Berry-Hannay relation in nonlinear optomechanics

Ludovico Latmiral,Federico Armata

doi:10.1038/s41598-020-59081-5

Abstract

We address the quantum-classical comparison of phase measurements in optomechanics in the general framework of Berry phases for composite systems. While the relation between Berry phase and Hannay angle has been proven for a large set of quadratic Hamiltonians, such correspondence has not been shown so far in the case of non-linear interactions (e.g. when three or more operators are involved). Remarkably, considering the full optomechanical interaction we recover the aforementioned mathematical relation with the Hannay angle obtained from classical equations of motion. Our results link at a fundamental level previous proposals to measure decoherence, such as the one expressed by Marshall et al., with the no-go theorem shown by Armata et al., which provides boundaries to understand the quantum-to-classical transition in optomechanics.

Highlights

We address the quantum-classical comparison of phase measurements in optomechanics in the general framework of Berry phases for composite systems
The archetypical optomechanical system consists in a single optical field of frequency ωf coupled to a inside an optical cavity quantum mechanical oscillator of mass m and frequency ω through the radiation
We assume to operate in the so called good cavity regime, where optical damping and photon leakage from the cavity are negligible over an entire mechanical period and light and mirror continuously interact until the field escapes the cavity: this regime is defined by the condition k ω

Summary

Introduction

Resorting to completely different models for the classical and the quantum picture, they proved that, under common and widely adopted experimental conditions (e.g. small coupling and mechanical thermal state), the observable phase shifts of the light field coincide This result has allowed them to challenge the visibility loss and revival as signatures respectively of quantum superposition and decoupling, and as probes of any decoherence process. Instead, they have inferred that correlations arise because of (classical) statistical uncertainty on the initial state of the system and lead to effects that are qualitatively identical and quantitatively larger than those theoretically predicted for a single-photon source[18].

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Conclusion