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Communications in Theoretical Physics

Optomechanical Dark State in a Dual-Species Bose—Einstein Condensate

Hui Jing, D. S. Goldbaum

Published Oct 1, 2012• 2 citations
Publisher

Abstract

We study cavity optomechanics of ultracold dual-species atomic mixtures with nonlinear collisions. Interspecies interactions provide a direct parametric coupling of fictitious mechanical elements which, through interfering with the intracavity optical field, leads to a switchable optically-dark state for either species. This demonstrates a matter-wave analog of recently observed mechanical wave mixing and quantum motional-state swapping, with applications in the construction of integrated phononic devices, and the cavity-enhanced detection of quantum degenerate atomic mixtures.

DOI
10.1088/0253-6102/58/4/18

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quant-pharXiv:2610.20040•Oct 15, 2026
We study cavity optomechanics of ultracold dual-species atomic mixtures with nonlinear collisions. Interspecies interactions provide a direct parametric coupling of fictitious mechanical elements which, through interfering with the intracavity optical field, leads to a switchable optically-dark state for either species. This demonstrates a matter-wave analog of recently observed mechanical wave mixing and quantum motional-state swapping, with applications in the construction of integrated phononic devices, and the cavity-enhanced detection of quantum degenerate atomic mixtures.
We theoretically investigate a second-order optomechanically induced transparency process of a cigar-shaped dual-species Bose–Einstein condensate with nonlinear collisions trapped inside an optomechanical cavity. We find that atomic collisions provide linear couplings, which facilitate the mechanical mixing of the dual-species Bose–Einstein condensate. We derive analytical expressions of the output transmission intensity of the probe field and the dimensionless amplitude of the second-order sideband. The numerical results show that the transmission intensity and the dimensionless amplitude of the second-order sideband can be controlled by the control field intensities, the effective detuning, and the effective coupling strength of the Bogoliubov mode of the dual-species Bose–Einstein condensate and optical mode. Furthermore, the interspecies and intraspecies interactions are also used to control the transmission intensity and the dimensionless amplitude of the second-order sideband.
Abstract We theoretically study photothermally and optomechanically induced transparency in a hybrid system of two coupled Fabry-Peŕot cavities. The left cavity hosts a dual-species Bose-Einstein condensate driven by pump and probe fields, while the right cavity couples to a mechanical resonator via photothermal effects. By tuning intercavity, optomechanical, and condensate-cavity couplings, both single and multiple transparency windows emerge. Interspecies and intraspecies interactions, along with effective coupling parameters, govern the transparency conditions, while the photothermal coefficient shapes the profiles. Absorption and dispersion spectra reveal that strong coupling enhances slow-light effects and group delay. These findings provide insights into tunable light-matter interactions for optical communication and photonic applications.
This dissertation contains a study of ultracold atoms in optical cavities. We particularly focus on two aspects of the coupled atom-cavity systems. In the first aspect, we implement the quantum nature of the light field to probe the quantum state of the atoms. This is interesting due to the nondestructive nature of the characterization of many-body atomic states. In the second aspect we study the cavity optomechanics that investigates the coupling of mechanical and optical degrees of freedom via radiation pressure. The optomechanical cavity provides an interesting nonlinear system to study the coupling between atoms and the intracavity field.In the context of cavity quantum electrodynamics we study the reflection of two counter-propagating modes of the light field in a high-Q ring cavity by ultracold atoms either in the Mott insulator state or in the superfluid state of an optical lattice. We find that the dynamics of the reflected light strongly depends on both the lattice spacing and the state of the matter-wave field. By using the Monte Carlo wave-function method to account for the cavity damping we also determine the two-time correlation function and the time-dependent physical spectrum of theretroreflected field. We find that the light field and the atoms become entangled if the latter are in a superfluid state. We also analyze quantitatively the entanglement between the atoms and the light.In cavity optomechanics the mechanical effect can either comes from a vibrating macroscopic oscillator or a collective density excitation of a Bose-Einstein condensate. First we use a Fabry-Perot-type cavity to study the opto-mechanically-induced bistable quantum phase transitions between superfluid and a Mott insulator states of an ultracold bosonic gases trapped inside the cavity. Secondly, we study the symmetricand antisymmetric collective density side modes of the BEC which results from the optomechanical effects of the light fields in a ring cavity.
We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed.
Cavity optomechanics represents a frontier research direction in quantum science and technology, centered on the control and exploration of interactions between electromagnetic fields and mechanical motion. Rooted in quantum mechanics, this field realizes efficient coupling and precise manipulation of optical fields and mechanical vibrations through the structural design and precise regulation of optical microcavities and mechanical oscillators, thereby revealing and harnessing novel quantum phenomena. In recent years, cavity optomechanics has evolved into an interdisciplinary frontier integrating quantum optics, condensed matter physics, and quantum precision measurement, exhibiting profound application in both fundamental physics research and quantum information science. With advancements in technologies such as nanomanufacturing and laser cooling, optomechanical interactions have been successfully demonstrated in various experimental systems. Among these platforms, cavity cold-atom systems stand out as one of the ideal platforms for implementing quantum optomechanics. Featuring exceptional environmental isolation, long quantum coherence times, and strong light-matter interaction, these systems provide a crucial testbed for exploring strong and even ultrastrong optomechanical coupling effects as well as rich nonlinear quantum phenomena. This paper reviews the recent progress in optomechanical control and manipulation based on cavity cold-atom systems. We first outline the fundamental principles of standard cavity optomechanical systems. Then, we describe the experimental realization of linear and nonlinear optomechanical couplings in cold-atom systems. After that, we focus on the representative applications of this platform in high-precision quantum sensing, quantum memory, and the preparation of macroscopic nonclassical states. Finally, we give an outlook and challenges in this field.