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arXiv:2604.04856

Modeling the non-Markovian Brownian motion of an optomechanical resonator

Aritra Ghosh, Malay Bandyopadhyay, M. Bhattacharya

quant-phcond-mat.mes-hallcond-mat.stat-mechphysics.opticsSubmitted Apr 6, 2026• Announced Apr 7, 2026• Revised Aug 18, 2026 (v2)

v1 · Apr 6, 2026 v2 · Aug 18, 2026

Abstract

We propose a representative, 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 propose a globally-admissible, phenomenological bath spectrum that extends the experimentally-observed, near-resonance non-Ohmic behavior beyond the measurement window while ensuring finite bath-induced renormalizations and quadrature fluctuations of the resonator. The corresponding model of the structured environment produces a nonlocal mechanical response whose analytic pole structure encodes the observed linewidth. The resulting dissipation kernel exhibits a power-law-modulated exponential decay with transient negativity, signaling 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.

Journal reference: Phys. Rev. A 114, 023514 (2026)
DOI: 10.1103/h74c-4lxd
Comments: v2: To appear in PRA

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We investigate how non-Markovian mechanical dissipation affects exceptional points in linearized optomechanical systems with red-sideband drive. For a chosen non-Ohmic mechanical bath, we derive analytical conditions for the memory-renormalized exceptional point by employing a pseudomode mapping, thereby demonstrating that structured environments displace the mode coalescence away from the Markovian prediction. Crucially, we reveal that failing to account for this memory-induced shift suppresses the divergent Petermann factor by orders of magnitude, showing that accurate bath modeling is essential for the successful operation of exceptional-point-based devices whenever reservoir-induced memory is non-negligible. We finally show that non-Markovianity modifies the cavity reflection spectrum, manifesting as a shallower optomechanically-induced-transparency dip, providing therefore an experimentally-accessible signature of structured mechanical environments.

All physical systems are to some extent open and interacting with their environment. This insight, basic as it may seem, gives rise to the necessity of protecting quantum systems from decoherence in quantum technologies and is at the heart of the emergence of classical properties in quantum physics. The precise decoherence mechanisms, however, are often unknown for a given system. In this work, we make use of an opto-mechanical resonator to obtain key information about spectral densities of its condensed-matter heat bath. In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify. We conclude by elaborating on further applications of opto-mechanical systems in open system identification.

Dissipation caused by nonhomogeneous bosonic finite chain environments (implementable in, e.g., segmented ion traps) is investigated through an exact diagonalization approach, avoiding common approximations used to describe open systems. Different spectral densities, including band gaps, can be engineered to separately assess different factors leading to memory effects, namely, the environment's size, temperature, proximity of the cutoff frequency, the spectral density's shape (sub-Ohmic, Ohmic, super-Ohmic), and the strength of its coupling to the system. Non-Markovianity is quantified with two recently introduced measures related to information backflow and nondivisibility of the system dynamical map. By sweeping the bath spectrum via tuning of the system frequency we show strongest memory effects at band-gap edges and provide an interpretation based on energy flow between system and environment. A system weakly coupled to a stiff chain ensures a Markovian dynamics, while the size of the environment as well as the local density of modes are not substantial factors. We show an opposite effect when increasing the temperature inside or outside the spectral band gap. Further, non-Markovianity arises for larger (negative and positive) powers of algebraic spectral densities, being the Ohmic case not always the most Markovian one.

We investigate how the exceptional-point structure of a dissipative cavity optomechanical system is inherited by experimentally accessible dynamical, spectral, and quantum-statistical observables. At optical-mechanical resonance, the effective non-Hermitian first-moment dynamics exhibits a second-order exceptional point, where two eigenvalues and their eigenvectors coalesce and the eigenvalue splitting follows the characteristic square-root dependence on perturbations. We show that the same square-root feature also governs transient photon and phonon populations, first-order coherence, spectral poles, and second-order intensity correlations. Below the exceptional point, the dynamics is non-oscillatory, whereas above it damped oscillations emerge together with frequency splitting of the spectral poles. At the exceptional point, the Jordan-block structure produces polynomial-exponential relaxation and a second-order spectral pole. Using the quantum regression theorem and Gaussian moment factorization, we further show that the stationary fluctuations satisfy the Siegert relation linking first- and second-order correlations. Although the zero-delay autocorrelations retain their thermal value, the finite-delay intensity correlations exhibit clear exceptional point signatures. This finding connects non-Hermitian mode coalescence with measurable dynamical and correlation observables in cavity optomechanics.

We investigate dynamics of an optomechanical system under the non-Markovian environment. In the weak optomechanical single-photon coupling regime, we provide an analytical approach fully taking into account the non-Markovian memory effects. When the cavity-bath coupling strength crosses a certain threshold, an oscillating memory state for the classical cavity field is formed. Due to the existence of the non-decay optical bound state, a nonequilibrium optomechanical thermal entanglement is preserved even without external driving laser. Our results provide a potential usage to generate and protect entanglement via non-Markovian environment.

Intrinsic damping rate and quality factor (

Q

) are key parameters in optomechanical systems. However, in high-Q devices, their measurement is often challenging because probe-induced dynamical backaction (DBA) and the need to resolve and accurately track the mechanical resonance limit the performance of state-of-the-art techniques. Here, we introduce an all-optical ringdown method in the unresolved-sideband regime that exploits the nonlinear, time-averaged optical response induced by strong mechanical motion. We derive an analytical model of the time-averaged optical cavity response probed by a weak frequency-scanning laser. During the evolution of the mechanical oscillator, the excited motion modulates the Lorentzian lineshape into a double-horned profile whose peak separation enables an accurate estimation of the modulation amplitude. Tracking this response during the mechanical ringdown allows the intrinsic damping rate to be determined without resolving the mechanical oscillation. We apply the method to a density-modulated phononic crystal membrane placed inside a high-finesse cavity and obtain mechanical quality factors consistent with independent measurements on the same platform. Our method requires a minimal optical setup, while offering an in situ diagnostic and reduced impact from probe-induced DBA and robustness against measurement noise. Finally, the model can describe other resonant systems dispersively coupled to coherent frequency modulations, providing new insights and measurement strategies that expand beyond the optomechanical platform.