Synchronization effects in a periodically driven two-level system

TL;DR

This paper investigates phase synchronization in a driven two-level quantum system coupled to a non-Markovian environment, revealing a resonance condition linked to Bessel function zeros that enhances phase-locking.

Contribution

It introduces a non-approximated, numerically exact analysis of synchronization effects in a driven two-level system with non-Markovian reservoirs, identifying a resonance condition for phase-locking.

Findings

Robust phase-locking occurs at a resonance ratio matching zeros of Bessel function J0.

Synchronization measure rapidly becomes finite at the resonance condition.

The phenomenon is explained via a static Fourier-based approximation.

Abstract

We study phase-synchronization in a driven two-level system coupled to a non-Markovian bosonic reservoir. The dynamics is described by treating the system-bath coupling and the coherent drive without invoking the rotating-wave approximation, and simulated using the numerically exact hierarchical equations of motion. We observe that a robust phase-locking develops and that the corresponding synchronization measure rapidly acquires a finite value when the system is tuned to what we identify as a resonant-ratio condition, namely when the ratio between the drive amplitude and its frequency coincides with a zero of the Bessel function $J_0$. We provide an explanation for this phenomenon by means of a static approximation derived from a Fourier analysis of the periodically driven Hamiltonian.