Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Mode dynamics of Bose–Einstein condensates in a single-well potential

We investigate dynamics of Bose–Einstein condensates(BECs) in a single-well potential using the mode-coupling method. Symmetry is shown to play a key role in the coupling between modes. A proper mode-coupling theory of the dynamics of BECs in a single-well potential should include at least four modes. In this context, the ideal BEC system can be decomposed into two independent subsystems when the coupling is caused by external potential perturbation and is linear. The mode dynamics of non-ideal BECs with interaction shows rich behavior. The combination of nonlinear coupling and initial condition leads to the different regimes of mode dynamics, from regularity to non-regularity, which also indicates a change of the dependence of coupling on the symmetry of modes.

Entanglement and thermalization in the extended Bose–Hubbard model after a quantum quench: A correlation analysis

Exploring the role of entanglement in quantum nonequilibrium dynamics is important to understand the mechanism of thermalization in an isolated system. We study the relaxation dynamics in a one-dimensional extended Bose–Hubbard model after a global interaction quench by considering several observables: the local Boson numbers, the nonlocal entanglement entropy, and the momentum distribution functions. We calculate the thermalization fidelity for different quench parameters and different sizes of subsystems, and the results show that the degree of thermalization is affected by the distance from the integrable point and the size of the subsystem. We employ the Pearson coefficient as the measurement of the correlation between the entanglement entropy and thermalization fidelity, and a strong correlation is demonstrated for the quenched system.

Quantum degenerate Bose–Fermi atomic gas mixture of 23Na and 40K

We report a compact experimental setup for producing a quantum degenerate mixture of Bose23Na and Fermi40K gases. The atoms are collected in dual dark magneto–optical traps(MOT) with species timesharing loading to reduce the light-induced loss, and then further cooled using the gray molasses technique on the D2line for23Na and D1line for40K. The microwave evaporation cooling is used to cool23Na in |F = 2, mF= 2〉 in an optically plugged magnetic trap, meanwhile,40K in |F = 9/2, mF= 9/2〉 is sympathetically cooled. Then the mixture is loaded into a large volume optical dipole trap where23Na atoms are immediately transferred to |1, 1〉 for further effective cooling to avoid the strong three-body loss between23Na atoms in |2, 2〉 and40K atoms in |9/2, 9/2〉. At the end of the evaporation in optical trap, a degenerate Fermi gas of40K with 1.9 × 10^(5) atoms at T/TF= 0.5 in the |9/2, 9/2〉 hyperfine state coexists with a Bose–Einstein condensate(BEC) of23Na with 8 × 10^(4) atoms in the |1, 1〉 hyperfine state at 300 n K. We also can produce the two species mixture with the tunable population imbalance by adjusting the 23Na magneto–optical trap loading time.

Periodically modulated interaction effect on transport of Bose–Einstein condensates in lattice with local defects

We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate(BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.

Ground-state vortex structures of a rotating binary dipolar Bose–Einstein condensate confined in harmonic plus quartic potential

We consider a binary dipolar Bose–Einstein condensate confined in a rotating harmonic plus quartic potential trap.The ground-state vortex structures are numerically obtained as a function of the contact interactions and the dipole–dipole interaction in both slow and rapid rotation cases. The results show that the vortex configurations depend strongly on the strength of the contact interactions, the relative strength between dipolar and contact interactions, as well as on the orientation of the dipoles. A variety of exotic ground-state vortex structures, such as pentagonal and hexagon vortex lattice,square vortex lattice with a central vortex, annular vortex lines, and straight vortex lines, are observed by turning such controllable parameters. Our results deepen the understanding of effects of dipole–dipole interaction on the topological defects.

Current–phase relations of a ring-trapped Bose–Einstein condensate with a weak link

The current–phase relations of a ring-trapped Bose–Einstein condensate interrupted by a rotating rectangular barrier are extensively investigated with an analytical solution. A current–phase diagram, single and multi-valued relation, is presented with a rescaled barrier height and width. Our results show that the finite size makes the current–phase relation deviate a little bit from the cosine form for the soliton solution in the limit of a vanishing barrier, and the periodic boundary condition selects only the plane wave solution in the case of high barrier. The reason for multi-valued current–phase relation is given by investigating the behavior of soliton solution.

Spatiotemporal Bloch states of a spin–orbit coupled Bose–Einstein condensate in an optical lattice

We study the spatiotemporal Bloch states of a high-frequency driven two-component Bose–Einstein condensate(BEC)with spin–orbit coupling(SOC) in an optical lattice. By adopting the rotating-wave approximation(RWA) and applying an exact trial-solution to the corresponding quasistationary system, we establish a different method for tuning SOC via external field such that the existence conditions of the exact particular solutions are fitted. Several novel features related to the exact states are demonstrated; for example, SOC leads to spin–motion entanglement for the spatiotemporal Bloch states, SOC increases the population imbalance of the two-component BEC, and SOC can be applied to manipulate the stable atomic flow which is conducive to control quantum transport of the BEC for different application purposes.

Domain walls and their interactions in a two-component Bose–Einstein condensate

We investigate domain wall excitations in a two-component Bose–Einstein condensate with two-body interactions and pair-transition effects. It is shown that domain wall excitations can be described exactly by kink and anti-kink excitations in each component. The domain wall solutions are given analytically, which exist with different conditions compared with the domain wall reported before. Bubble-droplet structure can be also obtained from the fundamental domain wall, and their interactions are investigated analytically. Especially, domain wall interactions demonstrate some striking particle transition dynamics. These striking transition effects make the domain wall admit quite different collision behavior, in contrast to the collision between solitons or other nonlinear waves. The collisions between kinks induce some phase shift, which makes the domain wall change greatly. Their collisions can be elastic or inelastic with proper combination of fundamental domain walls. These characters can be used to manipulate one domain wall by interacting with other ones.

Trapped Bose–Einstein condensates with quadrupole–quadrupole interactions

We numerically investigate the ground-state properties of a trapped Bose–Einstein condensate with quadrupole–quadrupole interaction.We quantitatively characterize the deformations of the condensate induced by the quadrupolar interaction.We also map out the stability diagram of the condensates and explore the trap geometry dependence of the stability.

Propagation of dark soliton interacting with domain wall in two immiscible Bose–Einstein condensates

Reflection and transmission are two behaviors of wave propagating to an interface. The immiscible binary mixtures of Bose–Einstein condensates can form the symmetry-breaking state, in which the domain wall on the center can serve as the interface. In this study, we explore in detail the propagation of a dark soliton interacting with the domain wall in the harmonic trap. We find that the low-energy dark soliton is easy to form the transmission and the high-energy dark soliton trends to reflect from the domain wall. Both reflection and transmission of dark soliton on the domain wall induce the sound radiation. But the sound radiation in the reflection derives from the collective oscillation of condensates, and it in the transmission comes not only from the collective oscillation, but also from the condensate filling in the dark soliton.

Accelerate Bose–Einstein condensate by interaction

In recent years,accelerating waves have attracted great research interests both due to their unique properties and tempting applications.Here we investigate the effect of the inter-particle interaction on accelerating of Bose–Einstein condensate(BEC).We show that spatially homogeneous interactions will have no accelerating effect on BEC regardless of the interaction form(contact,dipole–dipole,or any others).But spatially inhomogeneous interactions may lead to an accelerating motion of the condensate.As an example,the accelerating dynamic of BEC under a spatially linear modulated contact interaction is studied in detail.It is found that such an interaction will accelerate the condensate with a time varying acceleration.Furthermore,an interaction engineering scheme to achieve constantly accelerating BEC is proposed and studied numerically.Numerical results suggest that this engineering scheme can also suppress profile changing of the condensate during its evolution,thus realize an accelerating profile-keeping matter wave packet.Our analysis also applies to optical waves with Kerr nonlinearity.

Achieving ultracold Bose–Fermi mixture of^(87)Rb and^(40)K with dual dark magnetic-optical-trap

We demonstrate that dual dark magnetic-optical-traps(MOTs)have great importance in the two-species^(87)Rb and^(40)K mixture compared with dual bright MOTs.The dark MOT has a little improvement in the trapping of single-species^(87)Rb or^(40)K gases compared with bright MOT.For the case of loading two-species^(87)Rb and^(40)K simultaneously,the improvement of^(40)K in the dual dark MOTs is mainly from the reduction of light-assisted collision losses.The dual dark MOTs employ a pair of conical lenses to produce the hollow beam for repump laser with high efficiency.The number and density of^(87)Rb and^(40)K atoms after evaporative cooling in the hybrid magnetic trap with dark MOT loading are compared with those in bright MOT.The atoms with large number and high density make it easier to realize the quantum degenerate of Bose-Fermi mixture.

Dynamics of bright soliton in a spin–orbit coupled spin-1 Bose–Einstein condensate

We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton's spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton's spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.

Anderson localization of a spin–orbit coupled Bose–Einstein condensate in disorder potential

We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation.Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase,magnetic phase and stripe phase are studied.It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate.Moreover,in both magnetic phase and stripe phase,the localization length changes non-monotonically as the fitting interval increases.In magnetic phases,the Bose–Einstein condensate will experience spin relaxation in disorder potential.

Ultradilute self-bound quantum droplets in Bose–Bose mixtures at finite temperature

We theoretically investigate the finite-temperature structure and collective excitations of a self-bound ultradilute Bose droplet in a flat space realized in a binary Bose mixture with attractive inter-species interactions on the verge of meanfield collapse. As the droplet formation relies critically on the repulsive force provided by Lee–Huang–Yang quantum fluctuations, which can be easily compensated by thermal fluctuations, we find a significant temperature effect in the density distribution and collective excitation spectrum of the Bose droplet. A finite-temperature phase diagram as a function of the number of particles is determined. We show that the critical number of particles at the droplet-to-gas transition increases dramatically with increasing temperature. Towards the bulk threshold temperature for thermally destabilizing an infinitely large droplet, we find that the excitation-forbidden, self-evaporation region in the excitation spectrum, predicted earlier by Petrov using a zero-temperature theory, shrinks and eventually disappears. All the collective excitations, including both surface modes and compressional bulk modes, become softened at the droplet-to-gas transition. The predicted temperature effects of a self-bound Bose droplet in this work could be difficult to measure experimentally due to the lack of efficient thermometry at low temperatures. However, these effects may already present in the current cold-atom experiments.

The ground states and pseudospin textures of rotating two-component Bose–Einstein condensates trapped in harmonic plus quartic potential

The ground states of two-component miscible Bose–Einstein condensates（BECs） confined in a rotating annular trap are obtained by using the Thomas–Fermi（TF） approximation method.The ground state density distribution of the condensates experiences a transition from a disc shape to an annulus shape either when the angular frequency increases and the width and the center height of the trap are fixed,or when the width and the center height of the trap increase and the angular frequency is fixed.Meantime the numerical solutions of the ground states of the trapped two-component miscible BECs with the same condition are obtained by using imaginary-time propagation method.They are in good agreement with the solutions obtained by the TF approximation method.The ground states of the trapped two-component immiscible BECs are also given by using the imaginary-time propagation method.Furthermore,by introducing a normalized complex-valued spinor,three kinds of pseudospin textures of the BECs,i.e.,giant skyrmion,coaxial double-annulus skyrmion,and coaxial three-annulus skyrmion,are found.

Generating periodic interference in Bose–Einstein condensates

The interference between two condensates with repulsive interaction is investigated numerically by solving the onedimensional time-dependent Gross–Pitaevskii equation.The periodic interference pattern forms in two condensates,which are prepared in a double-well potential consisting of two truncated harmonic wells centered at different positions.Dark solitons are observed when two condensates overlap.Due to the existence of atom–atom interactions,atoms are transferred among the ground state and the excited states,which coincides with the condensate energy change.

Spin–orbit coupled Bose–Einstein condensates with Rydberg-dressing interaction

Interaction between Rydberg atoms can be used to control the properties of interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Here we investigate the effect of the Rydberg-dressing interaction on the ground-state properties of a Bose–Einstein condensate imposed by Raman-induced spin–orbit coupling. We find that,in the case of SU（2）-invariant s-wave interactions, the gas is only in the plane-wave phase and the zero-momentum phase is absent. In particular, we also predict an unexpected magnetic stripe phase composed of two plane-wave components with unequal weight when s-wave interactions are non-symmetric, which originates from the Rydberg-dressing interaction.

Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose-Einstein condensate are investigated by using the Hartree-Fock-Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.