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Physical Review A

Soliton and phonon production by an oscillating obstacle in a quasi-one-dimensional trapped repulsive Bose-Einstein condensate

Abdelaziz Radouani

Published Jul 1, 2004• 38 citations
Publisher

Abstract

We use the one-dimensional (1D) Gross-Pitaevskii equation to investigate the dynamical evolution of a dilute repulsive Bose-Einstein condensate (BEC) confined in an elongated static nonharmonic trap and stirred by an oscillating Gaussian obstacle moving at uniform speed in alternate direction. Direct numerical solutions of this equation show that above a critical obstacle velocity, the motion of the obstacle creates gray solitons and phonons. At first, when the velocity of the obstacle increases, the dissipation also increases. But the dissipation reaches a maximal value and then decreases dramatically and vanishes at high obstacle velocities. Our results at low obstacle velocities are similar to those previously obtained experimentally and by simulations in the case of vortice and phonon production in 3D and 2D trapped repulsive BEC's. But at high obstacle velocities, we show that the quasi-1D trapped repulsive BEC behaves as a quasisuperfluid medium with disappearance of gray soliton and phonon excitations. This extends previous results and provides the main dependence of the phenomenon on the obstacle characteristics.

DOI
10.1103/physreva.70.013602

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We use the one-dimensional (1D) Gross-Pitaevskii equation to investigate the dynamical evolution of a dilute repulsive Bose-Einstein condensate (BEC) confined in an elongated static nonharmonic trap and stirred by an oscillating Gaussian obstacle moving at uniform speed in alternate direction. Direct numerical solutions of this equation show that above a critical obstacle velocity, the motion of the obstacle creates gray solitons and phonons. At first, when the velocity of the obstacle increases, the dissipation also increases. But the dissipation reaches a maximal value and then decreases dramatically and vanishes at high obstacle velocities. Our results at low obstacle velocities are similar to those previously obtained experimentally and by simulations in the case of vortice and phonon production in 3D and 2D trapped repulsive BEC's. But at high obstacle velocities, we show that the quasi-1D trapped repulsive BEC behaves as a quasisuperfluid medium with disappearance of gray soliton and phonon excitations. This extends previous results and provides the main dependence of the phenomenon on the obstacle characteristics.
We numerically solve the time-dependent Gross-Pitaevskii equation (GPE) that describes the evolution of an elongated dilute repulsive atomic Bose-Einstein condensate trapped in a one-dimensional (1D) nonharmonic potential. We find that the gray solitons, which are propagative solutions of the 1D GPE, traveling at an initial constant velocity, smaller than the speed of sound, oscillate through the trapped condensate, but that this oscillatory motion is accompanied by a spontaneous emission of small sound waves. By examining the gray soliton trajectory and its velocity in the trapped repulsive Bose-Einstein condensate, we show that the oscillatory motion is uniform and nondissipative except at the returning points of the gray soliton, where it exhibits a slight radiative acceleration (antidamping). Our numerical results are in good agreement with previous theoretical predictions, but show the need to take radiation emission into account.
Abstract We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose–Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to a 1D OL trap can have both repulsive and attractive contact interactions. Dark-in-bright solitons are the excited states of bright solitons. The solitons, when subjected to a small perturbation, exhibit sustained breathing oscillation. Dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi-elastic. Results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross–Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.
We consider a trapped atomic Bose-Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross-Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through an annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose an expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.
Abstract We experimentally investigate the periodic vortex shedding dynamics in a highly oblate Bose–Einstein condensate using a moving penetrable Gaussian obstacle. The shedding frequency f v is measured as a function of the obstacle velocity v and characterized by a linear relationship of f v = a(v − v c) with v c being the critical velocity. The proportionality constant a is linearly decreased with a decrease in the obstacle strength, whereas v c approaches the speed of sound. When the obstacle size increases, both a and v c are decreased. We discuss a possible association of a with the Strouhal number in the context of universal shedding dynamics of a superfluid. The critical vortex shedding is further investigated for an oscillating obstacle and found to be consistent with the measured f v. When the obstacle’s maximum velocity exceeds v c but its oscillation amplitude is not large enough to create a vortex dipole, we observe that vortices are generated in the low-density boundary region of the trapped condensate, which is attributed to the phonon emission from the oscillating obstacle.
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.
We consider, both analytically and numerically, the evolution of two-dimensional (2D) nonlinear matter-wave pulses in a Bose-Einstein condensate with a disk-shaped trap and repulsive atom-atom interactions. Due to the strong confinement in the axial direction the sound speed of the system is c=(1/21/4)c0,{c=(1/2}^{1/4}{)c}_{0},c=(1/21/4)c0​, where c0{c}_{0}c0​ is the corresponding value without the trap. From the 3D order-parameter equation of the condensate, we derive a soliton-bearing Kadomtsev-Petriashvili equation with positive dispersion. When the trapping potential is weak in two transverse directions, a low-depth plane dark soliton can propagate in the condensate with a changing profile but preserving its structure down to the boundary of the condensate. We show that high-depth plane dark solitons are unstable to long-wavelength transverse disturbances. The instability appears as a longitudinal modulation of the soliton amplitude decaying into vortices. We also show how a dark lumplike 2D nonlinear excitation can be excited in the system. Furthermore, a dark lump decaying algebraically in two spatial directions can propagate rather stable in the condensate, but disappears near the boundary of the condensate where two vortices are nucleated. The vortices move in opposite directions along the boundary and when meeting merge creating a new lump. Finally, we also provide results for head-on and oblique collisions of two lumps in the system.