Transient Dynamics and Homogenization in Incoherent Collision Models

TL;DR

This paper compares the transient dynamics of incoherent collision models with controlled-swap interactions to traditional coherent models, revealing significant differences in memory effects and synchronization despite similar long-term behavior.

Contribution

It introduces and analyzes the effects of incoherent CSWAP interactions in collision models, highlighting their impact on transient dynamics and emergent phenomena.

Findings

Incoherent CSWAP interactions lead to different transient behaviors than coherent PSWAP.

Memory effects are influenced by the type of swap operation during transient dynamics.

Synchronization onset varies significantly between incoherent and coherent collision models.

Abstract

Collision models have attracted significant attention in recent years due to their versatility to simulate open quantum systems in different dynamical regimes. They have been used to study various interesting phenomena such as the dynamical emergence of non-Markovian memory effects and the spontaneous establishment of synchronization in open quantum systems. In such models, the repeated pairwise interactions between the system and the environment and also the possible coupling between different environmental units are typically modeled using the coherent partial-swap (PSWAP) operation as it is known to be a universal homogenizer. In this study, we investigate the dynamical behavior of incoherent collision models, where the interactions between different units are modeled by the incoherent controlled-swap (CSWAP) operation, which is also a universal homogenizer. Even though the asymptotic dynamics of the open system in case of both coherent and incoherent swap interactions appear to be identical, its transient dynamics turns out to be significantly different. Here we present a comparative analysis of the consequences of having coherent or incoherent couplings in collision models, namely, PSWAP or CSWAP interactions respectively, for the emergence of memory effects for a single qubit system and for the onset synchronization between a pair of qubits, both of which are strictly determined by the transient dynamics of the open system.