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arXiv:cond-mat/0011341 · Physical Review A

Cavity-assisted quasiparticle damping in a Bose-Einstein condensate

S. A. Gardiner, Klaus M. Gheri, P. Zoller

Published Apr 19, 2001• 15 citations
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Abstract

We consider an atomic Bose-Einstein condensate held within an optical cavity and interacting with laser fields. We show how the interaction of the cavity mode with the condensate can cause energy due to excitations to be coupled to a lossy cavity mode, which then decays, thus damping the condensate. We show how to choose parameters for damping specific excitations, and how to target a range of different excitations to potentially produce extremely cold condensates.

DOI
10.1103/physreva.63.051603

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We consider an atomic Bose-Einstein condensate held within an optical cavity and interacting with laser fields. We show how the interaction of the cavity mode with the condensate can cause energy due to excitations to be coupled to a lossy cavity mode, which then decays, thus damping the condensate. We show how to choose parameters for damping specific excitations, and how to target a range of different excitations to potentially produce extremely cold condensates.
We study the zero-temperature dynamics of Bose-Einstein condensates in driven high-quality optical cavities in the limit of large atom-field detuning in a one-dimensional model. We calculate the stationary ground state and the spectrum of coupled atom and field mode excitations for standing-wave cavities as well as for traveling-wave cavities. Finite cavity response times lead to damping or controlled amplification of these excitations. Analytic solutions in the Lamb-Dicke expansion are in good agreement with numerical results for the full problem and show that oscillation frequencies and the corresponding damping rates are qualitatively different for the two cases.
We measure the damping of excitations in cigar-shaped Bose-Einstein condensates of atomic vapor. By using postselection, excitation line shapes of the total population are compared with those of the undamped excitations. We find that the damping depends on the initial excitation energy of the decaying quasiparticle, as well as on the excitation momentum. We model the condensate as an infinite cylinder and calculate the damping rates of the different radial modes. The derived damping rates are in good agreement with the experimentally measured ones. The damping rates strongly depend on the destructive interference between pathways for damping, due to the quantum many-body nature of both excitation and the vacuum modes.
We present a general theory for calculating the damping rate of elementary density-wave excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. Thereby we give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density-wave mode, predicted recently by K\'onya et al. [Phys. Rev. A 89, 051601(R) (2014)]. The given density-wave mode constitutes the polaritonlike soft mode of the self-organization phase transition. The resonant enhancement takes place, in both the normal and the ordered phases, outside the critical region. We show that the large damping rate is accompanied by a significant frequency shift of this polariton mode. Going beyond the Born-Markov approximation and determining the poles of the retarded Green's function of the polariton, we reveal a strong coupling between the polariton and a collective mode in the phonon bath formed by the other density-wave modes.
In this thesis a number of aspects on possible manipulation of Bose-Einstein condensate in trapped atomic gases is investigated. First, a model for atom optical experiments involving Bose condensates is proposed and numerical simulations are presented to illustrate its characteristics. We demonstrate ways of focusing and splitting the condensate by modifying experimentally adjustable parameters. We show that there are at least two ways of implementing atom optical elements: one may modulate the interatomic scattering length in space, or alternatively, use a sinusoidal, externally applied potential. The temporal evolution of quasiparticle excitations is studied via the Gross-Pitaevskii Equation. Nonlinear mode mixing of quasiparticles is introduced, and is observed using a quasiparticle projection method. This is used as a basis of time-dependent finite temperature simulations, which we argue to be valid under regimes of high occupation number. An illustration via a closely related evaporative cooling simulation is provided. A phenomenological damping formalism for superfluidity near the λ point is adopted to describe the damping of excitations in a Bose-Einstein condensate. An estimate for the damping parameter is found. The damping formalism as a numerical tool to calculate the ground eigenstate of the condensate is explored. A novel, experimentally realisable interferometry for Bose-Einstein condensates using near-field diffraction is proposed. The scheme is based on the phenomenon of intermode traces or quantum carpets; we demonstrate the structured spatio-temporal pattern for the dilute, atomic Bose-Einstein condensate. The pattern is found to change with temperature, which allows us to perform interferometric temperature measurements. Finally, an output coupler for Bose-Einstein Condensates based on stimulated Raman transition is investigated. The spectrum and coherence are calculated for an atomic beam slowly coupled out of a trap containing a partially condensed Bose gas at finite temperatures. A number conserving Hartree-Fock-Bogliubov formalism has been used to incorporate finite temperature effects. Various different processes are found to become dominant for a suitable choice of the coupling parameters.
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.