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arXiv:2502.02979 · Physical Review Letters

Universality of Stationary Entanglement in an Optomechanical System Driven by Non-Markovian Noise and Squeezed Light

Su Direkci, Klemens Winkler, Corentin Gut, Markus Aspelmeyer, Yanbei Chen

Published Aug 19, 2025• 3 citations
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Abstract

Optomechanical systems subjected to environmental noise give rise to rich physical phenomena. We investigate entanglement between a mechanical oscillator and the reflected coherent optical field in a general, not necessarily Markovian environment. For the input optical field, we consider stationary Gaussian states and frequency-dependent squeezing. We demonstrate that for a coherent laser drive, either unsqueezed or squeezed in a frequency-independent manner, optomechanical entanglement is destroyed after a threshold that depends only on the environmental noises-independent of the coherent coupling between the oscillator and the optical field, or the squeeze factor. In this way, we have found a universal entangling-disentangling transition. We also show that for a configuration in which the oscillator and the reflected field are separable, entanglement cannot be generated by incorporating frequency-dependent squeezing in the optical field.

DOI
10.1103/vzhk-cdc3

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Optomechanical systems subjected to environmental noise give rise to rich physical phenomena. We investigate entanglement between a mechanical oscillator and the reflected coherent optical field in a general, not necessarily Markovian environment. For the input optical field, we consider stationary Gaussian states and frequency-dependent squeezing. We demonstrate that for a coherent laser drive, either unsqueezed or squeezed in a frequency-independent manner, optomechanical entanglement is destroyed after a threshold that depends only on the environmental noises-independent of the coherent coupling between the oscillator and the optical field, or the squeeze factor. In this way, we have found a universal entangling-disentangling transition. We also show that for a configuration in which the oscillator and the reflected field are separable, entanglement cannot be generated by incorporating frequency-dependent squeezing in the optical field.
We study an optomechanical system, where a mechanical oscillator interacts with a Gaussian input optical field. In the linearized picture, we analytically prove that if the input light field is the vacuum state, or is frequency-independently squeezed, the stationary entanglement between the oscillator and the output optical field is independent of the coherent coupling between them, which we refer to as the universality of entanglement. Furthermore, we demonstrate that entanglement cannot be generated by performing arbitrary frequency-dependent squeezing on the input optical field. Our results hold in the presence of general, Gaussian environmental noise sources, including non-Markovian noise.
Probing quantum entanglement with macroscopic objects allows us to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous light field via radiation pressure. In view of this, the system that is discussed comprises an optomechanical cavity driven by a coherent optical field in the unresolved sideband regime where we assume Gaussian states and dynamics. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we treat non-Markovian noise and take into account both the continuous optical field and the cavity mode. We apply our framework to the case of the Advanced Laser Interferometer Gravitational-Wave Observatory and discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises.
Probing quantum entanglement with macroscopic objects allows us to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous light field via radiation pressure. In view of this, the system that is discussed comprises an optomechanical cavity driven by a coherent optical field in the unresolved sideband regime where we assume Gaussian states and dynamics. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we treat non-Markovian noise and take into account both the continuous optical field and the cavity mode. We apply our framework to the case of the Advanced Laser Interferometer Gravitational-Wave Observatory and discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises. Published by the American Physical Society 2024
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.
As classical technology approaches its limits, exploration of quantum technologies is critical. Quantum optics will be the basis of various cutting-edge research and applications in quantum technology. In particular, quantum optics quite efficacious when applied to quantum networks and the quantum internet. Quantum Optomechanics, a subfield of quantum optics, contains some novel methods for entanglement generation. These entanglement production methods exploit the noise re-encoding process, which is most often associated with creating unwanted phase noise in optical circuits. Using the adapted two-photon formalism and experimental results, we simulate (in an experimentally viable parameter space) optomechanical entanglement generation experiments. These simulations consider dual coherent field input, displaced single-mode squeezed input, and displaced two-mode squeezed inputs. Unsqueezed inputs should yield an ENE_NEN​ of about 0.1 at room temperature, although very high measurement certainty is needed to observe this in the laboratory. Squeezing the displaced input fields increases the expected output entanglement significantly (maximum of ENE_NEN​ of about 1). Furthermore, when considering dual two-mode squeezed input (4 fields) in the simulation, the optomechanical cavity demonstrates squeezing angle-dependent entanglement distribution.
Quantum entanglement is pivotal in modern quantum technologies, spanning applications from quantum networks to quantum metrology. Controllable quantum entanglement in cavity optomechanical systems has been an enduring pursuit. We propose a unique method for flexible manipulation and switching of optomechanical entanglement in a squeezed-cavity-assisted optomechanical system consisting of a χ (2) -nonlinear optical cavity and an optomechanical cavity. Squeezing the nonlinear optical cavity through parametric pumping allows effective control of light-light and light-vibration interactions within the system. This capability of the squeezed system plays a key role in manipulating quantum entanglement. We find that quantum entanglement between the unsqueezed cavity mode and the mechanical mode can be effectively regulated by adjusting the pump laser parameters. Furthermore, by turning the phase of the pump, we can achieve highly flexible quantum switching between entanglement and separability. Additionally, we demonstrate increased entanglement between the squeezed cavity mode and the mechanical mode when completely suppressing the pump-induced optical input noise. Our findings pave the way not only towards the manipulation and protection of fragile quantum entanglement but also to achieve photon-phonon quantum control by exploiting quantum squeezing.