Quasiperiodic versus irreversible dynamics of an optically confined Bose-Einstein condensate

Abstract

We consider the evolution of a dilute Bose-Einstein condensate in an optical trap formed by a doughnut laser mode. By solving a one dimensional Gross-Pitaevskii equation and looking at the variance and the statistical entropy associated with the position of the system we can study the dynamical behavior of the system. It is shown that for small condensates nonlinear revivals of the macroscopic wave function are expected. For sufficiently large and dense condensates irreversible dynamics takes place for which revivals of regular dynamics appear as predicted in [9]. These results are confirmed by a two dimensional simulation in which the scales of energy associated with the two different directions mimic the experimental situation. 03.75.Fi, 42.50.Fx,

Optical dipole traps and atomic waveguides based on Bessel light beams

“…This density solution has a peak one-dimensional density ρ peak = 1.5(N/L z ) ∝ N 2/3 with a longitudinal length L z = 2z m . The Gross-Pitaevskii equation ( 14) has previously been investigated as a model for a onedimensional Bose-Einstein condensate in a number of situations, including the ground state [32] and dynamics [33] of cigar shaped traps [34][35][36], dark solitons [30,9,37,38], bright solitons for negative scattering lengths [29,30,39], gap solitons in optical lattices [8], atom waveguides [40][41][42], and as a model Luttinger liquid [43]. Here our goal is to highlight the utility of J 0 optical dipole traps for experimental studies of one-dimensional trapped gases.…”

Dynamics of a Bose–Einstein condensate in an anharmonic trap

“…Equation ( 13) is also valid for complex oscillation frequencies which corresponds to negative curvatures [19]. Thus, the dynamics of the condensate are completely determined by the set of ordinary differential equations ( 9), ( 12) and (13). To get the complete condensate wave function in the laboratory frame one has to insert the shifted coordinates ( 6) into (14).…”

“…Higher-order contributions to the trapping potential were either avoided or turned out to be negligible due to the large-scale magnetic field-generating elements. Anharmonic configurations were theoretically considered for a Gaussian [12] and a box-like [13] potential and were experimentally realized in the case of a magnetic mirror [14]. Current progress in generating Bose-Einstein condensates in magnetic microtraps [15,16] in which the trapping potential in general differs from the trivial parabolic shape raises the question of how the dynamics of the trapped condensate is affected by the anharmonicity of the potential.…”

“…Kagan et al [17] pointed out that the equations of motion for the internal condensate dynamics (13) can also be derived from a classical Hamiltonian. For the free motion in a trapping potential the total energy of the condensate is conserved and can be calculated for the wavefunction (15):…”