Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1502.00615 · Physical Review A

Mirror-field entanglement in a microscopic model for quantum optomechanics

Kanu Sinha, Shih-Yuin Lin, B. L. Hu

Published Aug 28, 2015• 22 citations
arXivHTMLPDF

Abstract

We use a microscopic model, the mirror-oscillator-field (MOF) model proposed by C. R. Galley, R. O. Behunin, and B. L. Hu [Phys. Rev. A 87, 043832 (2013)], to describe the quantum entanglement between a mirror's center-of-mass (c.m.) motion and a field. In contrast with the conventional approach where the mirror-field entanglement is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's c.m., the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. The major advantage in this approach is that it provides a self-consistent treatment of the three pertinent subsystems (the mirror's c.m. motion, its internal degrees of freedom, and the field) including their back-actions on each other, thereby giving a more accurate account of the quantum correlations between the individual subsystems. The optical and the mechanical properties of a mirror arising from its dynamical interaction with a quantum field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. As one of the new physical features that arise from this self-consistent treatment of the coupled optics and mechanics behavior we observe a coherent transfer of quantum correlations from the field to the mirror via its internal degrees of freedom. We find the quantum entanglement between the optical field and the mirror's center-of-mass motion upon coarse-graining over the internal degree of freedom. Further, we show that in certain parameter regimes the mirror-field entanglement is enhanced when the field interacts resonantly with the mirror's internal degree of freedom, a result which highlights the importance of including the internal structure of the mirror in quantum optomechanical considerations.

DOI
10.1103/physreva.92.023852

Related papers

A Microscopic Model for Quantum Optomechanics

Kanu Sinha

We study a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed in [1], for describing optomechanical interactions. In contrast with the conventional approach where the mirror-field interaction is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror’s CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. Considering the mirror’s internal and mechanical degrees of freedom as two separate degrees of freedom we derive the optomechanical properties of the coupled mirror and field system. The major advantage in this approach is that it provides a self-consistent treatment of the three relevant subsystems (the mirror’s motion, its internal degrees of freedom and the field) including their back-actions on each other, thereby giving a more accurate account of the coupled internal and external dynamics. The optical and the mechanical properties of a mirror arising from its dynamical interaction with the field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. We find that our results agree with those from the boundary condition approach in the appropriate limits and more generally the model provides a framework within which one can study optomechanical elements with different internal structures and mechanical properties, which makes it suited for studying hybrid systems. Considering the quantum dynamics of the coupled subsystems we look at the entanglement between the mirror’s motion and the field, showing that the internal degrees of the mirror, in the appropriate parameter regimes, can act as a means to coherently transfer quantum correlations between the field and the mechanics thus leading to a larger optomechanical entanglement. We then use the MOF model to study the entanglement between the motion of an atom and a field for the setup in [95] and find a larger optomechanical entanglement when the field is closer to the internal resonance. We also study the interaction between two mirrors as described by the MOF model, specifically looking at the entanglement between the motion of their centers of mass. Conclusively, we see that including the dynamics of the internal degrees of freedom of a mirror, which is the quintessential mediator of interaction between the mirror center of mass and the field, leads to qualitatively different physics, specifically in the quantum regime, thus giving a physically more complete treatment of mirror-field interactions.

•Jan 1, 2015•1 citation

Coupled dynamics of an atom and an optomechanical cavity

X. X. Yi, Hongchang Sun, L. C. Wang

We consider the motion of the end mirror of a cavity inside which a two-level atom trapped. The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom. We analyze this optical effect by showing the population of the atom in its internal degrees of freedom as a function of time. On the other side, fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration, leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.

arXiv:0807.2703•Jul 17, 2008•1 citation

Quantum Optomechanics with Imperfect Mirrors and Casimir-Polder Effect of Atoms with Different Dynamic Polarizabilities: A Unified Treatment via a Microscopic Model

Bergen Dahl, Bei-Lok Hu

This work aims at bringing the microphysics model of quantum optomechanics (QOM) proposed in [1] and developed in [2, 3] one step closer to be applicable to realistic experimental conditions, specifically, for imperfect mirrors, and for real materials. The atom/mirror-oscillator-field (AMOF) model features an internal degree of freedom for a mirror or an atom whose interaction with a quantum field determines the transmission functions of a mirror or the dynamic polarizability of an atom. We study three problems with this model: 1) An imperfect mirror moving in a cavity field, comparing results from the AMOF model with the boundary condition methods; 2) We analyze how well the dynamic polarizability derived from the AMOF model fits the tabulated data at different frequencies. 3) Combining these two parts we analyze the quantum fluctuations induced Casimir-Polder energy between a dilute atom space and a wall. We examine how well we can use the three constituent parameters of the idf oscillator in the AMOF model to match with published results on a meta-stable He* atom near a Au plate and found excellent agreements. These examples show that the AMOF model not only has a sound theoretical structure, because it is based on the microphysics dynamics of the basic constituents, it also has good practical values because it can produce accurate results for certain real materials.

quant-pharXiv:2608.22098•Aug 25, 2026

Optomechanical entanglement: How to prepare, verify and "steer" a macroscopic mechanical quantum state?

S. L. Danilishin, Haixing Miao, M Helge +1 more

We consider a generic optomechanical system and investigate quantum entanglement between the outgoing light fields and the mechanical motion of the mirror. In contract to traditional approach, we do not consider quantum correlations between the intracavity optical mode and the mechanical motion of a mirror, rather the correlations between the continuum of optical fields in the outgoing light wave and the mechanical degree of freedom. This entanglement is shown to be robust to thermal decoherence and depend on the ratio of measurement strength (light power) and decoherence rate ∝ T/Qm. Furthermore, we describe a feasible way to demonstrate quantum state steering, usinging time-variable homodyne detection scheme that allows to evade back-action. An intimate connection between optomechanical steerability and quantum state tomography [Phys. Rev. A 81, 012114 (2010)] is demonstrated.

•Jan 1, 2013•3 citations

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

Adrian E. Rubio Lopez, Hing-Tong Cho, Bei-Lok Hu

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.

quant-pharXiv:2608.29429•Sep 1, 2026

Generation of the mechanical Schrödinger cat state in a hybrid atom-optomechanical system

Najmeh Etehadi Abari, M. H. Naderi

In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.

Journal of the Optical Society of America B•Jun 2, 2020•9 citations
We use a microscopic model, the mirror-oscillator-field (MOF) model proposed by C. R. Galley, R. O. Behunin, and B. L. Hu [Phys. Rev. A 87, 043832 (2013)], to describe the quantum entanglement between a mirror's center-of-mass (c.m.) motion and a field. In contrast with the conventional approach where the mirror-field entanglement is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's c.m., the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. The major advantage in this approach is that it provides a self-consistent treatment of the three pertinent subsystems (the mirror's c.m. motion, its internal degrees of freedom, and the field) including their back-actions on each other, thereby giving a more accurate account of the quantum correlations between the individual subsystems. The optical and the mechanical properties of a mirror arising from its dynamical interaction with a quantum field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. As one of the new physical features that arise from this self-consistent treatment of the coupled optics and mechanics behavior we observe a coherent transfer of quantum correlations from the field to the mirror via its internal degrees of freedom. We find the quantum entanglement between the optical field and the mirror's center-of-mass motion upon coarse-graining over the internal degree of freedom. Further, we show that in certain parameter regimes the mirror-field entanglement is enhanced when the field interacts resonantly with the mirror's internal degree of freedom, a result which highlights the importance of including the internal structure of the mirror in quantum optomechanical considerations.
We study a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed in [1], for describing optomechanical interactions. In contrast with the conventional approach where the mirror-field interaction is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror’s CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. Considering the mirror’s internal and mechanical degrees of freedom as two separate degrees of freedom we derive the optomechanical properties of the coupled mirror and field system. The major advantage in this approach is that it provides a self-consistent treatment of the three relevant subsystems (the mirror’s motion, its internal degrees of freedom and the field) including their back-actions on each other, thereby giving a more accurate account of the coupled internal and external dynamics. The optical and the mechanical properties of a mirror arising from its dynamical interaction with the field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. We find that our results agree with those from the boundary condition approach in the appropriate limits and more generally the model provides a framework within which one can study optomechanical elements with different internal structures and mechanical properties, which makes it suited for studying hybrid systems. Considering the quantum dynamics of the coupled subsystems we look at the entanglement between the mirror’s motion and the field, showing that the internal degrees of the mirror, in the appropriate parameter regimes, can act as a means to coherently transfer quantum correlations between the field and the mechanics thus leading to a larger optomechanical entanglement. We then use the MOF model to study the entanglement between the motion of an atom and a field for the setup in [95] and find a larger optomechanical entanglement when the field is closer to the internal resonance. We also study the interaction between two mirrors as described by the MOF model, specifically looking at the entanglement between the motion of their centers of mass. Conclusively, we see that including the dynamics of the internal degrees of freedom of a mirror, which is the quintessential mediator of interaction between the mirror center of mass and the field, leads to qualitatively different physics, specifically in the quantum regime, thus giving a physically more complete treatment of mirror-field interactions.
We consider the motion of the end mirror of a cavity inside which a two-level atom trapped. The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom. We analyze this optical effect by showing the population of the atom in its internal degrees of freedom as a function of time. On the other side, fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration, leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
This work aims at bringing the microphysics model of quantum optomechanics (QOM) proposed in [1] and developed in [2, 3] one step closer to be applicable to realistic experimental conditions, specifically, for imperfect mirrors, and for real materials. The atom/mirror-oscillator-field (AMOF) model features an internal degree of freedom for a mirror or an atom whose interaction with a quantum field determines the transmission functions of a mirror or the dynamic polarizability of an atom. We study three problems with this model: 1) An imperfect mirror moving in a cavity field, comparing results from the AMOF model with the boundary condition methods; 2) We analyze how well the dynamic polarizability derived from the AMOF model fits the tabulated data at different frequencies. 3) Combining these two parts we analyze the quantum fluctuations induced Casimir-Polder energy between a dilute atom space and a wall. We examine how well we can use the three constituent parameters of the idf oscillator in the AMOF model to match with published results on a meta-stable He* atom near a Au plate and found excellent agreements. These examples show that the AMOF model not only has a sound theoretical structure, because it is based on the microphysics dynamics of the basic constituents, it also has good practical values because it can produce accurate results for certain real materials.
We consider a generic optomechanical system and investigate quantum entanglement between the outgoing light fields and the mechanical motion of the mirror. In contract to traditional approach, we do not consider quantum correlations between the intracavity optical mode and the mechanical motion of a mirror, rather the correlations between the continuum of optical fields in the outgoing light wave and the mechanical degree of freedom. This entanglement is shown to be robust to thermal decoherence and depend on the ratio of measurement strength (light power) and decoherence rate ∝ T/Qm. Furthermore, we describe a feasible way to demonstrate quantum state steering, usinging time-variable homodyne detection scheme that allows to evade back-action. An intimate connection between optomechanical steerability and quantum state tomography [Phys. Rev. A 81, 012114 (2010)] is demonstrated.
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 xxx remains small. Recent years saw several papers treating x2,x3x^2, x^3x2,x3 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 xxx. 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 NxNxNx coupling, with NNN the photon number, up to the recent x3x^3x3 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.
In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.