Bath-induced correlations in an infinite-dimensional Hilbert space

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.

Dynamics of indistinguishable free particles driven by a quantum bath

“…Additionally, we show the total probability of finding one particle in each subsystem belonging to a chosen bipartition; in fact, in the present paper, we choose two different geometrical bipartitions. Complementary to this calculation, we calculate also the total probability of finding two particles in either subsystem and zero particles in the other (this is similar to the mirror correlation calculated for distinguishable particles [10]).…”

“…The equivalence between Fock's space and the symmetric (antisymmetric) Wannier basis for indistinguishable particles was previously established in [10,11]. In this section we introduce the QME for many indistinguishable particles in the second quantization approach.…”

“…In Refs. [10,11] it was noted that the terms R † Rρ and RR † ρ generate coherence, while R † ρR and RρR † are responsible for inducing decoherence in the system.…”

“…In order to simplify the analysis of the QME (4) we will omit the term for the frequency cutoff hω c RR † in the effective Hamiltonian. This term only produces additional reversible coherence [10].…”

“…To describe these shift operators, we use the second quantization formalism. Previous experiences with these types of systems have been introduced using distinguishable particles [10,11]. These free models are many-body extensions of the well-known dissipative quantum-walk approach [12][13][14][15][16][17], which has been shown to be very suitable for describing the superposition of quantum states and decoherence phenomena in quantum information theory [18].…”