Verifying Quantum Memory in the Dynamics of Spin Boson Models

TL;DR

This paper explores quantum memory effects in spin boson models' non-Markovian dynamics, using criteria and numerically exact methods to detect and analyze quantum memory across different regimes.

Contribution

It applies two local quantum memory criteria to spin boson models and employs a numerically exact matrix product operator method for broad parameter regimes.

Findings

Quantum memory can be predicted at low temperatures with process tensors.

Dynamical maps can detect quantum memory at short times in resonant environments.

Quantum memory is confirmed in stationary regimes using correlated steady states.

Abstract

We investigate the nature of memory effects in the non-Markovian dynamics of spin boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its environment. We apply two such criteria, derived from different definitions put forward in the literature, to spin boson and two-spin boson models. For the computation of dynamical maps and process tensors, we employ a numerically exact method for non-Markovian open system dynamics based on matrix product operator influence functionals, that can be applied across broad parameter regimes. We find that, with access to single-intervention process tensors, one can generally predict quantum memory in the dynamics at low temperatures. Given instead only the dynamical map, we are still able to detect quantum memory in the case of resonant environments at short evolution times. Moreover, we confirm quantum memory in the stationary dynamical regime using process tensors with the correlated steady state of system and environment as initial condition.