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Localization of Bose-Einstein condensates in cavities induced by photon-atom interactions

Pedro dos Santos Gil

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

We consider a Bose-Einstein condensate loaded into an optical cavity subject to the combined action of an external potential and a cavity mode with mutually incommensurate periods. This configuration enables the localization of matter waves even in the absence of attractive two-body interactions. We analyze the families of the corresponding localized modes for both red- and bluedetuned atomic and cavity resonances in relatively shallow lattices. The parameter regimes supporting localization are identified. The system is found to exhibit multi-stability, previously discussed in terms of bistability, manifesting as distinct photon numbers under otherwise identical conditions. In addition, the system may display ”strict” bistability, characterized by two different atomic density distributions corresponding to the same photon number. The stability of the localized modes is examined.

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We consider a Bose-Einstein condensate loaded into an optical cavity subject to the combined action of an external potential and a cavity mode with mutually incommensurate periods. This configuration enables the localization of matter waves even in the absence of attractive two-body interactions. We analyze the families of the corresponding localized modes for both red- and bluedetuned atomic and cavity resonances in relatively shallow lattices. The parameter regimes supporting localization are identified. The system is found to exhibit multi-stability, previously discussed in terms of bistability, manifesting as distinct photon numbers under otherwise identical conditions. In addition, the system may display ”strict” bistability, characterized by two different atomic density distributions corresponding to the same photon number. The stability of the localized modes is examined.
We consider a Bose-Einstein condensate (BEC) loaded into a one-dimensional optical cavity under the combined action of an external potential and atom-cavity coupling with mutually incommensurate periods. Such configuration enables the localization of matter waves even in the absence of two-body interactions. We study families of localized modes within the mean-field approximation for red and blue detunings from atomic and cavity resonances in relatively shallow quasiperiodic lattices, beyond the validity of the tight-binding approximation. The parameter regimes supporting localization of atomic wave packets are identified. The system exhibits two types of bistability manifested as distinct photon numbers under otherwise identical conditions. One type arises from the coexistence of multiple families of localized modes, typical of conservative nonlinear systems, while the other stems from the multivalued dependence of the families on system parameters, characteristic of systems exhibiting hysteresis. BEC in a cavity may also display pseudodegeneracy, understood as the existence of two distinct atomic-density distributions corresponding to the same atomic and photon numbers (although different chemical potentials). The stability of the localized modes is analyzed. It is shown that, owing to the strong impact of long-range interactions on stability, a two-localized-mode configuration can operate as an logic gate.
We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.
We study an ultracold atom-cavity coupling system, which had been implemented in an experiment to display weak light nonlinearity [S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, Phys. Rev. Lett. 99, 213601 (2007)]. The model is described by a noninteracting Bose-Einstein condensate contained in a Fabry-P\'erot optical resonator, in which two incommensurate standing-wave modes are excited and thus form a quasiperiodic optical lattice potential for the atoms. Special emphasis is paid to the variation of the atomic wave function induced by the cavity light field. We show that bistability between the atomic localized and extended states can be generated under appropriate conditions.
A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.
We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as trivial and vortex-like bound states of 2D gap solitons. To highlight similarities between the behavior of coherent light and matter waves in periodic potentials, we draw useful parallels with the physics of coherent light waves in nonlinear photonic crystals and optically-induced photonic lattices.
We consider a two-component Bose–Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser also excites the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity–condensate system is developed under the discrete mode approximation (DMA), while matter–field coupling has been considered beyond the rotating wave approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter–field coupling strength.