Abstract

We provide an argument to infer stationary entanglement between light and a mechanical oscillator based on continuous measurement of light only. We propose an experimentally realizable scheme involving an optomechanical cavity driven by a resonant, continuous-wave field operating in the non-sideband-resolved regime. This corresponds to the conventional configuration of an optomechanical position or force sensor. We show analytically that entanglement between the mechanical oscillator and the output field of the optomechanical cavity can be inferred from the measurement of squeezing in (generalized) Einstein-Podolski-Rosen quadratures of suitable temporal modes of the stationary light field. Squeezing can reach levels of up to 50% of noise reduction below shot noise in the limit of large quantum cooperativity. Remarkably, entanglement persists even in the opposite limit of small cooperativity. Viewing the optomechanical device as a position sensor, entanglement between mechanics and light is an instance of object-apparatus entanglement predicted by quantum measurement theory.Received 4 December 2019Accepted 17 June 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033244Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasOptomechanicsQuantum opticsAtomic, Molecular & Optical

Highlights

  • Experiments in optomechanics operate routinely in a regime in which effects predicted by quantum theory can be observed

  • We propose an experimentally realizable scheme involving an optomechanical cavity driven by a resonant, continuous-wave field operating in the non-sideband-resolved regime

  • We show analytically that entanglement between the mechanical oscillator and the output field of the optomechanical cavity can be inferred from the measurement of squeezing in Einstein-Podolski-Rosen quadratures of suitable temporal modes of the stationary light field

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Summary

INTRODUCTION

Experiments in optomechanics operate routinely in a regime in which effects predicted by quantum theory can be observed This includes mechanical oscillators cooled to their ground state of center-of-mass motion [1,2], ponderomotive squeezing [3,4,5], entanglement between different light tones [6,7], entanglement between different mechanical oscillators [8,9], measurement back-action [10], back-action evasion [11,12,13], and optomechanical entanglement, that is, entanglement between the mechanical oscillator and light, in a pulsed regime [14,15].

ELEMENTS OF OPTOMECHANICS
Inference of optomechanical entanglement from measurement of light
Entanglement criteria
Temporal modes
RESULTS
Experimental task
Approximate formula for the EPR variance
Comparison with numerical results
Remarks on shot-noise levels and multimode entanglement
CONCLUSION
Exact formula for the EPR variance
Full Text
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