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arXiv:2502.02838 · Physical Review A

Characterizing stationary optomechanical entanglement in the presence of non-Markovian noise

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

Published Aug 21, 2025• 2 citations
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Abstract

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.

DOI
10.1103/gysx-m9p2

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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.
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.
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.
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.
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
The non-Gaussianity and entanglement in an optomechanical system with the dispersive coupling is theoretically considered for the coherent optical and vacuum mechanical input. The so-called non-Gaussianity is evaluated as a function of the modulus of coherent state parameter of the input optical field and the normalized optomechanical coupling constant. To detect and quantify the entanglement in the system, three criteria (a criterion based on the trace of the reduced density matrix squared, the Simon criterion, and that suggested by Shchukin and Vogel) are used. The results of application of these criteria are compared and critically analyzed. The situations in which these criteria agree among each other and in which they disagree are rationalized. An important conclusion of the work is that, in the regime of strong optomechanical coupling, the non-Gaussian entanglement in the system should be ascribed to the correlations of an exponentially high order.
We investigate how to generate continuous-variable entanglement between distant optomechanical and spin systems, by transferring input two-mode squeezed vacuum state to the system. Such a setup has been proposed for backaction evading gravitational-wave measurement, squeezing the output noise below the standard quantum limit. We find that the spin cavity entanglement saturates to a particular value when no mechanics are involved even though the entanglement of the input beam increases steadily, and drops down when the mechanical oscillator interacts with the cavity. Our study also reveals that the spin optical readout rate enables the robustness of the spin-cavity entanglement with input squeezing whereas the optomechanical coupling strength disables it. The entanglement reaches its maximum when the effective resonance frequency and bandwidth of the cavity match the spin system. Determining collective quadrature fluctuations, our analysis also shows that even though the entanglement between spin and cavity, and cavity and mechanics is significantly present; it is still impossible to obtain entanglement between spin and mechanical oscillator.