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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Chaotic dynamics of Bose-Einstein condensates in optical cavities

M. Diver, Gordon R. M. Robb, Gian‐Luca Oppo

Published May 1, 2013• 0 citations
Publisher

Abstract

Summary form only given. We perform a theoretical and numerical analysis of a system comprising a Bose-Einstein condensate (BEC) interacting with a laser beam in an optical cavity. Recent studies have modelled this system with two motional modes coupled with a light mode and have shown nonlinear behaviour, e.g. bistability [1,2]. Our approach tackles the full Gross-Pitaevskii equation coupled to the cavity field as well as expansions in a number of motional modes.We consider a fixed value of the cavity-pump detuning and increase the pump intensity to cross the region of bistability (see Fig. 1 left panel). The system then displays a variety of behaviours, including regular oscillations, chaotic dynamics, and quasi-periodic behaviour, as displayed in the right panel of Fig. 1. In Fig. 1 we have used a coupled-equation system comprising the Schrödinger wave equation and a cavity-field evolution [3], where we have adiabatically eliminated the latter leading to a conservative dynamics. The chaotic dynamics here is not induced by the detector noise and is an intrinsic property of the light-BEC interaction.Our second model considers a multiple-modes expansion. By using just three modes, the chaotic dynamics observed in the full simulation is recovered. The bifurcation structure, typical of conservative dynamics in the vicinity of a separatrix, is identified through the use of projections and power spectra. Our results suggest that chaotic oscillations in this system are deterministic in nature and arise purely from nonlinear effects. In more general terms, the model is a novel example of quantum matter exhibiting chaotic behaviour and invites further research.

DOI
10.1109/cleoe-iqec.2013.6801743

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Summary form only given. We perform a theoretical and numerical analysis of a system comprising a Bose-Einstein condensate (BEC) interacting with a laser beam in an optical cavity. Recent studies have modelled this system with two motional modes coupled with a light mode and have shown nonlinear behaviour, e.g. bistability [1,2]. Our approach tackles the full Gross-Pitaevskii equation coupled to the cavity field as well as expansions in a number of motional modes.We consider a fixed value of the cavity-pump detuning and increase the pump intensity to cross the region of bistability (see Fig. 1 left panel). The system then displays a variety of behaviours, including regular oscillations, chaotic dynamics, and quasi-periodic behaviour, as displayed in the right panel of Fig. 1. In Fig. 1 we have used a coupled-equation system comprising the Schrödinger wave equation and a cavity-field evolution [3], where we have adiabatically eliminated the latter leading to a conservative dynamics. The chaotic dynamics here is not induced by the detector noise and is an intrinsic property of the light-BEC interaction.Our second model considers a multiple-modes expansion. By using just three modes, the chaotic dynamics observed in the full simulation is recovered. The bifurcation structure, typical of conservative dynamics in the vicinity of a separatrix, is identified through the use of projections and power spectra. Our results suggest that chaotic oscillations in this system are deterministic in nature and arise purely from nonlinear effects. In more general terms, the model is a novel example of quantum matter exhibiting chaotic behaviour and invites further research.
We present a theoretical analysis of a Bose-Einstein condensate (BEC) enclosed in an optical cavity driven by an external laser beam. In the limit where the cavity-field dynamics is adiabatically eliminated, the interaction between the condensate and the cavity displays a range of nonlinear dynamical behaviors such as multistability, quasiperiodicity, and conservative chaotic oscillations. We show that chaotic oscillations are ubiquitous when repulsive atom-atom interactions are included in the model. Despite the complexity of the full coupled BEC-cavity system, the essential features of its nonlinear and chaotic behavior are low-dimensional and are well described by considering the evolution of only a few motional states of the BEC.
We present a theoretical analysis of a Bose-Einstein condensate (BEC) enclosed in an optical cavity driven by a modulated external laser beam where the cavity field variable is adiabatically eliminated. The modulation of the amplitude of the pump laser induces nonlinear resonances and the widespread presence of chaotic oscillations even when repulsive atom-atom interactions are negligible. Close to resonance, varying the modulation amplitude by just a few percent causes abrupt and erratic changes to the output laser intensity with peak power increasing by almost an order of magnitude. We also use a simplified model of the BEC-cavity system that considers only a small number of spatial modes of the BEC to show that, despite the disruptive presence of a modulation in the pump beam, the system can still be considered to be low-dimensional.
We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.
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.
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.