Bose-Einstein Condensation in Linear Sigma Model at Hartree Approximation

The BEG of charged pions is investigated in the framework of O（4） linear sigma model. By using Cornwall- Jackiw-Tomboufis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite isospin density. The critical temperature and phase diagram of BEG are discussed in the non-chiral limit at Hartree approximation.

Bose-Einstein condensation on an atom chip

This paper reports an experiment of creating Bose-Einstein condensate （BEC） on an atom chip. The chip-based Z-wire current with a homogeneous bias magnetic field creates a tight magnetic trap, which allows for a fast production of BEC. After a 4.17-s forced radio frequency evaporative cooling, a condensate with about 3000 atoms appears. The transition temperature is about 300 nK. This compact system is quite robust, allowing for versatile extensions and further studying of BEC.

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.

Pulse loading ^(87)Rb Bose-Einstein condensation in optical lattice:the Kapitza-Dirac scattering and temporal matter-wave-dispersion Talbot effect

We study ^（87）Rb Bose-Einstein condensation（BEC） loading into the pulse of the one-dimensional（1D） optical lattice experimentally.The lattice is turned on abruptly,held constant for a variable time,and then turned off abruptly.The measurement of the depth of the optical lattice is obtained by Kapitza-Dirac scattering.The temporal matter-wave-dispersion Talbot effect with ^（87）Rb BEC is observed by applying a pair of pulsed standing waves（as pulsed phase gratings） with the separation of a variable delay.

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.

Probability of Obtaining the Planck Constant, in a Universe Modeled as a Giant Black Hole by Bose Einstein Condensates of Gravitons Using Hawking Argument and Scaling

We use the methodology of A. D. Linde to model the probability of obtaining a cosmological constant which is in turn affected by scaling arguments for a Bose Einstein gravitational condensate as given by Chavanis, in 2015. The net result, is that the scaling argument so provided allows for a gravitational constant commensurate with the size of the Universe, using arguments which appear to be simple but which give, if one has the conditions for modeling the Universe as a “black hole” virtually 100 % chance for the cosmological constant arising.

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.

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.

Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates

We present several families of exact solutions to a system of coupled nonlinear Schrodinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.

Quench Dynamics of Bose–Einstein Condensates in Boxlike Traps

By quenching the interatomic interactions, we investigate the nonequilibrium dynamics of two-dimensional Bose–Einstein condensates in boxlike traps with power-law potential boundaries. We show that ring dark solitons can be excited during the quench dynamics for both concave and convex potentials. The quench's modulation strength and the steepness of the boundary are two major factors influencing the system's evolution. In terms of the number of ring dark solitons excited in the condensate, five dynamic regimes have been identified. The condensate undergoes damped radius oscillation in the absence of ring dark soliton excitations. When it comes to the appearance of ring dark solitons, their decay produces interesting structures. The excitation patterns for the concave potential show a nested structure of vortex-antivortex pairs. The dynamic excitation patterns for the convex potential, on the other hand, show richer structures with multiple transport behaviors.

Effects of Spatial Noncommutativity on Energy Spectrum of a Trapped Bose-Einstein Condensate

In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose- Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutatlvity on energy spectrum of the condensate, it indicates that the ground-state energy incorporating the spatial noncommutativity is reduced to a lower level, which depends upon the noncommutativity parameter 8. The gap between the noncommutative space and commutative one for the ground-state level of the condensate should be a signal of spatial noncommutativity.

Interactions between bright solitons in different species of Bose-Einstein condensates

The dynamics of a bright bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied. The interaction between bright solitons in different species with small separation is derived. Unlike the interaction between solitons of the same species, it is independent of the phase difference between solitons. It may be of attraction or repulsion. In the former case, each soliton will oscillate about and pass through each other around the mass-center of the system, which will also oscillate harmonically due to the harmonic trapping potential.

Quantum Tunneling of a Dipolar Bose-Einstein Condensate in Optical Lattice

We study quantum tunneling of a dipolar Bose-Einstein condensate in optical lattice when the spin system initially is prepared in a squeezed coherent state. It is found that there exists quantum tunneling between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, quantum tunneling disappears between lattices l and l ＋ 1, and that l and l - 1. Correspondingly, the magnetic soliton appears.

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.

Localized Asymmetric Atomic Matter Waves in Two-Component Bose-Einstein Condensates Coupled with Two-Photon Microwave Field

We investigate localized atomic matter waves in the two-photon microwave field. Interestingly, the oscillations two-component Bose-Einstein condensates coupled by of localized atomic matter waves will gradually decay and finally become non-oscillating behavior even if existing coupling field. In particular, atom numbers occupied in two different hyperfine spin states will appear asymmetric occupations after some time evolution.

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates. It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions. It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.

Nonlinear Waves in a Cigar-Shaped Bose-Einstein Condensate with Dissipation

We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensatewith dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of ~/ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.

Effect of a localized impurity on soliton dynamics in the Bose-Einstein condensates

By using a multiple-scale method, we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates. It is shown that a dark soliton can be transmitted through a repulsive （or attractive） impurity, while at the position of the localized impurity the soliton can be quasitrapped by the impurity. Additionally, we find that the strength of the localized impurity has an important effect on the dark soliton dynamics. With increasing strength of the localized impurity, the amplitude of the dark soliton becomes bigger, while its width is narrower, and the soliton propagates slower.

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.

Tunneling of Bose-Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

The tunneling effect of Bose-Einstein condensate （BEC） in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.