Quantum optomechanics with arbitrary mirror displacement: nonlinear Langevin equation with non-Markovian back-action noises

• URL: http://arxiv.org/abs/2608.29429v1
• Date: Sat, 29 Aug 2026 20:21:08 GMT
• Title: Quantum optomechanics with arbitrary mirror displacement: nonlinear Langevin equation with non-Markovian back-action noises
• Abstract summary: Quantum optomechanics (QOM) explores the interaction between a quantum field, often confined in a cavity, and the quantum motion of mirrors, membranes or material media.<n>Recent years saw several papers treating $x2, x3$ orders in the mirror displacement.<n>We derive a nonlinear Langevin equation driven by these back-action noises from the quantum field.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum optomechanics (QOM) explores the interaction between a quantum field, often confined in a cavity, and the quantum motion of mirrors, membranes or material media, usually assumed slow enough with negligible particle production, which is the central concern of dynamical Casimir effects, and a drive laser field for effective control. This rapidly developing field has a wide range of applications, from quantum sensing to the detection of gravitational waves. Because the opto-mechanical coupling is nonlinear, most theoretical investigations assume that the amplitude of mirror motion $x$ remains small. Recent years saw several papers treating $x^2, x^3$ orders in the mirror displacement. In our work we take a different route, deploying the functional perturbative method presented in [1] and enriched in [2], applicable for sufficiently weak opto-mechanical couplings. With this we can treat arbitrary displacement of the mirror, not just at a higher order in a power series expansion in $x$. We first derive the influence action of the quantum field and its non-Markovian noises back-reacting on the moving mirror with self-consistency. From it we derive a nonlinear Langevin equation driven by these back-action noises from the quantum field. We then show how results from our general modeling and treatment can be linked with the models and the Langevin equations presented in the literature, starting with the popular radiation pressure $Nx$ coupling, with $N$ the photon number, up to the recent $x^3$ order results. We hope this new approach and the results presented here can provide useful theoretical support for high precision QOM experimentation in the future.

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