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arXiv:1002.3108 · Physical Review Letters

Collective Dynamics of Bose-Einstein Condensates in Optical Cavities

Jonathan Keeling, M. J. Bhaseen, Benjamin D. Simons

Published Jul 20, 2010• 174 citations
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Abstract

Experiments on Bose-Einstein condensates in optical cavities have observed a coherent state of the matter-light system-superradiance. The nature of these experiments demands consideration of collective dynamics. Including cavity leakage and the backreaction of the cavity field on the condensate, we find a rich phase diagram including multiphase coexistence regions, and persistent optomechanical oscillations. The proximity of the phase boundaries results in a critical slowing down of the decay of many-body oscillations, which can be enhanced by large cavity loss.

DOI
10.1103/physrevlett.105.043001

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Experiments on Bose-Einstein condensates in optical cavities have observed a coherent state of the matter-light system-superradiance. The nature of these experiments demands consideration of collective dynamics. Including cavity leakage and the backreaction of the cavity field on the condensate, we find a rich phase diagram including multiphase coexistence regions, and persistent optomechanical oscillations. The proximity of the phase boundaries results in a critical slowing down of the decay of many-body oscillations, which can be enhanced by large cavity loss.
We investigate the multiple stable macroscopic quantum states of a Bose-Einstein condensate in an optomechanical cavity with pump-cavity field detuning and atom-photon interaction following the experimental realization of the quantum phase transition [Nature (London) 464, 1301 (2010)]. The spin-coherent-state variational method is useful in exploring the multistability since it has the advantage of including both normal and inverted pseudospin states. In the blue detuning regime the usual transition from normal to superradiant phases still exists, however, when the atom-field coupling increases to a certain value, called the turning point, the superradiant phase collapses due to the resonant damping of the mechanical oscillator. As a consequence, the system undergoes at this point an additional phase transition to the normal phase of the atomic population inversion state. In particular, the superradiant phase disappears completely at strong photon-phonon interaction, resulting in the direct atomic population transfer between two atomic levels. Moreover, the coupling-induced collapse and revival of the superradiant state are also found in the red detuning region.
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.
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Cavity optomechanics studies the coupling between a mechanical oscillator and the electromagnetic field in a cavity. We report on a cavity optomechanical system in which a collective density excitation of a Bose-Einstein condensate serves as the mechanical oscillator coupled to the cavity field. A few photons inside the ultrahigh-finesse cavity trigger strongly driven back-action dynamics, in quantitative agreement with a cavity optomechanical model. We approach the strong coupling regime of cavity optomechanics, where a single excitation of the mechanical oscillator substantially influences the cavity field. The results open up new directions for investigating mechanical oscillators in the quantum regime and the border between classical and quantum physics.
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 ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.