Journal of Physics B Atomic Molecular and Optical Physics

Phase effects of a two-dimensional Bose–Einstein condensate

Yan Deng, Wenhua Hai, Gengbiao Lu, Shiguang Rong

Published May 30, 2012• 3 citations

Abstract

We investigate the phase effects of a periodically driven Bose–Einstein condensate (BEC) held in a spatially two-dimensional (2D) harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross–Pitaevskii equation is found, which depicts the shock wave with chaotic or periodic amplitude and phase. The atomic densities are illustrated numerically, and the circularly symmetric distributions in the separable phase and the axially symmetric BEC clusters in the inseparable phase are shown. It is demonstrated that the periodic driving may lead to chaos for both phases, which plays a role in avoiding the escape of the solution and restraining the BEC collapse and blast. The results suggest a method for controlling the directed transports of the 2D BEC.

DOI: 10.1088/0953-4075/45/13/135301

Related papers

Chaos in a Bose—Einstein condensate

Zhixia Wang, Zhengguo Ni, Fuzhong Cong +2 more

It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose—Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross—Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases.

Chinese Physics BNov 1, 201012 citations

Chaotic shock waves of a Bose-Einstein condensate

Wenhua Hai, Qianquan Zhu, Shiguang Rong

It is demonstrated that the well-known Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate (BEC) driven by the time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases. When the periodic driving is switched off and the number of condensed atoms is conserved, we obtained the exact stationary states and nonstationary states. The former contains the stable ``nonpropagated'' shock wave, and in the latter the shock wave alternately collapses and grows for the harmonic trapping or propagates with exponentially increased shock-front speed for the antitrapping. It is revealed that the existence of chaos plays a role for suppressing the blast of matter wave. The results suggest a method for preparing the exponentially accelerated BEC shock waves or the stable stationary states.

arXiv:0806.3806Physical Review AFeb 3, 200923 citations

Regular and chaotic Bose-Einstein condensate in an accelerated Wannier-Stark lattice

Wenhua Hai, Gengbiao Lu, Honghua Zhong

We investigate a Bose-Einstein condensate (BEC) held in a quasi-one-dimensional Wannier-Stark lattice which is a combination of linear potential with an accelerating optical lattice. It is demonstrated that the system can be reduced to a periodically driven Gross-Pitaevskii one, in which we find the exact analytical solution and the regular and chaotic numerical solutions with accelerated atomic flow densities. The higher instabilities in the transport of BEC are predicted for the positive interatomic interaction. The results suggest an experimental scheme to generate and control the accelerated regular and chaotic matter waves.

arXiv:0901.3868Physical Review AMay 7, 20099 citations

Bose—Einstein condensates with tunable spin—orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics

Chen Jiao, Jun-Cheng Liang, Zi-Fa Yu +3 more

We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose—Einstein condensates (BECs) with tunable spin—orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross—Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.

Frontiers of PhysicsAug 9, 20227 citations

Superfluid dynamics of a Bose–Einstein condensate in a periodic potential

C Menotti, A Smerzi, A Trombettoni

We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in a one-dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce two different, density dependent, effective masses and group velocities. The Bogoliubov spectrum predicts the existence of sound waves, and the arising of energetic and dynamical instabilities at critical values of the BEC quasi-momentum which dramatically affect its coherence properties. We investigate the dependence of the dipole and Bloch oscillation frequencies in terms of an effective mass averaged over the density of the condensate. We illustrate our results with several animations obtained solving numerically the time-dependent Gross–Pitaevskii equation.

arXiv:cond-mat/0310780New Journal of PhysicsSep 15, 200389 citations

Shock waves in a Bose-Einstein condensate under transverse harmonic confinement

Luca Salasnich

We find exact solutions of the hydrodynamic equations of a dilute and ultracold atomic Bose-Einstein condensate confined in the cylindric radial direction by a harmonic potential and freely travelling in the longitudinal axial direction. The dynamics of these solutions, which generalize the ones obtained for a purely one-dimensional superfluid in the regime of quasi-condensation, gives rise to a shock-wave front whose period of formation is analytically estimated. We suggest that these shock waves can be experimentally produced by engineering the initial density and phase of an atomic Bose-Einstein condensate.

Apr 28, 20150 citations