensional Hilbert space, revealing maximum coherence at a specific time before dissipation dominates.

Contribution

It demonstrates bath-induced quantum coherence and correlations in an infinite-dimensional setting and identifies the time-scale for maximum bath-induced coherence.

Findings

Bath-induced coherence peaks at a specific time before dissipation

Reduced density matrix cannot be factorized at T > 0

Quantum discord confirms the quantum nature of correlations

Abstract

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T > 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.