Geometric Phase in Quantum Synchronization

TL;DR

This paper explores how a quantum limit-cycle oscillator acquires a geometric phase during slow rotation of its quantization axis, revealing a structure akin to synchronization phenomena and uncovering effects like synchronization blockade.

Contribution

It introduces a kinematic approach to define geometric phases in nonunitary quantum evolution and derives an analytic expression for the geometric phase in a specific regime.

Findings

Geometric phase appears in quantum limit-cycle oscillators under slow rotation.

The geometric phase structure resembles the Arnold tongue of synchronization.

Synchronization blockade causes the vanishing of the geometric phase structure.

Abstract

We consider a quantum limit-cycle oscillator implemented in a spin system whose quantization axis is slowly rotated. Using a kinematic approach to define geometric phases in nonunitary evolution, we show that the quantum limit-cycle oscillator attains a geometric phase when the rotation is sufficiently slow. In the presence of an external signal, the geometric phase as a function of the signal strength and the detuning between the signal and the natural frequency of oscillation shows a structure that is strikingly similar to the Arnold tongue of synchronization. Surprisingly, this structure vanishes together with the Arnold tongue when the system is in a parameter regime of synchronization blockade. We derive an analytic expression for the geometric phase of this system, valid in the limit of slow rotation of the quantization axis and weak external signal strength, and we provide an intuitive interpretation for this surprising effect.