The Langevin-equation description of optomechanics with the dispersive and dissipative optomechanical coupling

• URL: http://arxiv.org/abs/2607.08530v1
• Date: Thu, 09 Jul 2026 14:26:38 GMT
• Title: The Langevin-equation description of optomechanics with the dispersive and dissipative optomechanical coupling
• Abstract summary: The description of the optomechanical system is commonly based on the quantum Langevin equation formalism.<n>In this work, using the aforementioned approach, we derived the equations for the ladder operator of the intracavity field.<n>We found that, staying inside the range of applicability of the Langevin equation formalism, the relation between the fields at the input mirror may not be correct.
• Score: 51.56484100374058
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The description of the optomechanical system is commonly based on the quantum Langevin equation formalism. This framework is introduced phenomenologically or based on a model Hamiltonian. However, once dealing with the optomechanical Fabry-Perot cavity or the modified Michelson-Sagnac interferometer with a semitransparent mechanically active membrane inside, a model-free consideration is also possible by using an alternative approach. Such an approach, which is based on the classical wave equations in the systems, is popular in the gravitational-wave community where it is termed as input-output relations approach. In this work, using the aforementioned approach, we derived the equations for the ladder operator of the intracavity field, stochastic back-action force, and the relation between the fields at the input mirror. Then we simplified the obtained results down to the range of applicability of the Langevin equation formalism and compared these with the corresponding predictions of the latter formalism. This enabled us to critically assess the validity of the Langevin equation formalism and rectify its range of applicability. In the case where the dissipative optomechanical coupling is involved we identified appreciable problems with this formalism. We found that, disregarding the fact that decay rate of the optomechanical Fabry-Perot cavity depends on its length, no dissipative optomechanical coupling is generated. This is in contrast with the prediction of the standard Langevin-equation based treatment. We found that, staying inside the range of applicability of the Langevin equation formalism, the relation between the fields at the input mirror may not be correct. We found that the Langevin equation formalism misses a phase factor at the input field, this factor turns out to be important for the situation involving the dissipative optomechanical coupling.

Related papers

• Quantum simulation of the Liouville equation in classical mechanics with discontinuous potential via Schrödingerization [42.22857110018992]
  We develop quantum simulation algorithms for the Liouville equation of classical mechanics with discontinuous potential.<n>We combine Hamiltonian-preserving schemes by Jin and Wen in Commun. Math. Sci. 3(3), 285-315 (2005) with the Schrdingerization method, which embeds the resulting nonunitary semi-discrete dynamics into a unitary Schrdinger type system.
  arXiv  Detail & Related papers  (2026-06-13T02:49:05Z)
• Generalising gravitationally induced decoherence beyond linear environmental interactions in a microscopic quantum mechanical toy model [0.0]
  We consider an interaction formulated in terms of Weyl elements of the environment's position operators.<n>We show that the first-order term reproduces the decoherence model of Xu, Blencowe (2022) and Domi et al. (2024)
  arXiv  Detail & Related papers  (2026-05-25T15:17:00Z)
• Time-Dependent Logarithmic Perturbation Theory for Quantum Dynamics: Formulation and Applications [0.0]
  We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics.<n>The hierarchy of equations defining the perturbative corrections is governed by a gauge-rotated Hamiltonian of the unperturbed system.<n>The present approach offers a promising alternative for analytical studies of time-dependent multi-photon processes in the perturbative regime.
  arXiv  Detail & Related papers  (2026-04-16T09:33:02Z)
• Comparison of the standard and dressed-picture master equations for the quantum Rabi model in the ultrastrong coupling regime [78.55450146498553]
  This chapter investigates the effects of relaxation and dephasing on the quantum Rabi model in the ultrastrong coupling regime.<n>It provides explicit formulas to implement and numerically solve the resulting nonunitary dynamics.
  arXiv  Detail & Related papers  (2026-04-10T01:22:07Z)
• Quantum optomechanics of lossy bodies: general approach and structured squeezed vacuum effects [51.56484100374058]
  We investigate the overall optomechanical force experienced by a macroscopic lossy object in free space under external quantum illumination.<n>By driving the scattering field with an anisotropic, multimode squeezed vacuum state, the spatial profile of the electromagnetic quantum fluctuations can be engineered to exhibit broken rotational symmetry.<n>We establish a general formalism for macroscopic quantum optomechanics that operates beyond the constraints of thermal equilibrium.
  arXiv  Detail & Related papers  (2026-04-07T13:25:43Z)
• Linear response theory for cavity QED materials at arbitrary light-matter coupling strengths [41.94295877935867]
  We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling.<n>We compare two different approaches to obtain thermal Green functions.<n>We use a mean-field decoupling of high-order Green functions in order to obtain a closed, solvable system of equations.
  arXiv  Detail & Related papers  (2024-06-17T18:00:07Z)
• Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism [55.2480439325792]
  We analytically derive the modified Langevin noise formalism from the established canonical quantization of the electromagnetic field in macroscopic media. We prove that each of the two field parts can be expressed in term of particular bosonic operators, which in turn diagonalize the electromagnetic Hamiltonian.
  arXiv  Detail & Related papers  (2024-04-07T14:37:04Z)
• Decoherence and entropy generation at one loop in the inflationary de Sitter spacetime for Yukawa interaction [2.9849762483081275]
  We extend previous analysis on decoherence in a fermion and scalar quantum field theory. We use a non-equilibrium effective field theory formalism, suitable for open quantum systems such as this. Our result is qualitatively similar to an earlier one found by using the influence functional technique for a massive Yukawa theory.
  arXiv  Detail & Related papers  (2023-07-25T12:14:19Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• An open scattering model in polymerized quantum mechanics [0.0]
  We derive a quantum master equation in the context of a polymerized open quantum mechanical system for the scattering of a Brownian particle. We discuss some physical properties of the master equation associated to effective equations for the expectation values of the fundamental operators.
  arXiv  Detail & Related papers  (2022-07-18T16:52:18Z)
• Lindblad master equations for quantum systems coupled to dissipative bosonic modes [0.0]
  We derive Lindblad master equations for a subsystem whose dynamics is coupled to bosonic modes. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins. This master equation accurately predicts the Dicke phase transition and gives the correct steady state.
  arXiv  Detail & Related papers  (2022-03-07T11:21:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.