Modeling the non-Markovian Brownian motion of an optomechanical resonator

• URL: http://arxiv.org/abs/2604.04856v1
• Date: Mon, 06 Apr 2026 17:01:27 GMT
• Title: Modeling the non-Markovian Brownian motion of an optomechanical resonator
• Abstract summary: We propose a globally-admissible spectral density of the bath for the non-Markovian Brownian motion of an optomechanical resonator.<n>We reproduce the observed local-power-law behavior near the mechanical resonance while remaining well defined globally.<n>Our results provide a consistent route from locally-inferred spectral properties to globally-admissible open-system descriptions.
• Score: 23.831322147151138
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a globally-admissible phenomenological spectral density of the bath for the non-Markovian Brownian motion of an optomechanical resonator, motivated by the near-resonance experimental observation of a non-Ohmic spectrum in [Nat. Commun. 6, 7606 (2015)]. To avoid divergences arising from a naive global extrapolation, we construct this phenomenological bath spectral density that reproduces the observed local-power-law behavior near the mechanical resonance while remaining well defined globally, ensuring the finiteness of the bath-induced renormalizations and quadrature fluctuations of the resonator. The corresponding model of the structured environment produces a nonlocal mechanical susceptibility whose analytic pole structure encodes the observed linewidth. The resulting dissipation kernel exhibits a power-law-modulated exponential decay with transient negativity, signaling strong memory effects. In the weak-coupling regime, the optical readout based on homodyne detection enables near-resonance spectroscopy and, with a calibrated drive on the resonator, permits, in principle, the reconstruction of the full mechanical susceptibility, thereby providing access to both the dissipative and dispersive bath contributions. Our results provide a consistent route from locally-inferred spectral properties to globally-admissible open-system descriptions and establish a framework for probing structured environments in cavity optomechanics.

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