Quantum indirect synchronization

TL;DR

This paper demonstrates that two coupled quantum two-level systems can achieve phase synchronization indirectly through their interaction, even without direct coupling to an external drive, expanding understanding of quantum synchronization mechanisms.

Contribution

It introduces the concept of indirect quantum synchronization between coupled systems without direct external drive interaction, supported by phase diagram analysis using Husimi Q functions.

Findings

Phase locking occurs in coupled quantum systems with environmental decoherence.

Synchronization strength can be measured using the S function.

Indirect synchronization is feasible without direct external coupling.

Abstract

It is well known that a system with two or more levels exists a limit cycle and can be synchronized with an external drive when the system and the drive are directly coupled. One might wonder if a system can synchronize with the external drive when they are not coupled directly. In this paper, we examine this case by considering a composite system consisting of two coupled two-level quantum systems, one of which is driven by an external field, while another couples to the driven one. Due to the decoherence caused by environments, the composite system would stay in a mixed state, and an effective limit cycle is formed, so phase locking could occur. We find the phase locking phenomenon in the phase diagram characterized by Husimi $Q$ function, and the synchronization can be generated consequently that we will refer to indirect synchronization. The $S$ function defined in the earlier study can also be used to measure the strength of synchronization. We claim that indirect synchronization is possible. This result provides us with a method to synchronize a quantum system that coupled to its neighbour without interacting with external drive directly.