Gravitational Decoherence Estimation in Optomechanical Systems

TL;DR

The paper develops a quantum estimation framework to bound the precision with which gravitationally induced decoherence, captured by $\Lambda_g$, can be inferred from optomechanical systems using single‑mode Gaussian probes. By expressing dynamics through the evolving covariance matrix and applying the Gaussian QFI formalism, it reveals how gravitational diffusion imprints squeezing and cross‑quadrature correlations that inform estimation accuracy. The results show squeezed vacuum probes yield the highest QFI at short times, with robustness and regime dependence creating a trade‑off between quantum advantage and decoherence, guiding experimental design toward underdamped, short‑time operation. This work provides a concrete, quantitative link between gravity‑related decoherence models and experimentally accessible metrological performance in realistic optomechanical setups.

Abstract

We develop a comprehensive quantum estimation framework to quantify how precisely gravitationally induced decoherence can be inferred in optomechanical systems, using single-mode Gaussian probe states. Our approach combines a microscopic description of the gravitational diffusion mechanism with quantum Fisher information to determine the ultimate sensitivity achievable in principle. We show that gravitational diffusion leaves distinct, measurable signatures in the mechanical state, both during transient evolution and in the stationary regime. Finally, we identify how probe state preparation shapes the attainable precision, thereby establishing fundamental limits for detecting and estimating gravity-driven decoherence.

Figures (7)

• Figure 1: A pictorical scheme of the phenomenon: Conceptual diagram of an optomechanical system subject to gravitational decoherence. A mechanical oscillator (a simple pendulum as a moving mirror) coupled to an optical field in a cavity is used as a quantum probe.
• Figure 2: Evolution of purity for initial energy $n_0=4$ in different quantum states. As expected, purity decreases with time due to dissipation and decoherence. Squeezed states exhibit faster decoherence compared to coherent states, indicating greater susceptibility to environmental interactions.
• Figure 3: Purity of single-mode squeezed vacuum states for various squeezing parameters $r$, with $\Lambda_g = 10^{-8}$. Top: long-time behavior. Bottom: transient dynamics with short-time oscillations due to the interplay between gravitational decoherence and thermal noise. States with higher squeezing show faster purity decay, indicating greater sensitivity to dissipation.
• Figure 4: QFI as a function of $t$ and $\Lambda_g$, with squeezed vacuum as initial state. One can see clearly that the QFI asymptotically approaches a steady value, as decoherence acts.
• Figure 5: QFI as a function of time $t$ and the parameter $\Lambda_g$, using squeezed vacuum states as probe. For large (unphysical) values of $\Lambda_g$, the QFI drops rapidly, highlighting the protocol’s sensitivity within the physically relevant regime.