Dynamics of quantum coherences at strong coupling to a heat bath

TL;DR

This paper extends path integral Monte Carlo methods to efficiently track quantum coherences in open systems under strong environmental coupling, revealing relaxation dynamics and phase transitions in two-level quantum systems.

Contribution

It introduces an improved simulation approach for strong coupling regimes, enabling long-time coherence analysis and comparison with analytical models.

Findings

Successfully simulated coherence dynamics in strong coupling regimes.

Extracted relaxation rates for sub-Ohmic environments at finite temperatures.

Identified quantum phase transition from delocalized to localized states.

Abstract

The standard approach for path integral Monte Carlo simulations of open quantum systems is extended as an efficient tool to monitor the time evolution of coherences (off-diagonal elements of the reduced density matrix) also for strong coupling to environments. Specific simulations are performed for two level systems embedded in Ohmic and sub-Ohmic reservoirs in the domains of coherent and incoherent dynamics of the polarization. In the latter regime, the notorious difficulty to access the long time regime is overcome by combining simulations on moderate time scales with iteratively calculated initial densities. This allows to extract relaxation rates for sub-Ohmic environments at finite temperatures and over a broad range of couplings and to compare them to analytical predictions. The time evolution of the von Neumann entropy provides insight into the quantum phase transition at thermal equilibrium from a delocalized to a localized state at zero temperature.