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arXiv:cond-mat/9712287 · Physical Review A

Thermal dephasing and the echo effect in a confined Bose-Einstein condensate

Anatoly B. Kuklov, N. Chencinski

Published Jun 1, 1998• 5 citations
arXivHTMLPDF

Abstract

Thermal fluctuations of the normal component induce dephasing---reversible damping of the low-energy collective modes of a confined Bose-Einstein condensate. The dephasing rate is calculated for the isotropic oscillator trap, where the Landau damping is expected to be suppressed. This rate is characterized by a steep temperature dependence. It is weakly amplitude dependent, and is sensitive to the total number of atoms in the trap. The value of the rate belongs to the range of the damping rates observed by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)]. We suggest that a reversible nature of the damping caused by the thermal dephasing in the isotropic trap can be tested by the echo effect. A reversible nature of the Landau damping is also discussed, and a possibility of observing the echo effect in an anisotropic trap is considered as well. The parameters of the echo for the isotropic trap are calculated in the weak echo limit. Results of the numerical simulations of the echo are also presented.

DOI
10.1103/physreva.57.4699

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Thermal fluctuations of the normal component induce dephasing---reversible damping of the low-energy collective modes of a confined Bose-Einstein condensate. The dephasing rate is calculated for the isotropic oscillator trap, where the Landau damping is expected to be suppressed. This rate is characterized by a steep temperature dependence. It is weakly amplitude dependent, and is sensitive to the total number of atoms in the trap. The value of the rate belongs to the range of the damping rates observed by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)]. We suggest that a reversible nature of the damping caused by the thermal dephasing in the isotropic trap can be tested by the echo effect. A reversible nature of the Landau damping is also discussed, and a possibility of observing the echo effect in an anisotropic trap is considered as well. The parameters of the echo for the isotropic trap are calculated in the weak echo limit. Results of the numerical simulations of the echo are also presented.
Low energy collective mode of a confined Bose-Einstein condensate should demonstrate the echo effect in the regime of Landau damping. This echo is a signature of reversible nature of Landau damping. General expression for the echo profile is derived in the limit of small amplitudes of the external pulses. Several universal features of the echo are found. The existence of echo in other cases of reversible damping -- Fano effect and Caldeira-Leggett model -- is emphasized. It is suggested to test reversible nature of the damping in the atomic traps by conducting the echo experiment.
We develop an analytical approach for calculating the Landau damping of collective modes in the Bose-Einstein condensate trapped by an anisotropic harmonic potential. Based on a variational ground-state wave function obtained by solving the time-independent Gross-Pitaevskii equation beyond Thomas-Fermi approximation, we solve the Bogoliubov--de Gennes equations describing thermal excited quasiparticles and provide divergence-free analytical solutions for the Bogoliubov amplitudes and coupling matrix elements that characterize the interaction between the collective modes and the quasiparticles. With these analytical results we evaluate the Landau damping rates of several collective modes for various anisotropic parameters of the trapping potential in terms of the formulas derived from a time-dependent mean-field theory. In addition, we discuss the dependence of the damping rates on temperature, particle number, trapping frequency, and anisotropic parameter of the system, and compare our theoretical results with experimental and numerical data reported in literature.
We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is inhomogeneous and the collective excitations are characterized by a set of discrete confined phononlike excitations. We derive a general convenient analytical description for the damping rate, which takes into account the trapping potential and the optical lattice for the Landau and Beliaev processes at any temperature TTT. At high temperature or weak spatial confinement, we show that both mechanisms display a linear dependence on TTT. In the quantum limit, we find that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of TTT. Our theoretical predictions for the damping rate under the thermal regime is in complete correspondence with the experimental values reported for the one-dimensional (1D) condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a resonant effect for the condensate lifetime. Also, we study the influence of the attractive or repulsive nonlinear terms on the decay rate of the collective excitations. A general expression for the renormalized Goldstone frequency is obtained as a function of the 1D nonlinear self-interaction parameter, laser intensity, and temperature.
This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose–Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas–Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.
We discuss some recent work on the dephasing of Bose-Einstein condensates of interacting atoms due to fluctuations in the chemical potential μ. At vanishing temperature such fluctuations are due to the uncertainty of the number of particles in the condensate caused by the depletion effect. The dephasing is in this case a non-diffusive (and in principle reversible) effect called ‘collapse’ (and ‘revival’). Above a certain cross-over temperature the dephasing proceeds mainly via a diffusive process which follows in time a short and ineffective phase collapse. The phase-diffusion constant is dominated by the temperature dependent condensate-number fluctuations caused by the scattering of low-energy excitations off the condensate. We also discuss the (in general subdominant) contribution of the occupation-number fluctuations in quasi-particle states in the thermal cloud. For simplicity we discuss here results for a box-like trapping potential.
Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles can demonstrate the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode, and N. The corresponding time values have been derived analytically under certain approximations and numerically for the parabolic atomic trap. The revival of the mode amplitude at a time of several seconds, as direct evidence of the effect, can occur if the normal component is significantly suppressed.