Disk-shaped Bose-Einstein Condensates Research Articles

True Mechanism of Spontaneous Order from Turbulence in Two-Dimensional Superfluid Manifolds.

In a 2D turbulent fluid containing pointlike vortices, Lars Onsager predicted that adding energy to the fluid can lead to the formation of persistent clusters of like-signed vortices, i.e., Onsager vortex (OV) clusters. In the evolution of 2D superfluid turbulence in a uniform disk-shaped Bose-Einstein condensate (BEC), it was discovered that a pair of OV clusters with opposite signs can form without any energy input. This striking spontaneous order was explained as being due to a vortex evaporative-heating mechanism, i.e., annihilations of vortex-antivortex pairs which remove the lowest-energy vortices and thereby boost the mean energy per vortex. However, in our search for exotic OV states in a boundaryless 2D spherical BEC, we found that OV clusters never form despite the annihilations of vortex pairs. Our analysis reveals that contrary to the general belief, vortex-pair annihilation emits intense sound waves, which damp the motion of all vortices and hence suppress the formation of OV clusters. We also present unequivocal evidence showing that the true mechanism underlying the observed spontaneous OV state is the vortices exiting the BEC boundaries. Uncovering this mechanism paves the way for a comprehensive understanding of emergent vortex orders in 2D manifolds of superfluids driven far from equilibrium.

Influence of a dark soliton on the reflection of a Bose–Einstein condensate by a square barrier

We study the quantum reflection of a two-dimensional disk-shaped Bose–Einstein condensate with dark soliton excitation by a square potential barrier. For the given geometry, the dark soliton initially located at the centre of the condensate cloud survives long enough to investigate the reflection process. We show the time evolution of the reflection probability with respect to various widths of the barrier. The asymptotic value of the reflection probability is decreased by the existence of a dark soliton, and is highly sensitive to the initial orientation of the dark soliton, which also affects the excitation properties during the process of condensate and barrier interaction.

Spontaneous symmetry breaking in linearly coupled disk-shaped Bose-Einstein condensates

We study effects of tunnel coupling on a pair of parallel disc-shaped Bose–Einstein condensates with the self-attractive intrinsic nonlinearity. Each condensate is trapped in a combination of in-plane and transverse harmonic-oscillator potentials. It is shown that, depending on the self-interaction strength and tunnelling coupling, the ground state of the system exhibits a phase transition which links three configurations: a symmetric one with equal numbers of atoms in the coupled condensates, an asymmetric configuration with a population imbalance (a manifestation of the macroscopic quantum self-trapping), and the collapsing state. A modification of the phase diagram of the system in the presence of vortices in the disc-shaped condensates is reported too. The study of dynamics around the stationary configurations reveals properties which strongly depend on the symmetry of the configuration.

Bose-Einstein condensation in dark power-law laser traps

We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order $\ensuremath{\ell}$ allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a ``finger'' or of a ``hockey puck'' in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.

Two-Dimensional Soliton Interaction for Multi-component Bose–Einstein Condensates

For two-component disk-shaped Bose–Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev–Petviashvili-I equation at the lowest order from the original coupled Gross–Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev–Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.

Disk-shaped Bose–Einstein condensates in the presence of an harmonic trap and an optical lattice

We study the existence and stability of solutions of the two-dimensional nonlinear Schrodinger equation in the combined presence of a parabolic and a periodic potential. The motivating physical example consists of Bose-Einstein condensates confined in an harmonic (e.g., magnetic) trap and an optical lattice. By connecting the nonlinear problem with the underlying linear spectrum, we examine the bifurcation of nonlinear modes out of the linear ones for both focusing and defocusing nonlinearities. In particular, we find real-valued solutions (such as multipoles) and complex-valued ones (such as vortices). A primary motivation of the present work is to develop "rules of thumb" about what waveforms to expect emerging in the nonlinear problem and about the stability of those modes. As a case example of the latter, we find that among the real-valued solutions, the one with larger norm for a fixed value of the chemical potential is expected to be unstable.

Interactions between two solitons with an arbitrary collision direction in two-dimensional Bose-Einstein condensates

Interactions between two solitary waves with an arbitrary collision direction in disk-shaped Bose-Einstein condensates are investigated by using the modified Poincare-Lighthill-Kuo (PLK) perturbation technique. The results show that the two-dimensional system have a solution of two dark solitons with small-amplitude, but finite amplitude which propagating in two different directions. This solution can be described by two Boussinesq-Korteweg-de Vries (B-KdV) equations in the respective reference frames. The solitary wave solutions and their analytical phase shifts are obtained. Moreover, the solution and its stability are discussed by numerical simulation. Particularly, it is found that the phase shifts strongly depend on the angle between two propagation directions of two solitons, which is quite different from that in one-dimensional system.

Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates

By applying the standard adiabatic approximation and using the accurate analytical expression for the corresponding local chemical potential obtained in our previous work [Phys. Rev. A 75, 063610 (2007)] we derive an effective 1D equation that governs the axial dynamics of mean-field cigar-shaped condensates with repulsive interatomic interactions, accounting accurately for the contribution from the transverse degrees of freedom. This equation, which is more simple than previous proposals, is also more accurate. Moreover, it allows treating condensates containing an axisymmetric vortex with no additional cost. Our effective equation also has the correct limit in both the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to derive fully analytical expressions for ground-state properties such as the chemical potential, axial length, axial density profile, and local sound velocity. These analytical expressions remain valid and accurate in between the above two extreme regimes. Following the same procedure we also derive an effective 2D equation that governs the transverse dynamics of mean-field disk-shaped condensates. This equation, which also has the correct limit in both the quasi-2D and the Thomas-Fermi regime, is again more simple and accurate than previous proposals. We have checked the validity of our equations by numerically solving the full 3D Gross-Pitaevskii equation.

Topological Dragging of Solitons

We put forward properties of solitons supported by optical lattices featuring topological dislocations and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.

Davey-Stewartson description of two-dimensional nonlinear excitations in Bose-Einstein condensates

We study nonlinear modulation of collective excitations in disk-shaped Bose-Einstein condensates with a repulsive interatomic interaction. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and a long-wavelength mean field, generated by the self-interaction of the wave packet, are governed by Davey-Stewartson (DS) equations. Consequently, two-dimensional soliton (dromion) solutions can develop and propagate. We further derive a set of DS equations with variable coefficients for the situation where a slowly varying trapping potential in transverse directions has been taken into consideration. Finally, the dromion solutions and their stability are investigated by numerical simulations.

THREE-WAVE SOLITON EXCITATIONS IN A DISK-SHAPED BOSE–EINSTEIN CONDENSATE

A three-wave resonant interaction of collective modes and related soliton excitations in a disk-shaped Bose–Einstein condensate are investigated. The phase-matching conditions for the resonant interaction are satisfied by suitably choosing the wavevectors and the frequencies of the collective modes. A set of nonlinearly coupled envelope equations describing the spatio-temporal evolution of the three-wave resonant interaction are derived by using a method of multiple-scales, and some explicit (2+1)-dimensional three-wave soliton solutions are also presented and discussed.

Three-Wave Resonant Interaction of Bogoliubov Excitations in a Bose–Einstein Condensate with Diffraction**The project supported by National Natural Science Foundation of China under Grant No. 10274021

We investigate the three-wave resonant interaction (TWRI) of Bogoliubov excitations in a disk-shaped Bose–Einstein condensate with the diffraction of the excitations taken into account. We show that the phase-matching condition for the TWRI can be satisfied by a suitable selection of the wavevectors and the frequencies of the three exciting modes involved in the TWRI. Using a method of multiple-scales we derive a set of nonlinearly coupled envelope equations describing the TWRI process and give some explicit solitary-wave solutions.

Dimensional reduction in Bose-Einstein-condensed alkali-metal vapors

We investigate the effects of dimensional reduction in atomic Bose-Einstein condensates (BECs) induced by a strong harmonic confinement in the cylindric radial direction or in the cylindric axial direction. The former case corresponds to a transition from three dimensions (3D) to 1D in cigar-shaped BECs, while the latter case corresponds to a transition from 3D to 2D in disk-shaped BECs. We analyze the first sound velocity in axially homogeneous cigar-shaped BECs and in radially homogeneous disk-shaped BECs. We consider also the dimensional reduction in a BEC confined by a harmonic potential both in the radial direction and in the axial direction. By using a variational approach, we calculate monopole and quadrupole collective oscillations of the BEC. We find that the frequencies of these collective oscillations are related to the dimensionality and to the repulsive or attractive interatomic interaction.