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.     

Dynamic Structure Factor of an Optically Trapped Dipolar Bose–Einstein Condensate

Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.     

具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化

运用变分法研究了具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化特性,分析了调谐囚禁电势对暗孤子运动的影响.结果表明,囚禁在调谐势阱中的暗孤子将振动,势阱强度和三体作用的符号影响了暗孤子的演化,并改变了BEC系统的振动特性.     

Optomechanical Dark State in a Dual-Species Bose-Einstein Condensate

We study cavity optomechanics of ultracold dual-species atomic mixtures with nonlinear collisions.Interspecies interactions provide a direct parametric coupling of fictitious mechanical elements which,through interfering with the intracavity optical field,leads to a switchable optically-dark state for either species.This demonstrates a matter-wave analog of recently observed mechanical wave mixing and quantum motional-state swapping,with applications in the construction of integrated phononic devices,and the cavity-enhanced detection of quantum degenerate atomic mixtures.     

Exact Nonstationary Solutions of a Two-Component Bose-Einstein Condensate

We investigate the exact nonstationary solutions of a two-component Bose Einstein condensate which compose of two species having different atomic masses. We also consider the interesting behavior of the atomic velocity and the flow density. It is shown that the motion of the two components can be controlled by the experimental parameters.     

Geometric Phase and Bose-Einstein Condensate

We show that a geometric phase may appear in the Bose-Einstein condensate (BEC) in which an adiabatic procedure happens, then a perturbation expression of geometric phase is obtained for the case of time-averaged orbiting potential trap. The phase caused by the adiabatic bias magnetic field in one BEC may interfere with another, which is similar to the phase interference of Aharonov-Susskind effect, and can be observed by experiments.     

Dark Matter as a Cosmic Bose-Einstein Condensate and Possible Superfluid

Dark matter arising from spontaneous symmetry breaking of a neutral scalar field coupled to gravity comprises ultra low mass bosons with a Bose-Einstein condensation temperature far above the present background temperature. Assuming galactic halos to consist of a Bose-Einstein condensate of astronomical extent, we calculate the condensate coherence length, transition temperatures, mass distribution, and orbital velocity curves, and deduce the particle mass and number density from the observed rotation curves for the Andromeda and Triangulum galaxies. We also consider the possibility of superfluid behaviour in the halos of rotating galaxies, and estimate the critical angular frequency and line density for formation of quantised vortices.     

Electromagnetically Induced Transparency in an Atom-Molecule Bose-Einstein Condensate

We propose a new measurement scheme for the atom-molecule dark state by using electromagnetically induced transparency (EIT) technique. Based on a density-matrix formalism, we calculate the absorption coefficient numerically. The appearance of the EIT dip in the spectra profile gives clear evidence for the creation of the dark state in the atom-molecule Bose-Einstein condensate.     

Solitary Vortex Evolution in Two-Dimensional Harmonically Trapped Bose-Einstein Condensates

We investigate solitary vortex evolution in two-dimensional Bose-Einstein condensates based on the Gross-Pitaevskii equation model. Through the variational method, together with the novel Gaussian ansatz incorporating asymmetric perturbation effects, we arrive at the analytical solitary vortex solution with two typical forms:a symmetric quasi-stable solution under certain parametric settings and a diverging propagation case arising from an initial asymmetric perturbation. The derived pictorial evolutionary patterns of the solitary vortices are compared with those from a pure numerical analysis, and by identifying the key qualitative features, we show the applicability of the theoretical treatment presented here.     

Quantum Dynamics of a Raman Atom Laser by Using a Feshbach-Resonance-Tuned Atomic Bose-Einstein Condensate

We study a Raman atom laser output coupler by considering a Feshbach-resonance-tuned atomic Bose-Einstein condensate which is often viewed as a dilute system since the collisions can be tuned. However, the dimer formation can be triggered by using a Feshbach technique in a magnetic trap. We examine the quantum dynamics and statistics of this system analytically, including the quadrature-squeezed effects and the mutual coherence of the output atoms and the formed dimers.     

Landau Damping of Collective Mode in a Quasi-One-Dimensional Repulsive Bose-Einstein Condensate

We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.     

Bose-Einstein Condensate in a Linear Trap with a Dimple Potential

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.     

Output Rate of Atomic Four-Wave Mixing in Two-Component Bose-Einstein Condensate

In this letter, following the proposal of Heurich, et al. [Phys. Rev. A63 (2001) 033605], we analyze and discuss output rate of atomic four-wave mixing in the two-component Bose-Einstein condensate under the condition of the steady state. The results show that the magnitude of the signal beam increases with the increase of the intensity of the probe beam, up to a saturated value, then it decreases as the probe beam increases. The influence of the interaction range on the signal beam is also predicted. In particular, it is worth while pointing out that in contrast to the previoussolutions, our obtained analytical solutions are of very simple and explicit forms, which open the door for further investigating the related physical mechanisms.     

Vortices in a Rotating Spin-Orbit-Coupled Bose-Einstein Condensate under Extreme Elongation in a Harmonic Plus Quartic Trap

We consider the ground-state properties of a rotating spin-orbit-coupled Bose-Einstein condensate under extreme elongation in a harmonic plus quartic potential. The effects of spin-orbit coupling and rotation on the ground-state vortex structures are investigated. In the absence of spin-orbit coupling, new nucleated vortices gradually form vortex lines and annular vortex structures with the increase of the rotation frequency. In the presence of spin-orbit coupling, part of the vortices arrange in a line and form a stable vortex chain, and the remanent vortices coexist in pairs aside such vortex chain. More specially, the remanent vortices of each component repel each other and form vortex pair for isotropic spin-orbit coupling, while attract each other and locate in the same positions for anisotropic spin-orbit coupling.     

Exact Analytical Solutions to the Two—Mode Mean—Field Model Describing Dynamics of a Split Bose—Einstein Condensate

We present the analytical solutions to the two-mode mean-field model for a split Bose-Einstein condensate.These explicit solutions completely determine the system‘s dynamics under the two-mode mean-field approximation for all possible initial conditions.     

Quantum Statistical Behaviors of Interaction of an Atomic Bose-Einstein Condensate with Laser

We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose-Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy-Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.     

Quantum Statistical Behaviors of Interaction of an Atomic Bose-Einstein Condensate with Laser

We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy-Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.``     

Phase of Bose-Einstein Condensate Interacting with a Time-Dependent Laser Field

By using of the invariant theory, we have studied phase of Bose-Einstein condensate in a double-well potential interacting with a time-dependent single-mode traveling-wave laser field, the dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution. PACS number: 03.65.Vf; 03.75.Mn.     

Energy Spectrum of Two-Component Bose-Einstein Condensates in Optical Lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We find that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.