Decoherence, entanglement decay, and equilibration produced by chaotic environments

TL;DR

This paper studies how chaotic environments cause decoherence and equilibration in quantum systems, showing that chaos and the environment's effective Hilbert space dimension influence the loss of coherence and entanglement.

Contribution

It introduces the concept of effective Hilbert space dimension to explain decoherence and demonstrates that chaotic environments lead to equilibration to diagonal states in the energy basis, even with few degrees of freedom.

Findings

Decoherence is characterized by quantum Loschmidt echoes.

Chaotic environments induce decoherence without revivals in the semiclassical regime.

Entanglement between two systems diminishes, leading to near-separable states after equilibration.

Abstract

We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long times scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.