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arXiv:2610.15749

Nonperturbative optomechanics with thin, weakly reflective intracavity dielectrics

Andrew Laeuger, Nancy Aggarwal

physics.opticscond-mat.mes-hallgr-qcquant-phSubmitted Oct 11, 2026• Announced Oct 13, 2026
arXivHTMLPDF

Abstract

Levitated dielectric sensors are often treated as perturbative probes of a pre-existing optical field. We show that this picture fails for a novel sensor geometry: a dielectric plate whose transverse extent captures the full optical mode. Even an optically thin sensor with modest refractive index can heavily restructure the intracavity fields, effectively partitioning a cavity into two subcavities with substantial cross-coupling and producing new optical resonances and trapping sites with properties which deviate from the standard intuition. Conventional perturbative expressions for the cavity frequency shift and optomechanical coupling depart from the exact solution at thicknesses as small as $\simλ/(10n)$. Furthermore, cavity locking decreases the coupling and increases the trap stiffness by orders of magnitude, and the coupled subcavity structure permits appreciable optical cooling at zero detuning, a distinct behavior unique to this nonperturbative regime. These effects, sharing a common origin, establish a distinct regime of cavity optomechanics in which the sensor is no longer merely a probe of the cavity field, but an element that helps define it.

Comments
Main text: 5 pages, 6 figures. Supplemental Material: 5 pages, 6 figures. Comments welcome

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•Jan 1, 2013•0 citations
Levitated dielectric sensors are often treated as perturbative probes of a pre-existing optical field. We show that this picture fails for a novel sensor geometry: a dielectric plate whose transverse extent captures the full optical mode. Even an optically thin sensor with modest refractive index can heavily restructure the intracavity fields, effectively partitioning a cavity into two subcavities with substantial cross-coupling and producing new optical resonances and trapping sites with properties which deviate from the standard intuition. Conventional perturbative expressions for the cavity frequency shift and optomechanical coupling depart from the exact solution at thicknesses as small as ∼λ/(10n)\simλ/(10n)∼λ/(10n). Furthermore, cavity locking decreases the coupling and increases the trap stiffness by orders of magnitude, and the coupled subcavity structure permits appreciable optical cooling at zero detuning, a distinct behavior unique to this nonperturbative regime. These effects, sharing a common origin, establish a distinct regime of cavity optomechanics in which the sensor is no longer merely a probe of the cavity field, but an element that helps define it.
Cavity optomechanical models typically treat a sensor either as a perturbative polarizable object in a pre-existing optical field, or solve the field at a fixed equilibrium and linearize in a fixed optical-mode basis. Neither self-consistently determines the spatially resolved cavity field, the optical force, the mechanical equilibrium, and the back-action when a finite-thickness dielectric plate intercepts the entire optical mode and restructures the intracavity field. In this companion paper to [1], we develop that treatment by extending the vacuum two-photon formalism to finite-thickness planar dielectrics, incorporating their Fresnel reflection, internal propagation, optical forces, and mechanical back-action directly into the field equations. We derive the carrier and sideband transfer functions needed to describe the coupled optical-mechanical system, including optomechanical cooling and the response to external perturbations. The result is a systematic starting point for calculating detector response and noise budgets for cavity experiments with intracavity dielectrics, including gravitational wave detectors deploying levitated sensors.
A major goal within the field of optomechanics is to achieve the single-photon strong-coupling regime, wherein even a mechanical displacement as small as the zero-point uncertainty is enough to shift an optical cavity resonance by more than its linewidth. This goal is difficult, however, due to the small zero-point motion of conventional mechanical systems. Here, we show that an atom trapped in and coupled to a cavity constitutes an attractive platform for realizing this regime. In particular, while many experiments focus on achieving strong coupling between a photon and the atomic internal degree of freedom, this same resource also naturally enables one to obtain optomechanical strong coupling, in combination with the low mass of an atom and the isolation of its motion from a thermal environment. As an example, we show that an optomechanically induced photon blockade can be realized in realistic setups, and provide signatures of how this effect can be distinguished from the conventional Jaynes-Cummings blockade associated with the two-level nature of the atomic transition.
Conventional membrane-in-the-middle (MIM) optomechanical systems offer limited control over the optical linewidth, which can limit their performance when operating in the unresolved-sideband regime. We investigate cavity optomechanics with a photonic-crystal Fano membrane placed at the center of a Fabry-Pérot (FP) cavity. In contrast to a conventional dielectric membrane, the photonic-crystal membrane supports a localized optical resonance, which hybridizes with the cavity field and enables spectral engineering of the relevant optical modes. Besides the usual dispersive optomechanical coupling associated with cavity-length changes, the membrane motion also modifies the Fano-mode resonance and its hybridization with the cavity field. We consider two limits set by the membrane reflectivity: a transparent-membrane regime with a single FP-like mode, and a reflective-membrane regime with two coupled subcavity modes. In the latter case, only the symmetric cavity mode hybridizes with the Fano mode, while the antisymmetric mode remains decoupled. Using quantum Langevin equations together with a transfer-matrix description of the optical scattering problem, we show that the Fano-induced hybridization can generate narrow optical normal modes that remain efficiently accessible to the external drive for experimentally realistic parameters. These modes can provide effective sideband resolution and enable ground-state cooling of the membrane motion even when the bare cavity is in the unresolved-sideband regime. Our results establish Fano MIM systems as a promising platform for spectral and optomechanical engineering.
Goos-Hänchen Shift in PT\mathcal{PT}PT-Symmetric and Passive Cavity Optomechanical Systems
We theoretically investigate the control of the Goos-Hänchen shift (GHS) of a reflected weak probe field in both parity-time (PT\mathcal{PT}PT)-symmetric and conventional optomechanical systems. The proposed scheme consists of a single optomechanical platform where a passive optical cavity is coupled to an active mechanical resonator, in contrast to standard passive-passive configurations. Analysis of the eigenfrequency spectrum reveals the emergence of an exceptional point under balanced gain-loss conditions at a tunable effective optomechanical coupling strength. Using the transfer-matrix method combined with stationary-phase analysis, we examine the GHS across broken and unbroken PT\mathcal{PT}PT phases and compare it with that in the conventional system. The lateral shift exhibits strong phase dependence: it is markedly enhanced in the unbroken regime relative to both the broken phase and the passive configuration. We further show that the GHS can be actively tuned through the cavity detuning and the intracavity medium length. These results provide a controlled means for manipulating beam shifts in optomechanical systems and suggest pathways toward tunable photonic components and precision optical sensing.
We theoretically investigate a hybrid optomechanical system including two coupled optomechanical cavities in the presence of two strong pump fields and a weak probe field. The photon-hopping coupling of the cavities gives rise to two cavity supermodes whose resonant frequencies can be obtained in the probe transmission spectrum. In a strong photon-hopping coupling regime, there is a large coupling rate between the probe field and one of the two cavity supermodes that is called a bright mode. The optomechanical couplings between the bright mode and two mechanical resonators can cause double optomechanically induced transparency (OMIT), which can be employed to both separately and simultaneously store two weak probe pulses with different central frequencies. We obtain the group delay (light storage time) of the probe field in the hybrid optomechanical system. The results suggest that compared with that of a single cavity optomechanical system, the maximum value of the storage time roughly quadrupled in a particular case. The physical origin of the results is discussed. The hybrid optomechanical system opens an avenue of light storage in cavity optomechanics.
An exciting scientific goal, common to many fields of research, is the development of ever-larger physical systems operating in the quantum regime. Relevant to this dissertation is the objective of preparing and observing a mechanical object in its motional quantum ground state. In order to sense the object's zero-point motion, the probe itself must have quantum-limited sensitivity. Cavity optomechanics, the interactions between light and a mechanical object inside an optical cavity, provides an elegant means to achieve the quantum regime. In this dissertation, I provide context to the successful cavity-based optical detection of the quantum-ground-state motion of atoms-based mechanical elements; mechanical elements, consisting of the collective center-of-mass (CM) motion of ultracold atomic ensembles and prepared inside a high-finesse Fabry-P'erot cavity, were dispersively probed with an average intracavity photon number as small as 0.1. I first show that cavity optomechanics emerges from the theory of cavity quantum electrodynamics when one takes into account the CM motion of one or many atoms within the cavity, and provide a simple theoretical framework to model optomechanical interactions. I then outline details regarding the apparatus and the experimental methods employed, highlighting certain fundamental aspects of optical detection along the way. Finally, I describe background information, both theoretical and experimental, to two published results on quantum cavity optomechanics that form the backbone of this dissertation. The first publication shows the observation of zero-point collective motion of several thousand atoms and quantum-limited measurement backaction on that observed motion. The second publication demonstrates that an array of near-ground-state collective atomic oscillators can be simultaneously prepared and probed, and that the motional state of one oscillator can be selectively addressed while preserving the near-zero-point motion of neighboring oscillators.