Collective oscillations of a quasi-one-dimensional Bose condensate under damping (original) (raw)
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Physical Review A, 2004
The collective oscillations of one-dimensional (1D) repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean-field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean-field regime we predict bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point. We confirm the analytical predictions by direct numerical simulations of the 1D Gross-Pitaevskii equation and the effective nonlinear Schrödinger equation with quintic nonlinearity and trap potential.
Physical Review A, 2011
Continuous center-of-mass position measurements performed on an interacting harmonically trapped Bose-gas are considered. Using both semi-analytical mean-field approach and completely quantum numerical technique based on positive P-representation, it is demonstrated that the atomic delocalization due to the measurement back action is smaller for a strongly interacting gas. The numerically calculated second-order correlation functions demonstrate appearance of atomic bunching as a result of the center-of-mass measurement. Though being rather small the bunching is present also for strongly interacting gas which is in contrast with the case of unperturbed gas. The performed analysis allows to speculate that for relatively strong interactions the size of atomic cloud determined with a single snapshot measurement can become smaller than the ground-state cloud size.
EQUATIONS OF COUPLED CONDENSATE AND NON-CONDENSATE DYNAMICS IN A TRAPPED BOSE GAS
We constructed equations of the condensed Bose gas dynamics at nonzero temperatures on the bases of the first principles of statistical mechanics. We derived the equation of motion for the con-densate wavefunction and the quantum kinetic equation for the distribution function of excited atoms. The obtained generalized Gross–Pitaevskii equation for a condensate includes the effect of collisions with thermal cloud atoms (non-condensate). The Boltz-mann quantum kinetic equation for a non-condensate was obtained by means of Zubarev's method of nonequilibrium statistical operator .
Statics and dynamics of quasi one-dimensional Bose–Einstein condensate in harmonic and dimple trap
Laser Physics, 2016
We investigate a quasi one-dimensional 87 Rb Bose-Einstein condensate in a harmonic trap with an additional dimple trap (dT) in the center. Within a zero-temperature Gross-Pitaevskii mean-field description we provide a one-dimensional physical intuitive model, which we solve by both a time-independent variational approach and numerical calculations. With this we obtain at first equilibrium results for the emerging condensate wave function which reveal that a dimple trap potential induces a bump or a dip in case of a red-or a blue-detuned Gaussian laser beam, respectively. Afterwards, we investigate how this dT induced bump/dip-imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the generic case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the dT induced bump in the condensate wave function remains present, whereas the dip starts decaying after a characteristic time scale which decreases with increasing blue-detuned dT depth. Secondly, once the red-or blue-detuned dT is switched off, we find that bright shock-waves or gray/dark bi-soliton trains emerge which oscillate within the harmonic confinement with a characteristic frequency.
Localized breathing oscillations of Bose-Einstein condensates in periodic traps
Physical Review A, 2002
We demonstrate the existence of localized oscillatory breathers for quasi-one-dimensional Bose-Einstein condensates confined in periodic potentials. The breathing behavior corresponds to position oscillations of individual condensates about the minima of the potential lattice. We deduce the structural stability of the localized oscillations from the construction. The stability is confirmed numerically for perturbations to the initial state of the condensate, to the potential trap, as well as for external noise. We also construct periodic and chaotic extended oscillations for the chain of condensates. All our findings are verified by direct numerical integration of the Gross-Pitaevskii equation in one dimension.
Dynamics of a Bose-Einstein condensate in optical trap
2001
The dynamics of a 2D Bose-Einstein condensate in optical trap is studied taking into consideration fluctuations of the far-off-resonance laser field intensity. The problem is described in the frame of the mean field Gross-Pitaevskii equation with randomly varying trap potential. An analytic approach based on the moments method has been employed to describe the noise induced evolution of the condensate properties. Stochastic parametric resonance in oscillations of the condensate width is proved to exist. For the condensate with negative scattering length of atoms, it is shown that the noise can delay or even arrest the collapse. Analytical predictions are confirmed by numerical simulations of the underlying PDE and ODE models.
Physical Review A, 2006
We present a theoretical treatment of the surprisingly large damping observed recently in onedimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuationdissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentallyobserved damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.
Physical Review a, 2006
We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.
Bose-Einstein condensation of atomic gases in a general harmonic oscillator
1996
We present an analysis of Bose-Einstein condensation for a system of non-interacting spin-0 particles in a harmonic oscillator confining potential trap. We discuss why a confined system of particles differs both qualitatively and quantitatively from an identical system which is not confined. One crucial difference is that a confined system is not characterized by a critical temperature in the same way as an unconfined system such as the free boson gas. We present the results of both a numerical and analytic analysis of the problem of Bose-Einstein condensation in a general anisotropic harmonic oscillator confining potential.