Dark Lump Excitations in Bose—Einstein Condensates

We investigate the dynamics of two-dimensional matter-wave pulses in a Bose-Einstein condensate with diskshaped traps.For the case of repulsive atom-atom interactions,a Kadomtsev-Petviashvili equation with positive dipersion is derived using the method of multiple scales.The results show that it is possible to excite dark lump-like two-dimensional nonlinear excitations in the Bose-Einstein condensate.     

Quantum Statistical Properties in Two—Species Bose—Einstein Condensates

We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species,the interspecies nonlinear interaction,and the Jisephson-like tunneling interaction.It is found that the two condensates may periodically exhibit sub-Poissonian distribution.It is revealed that the correlation between the two condensates can be nonclassical,which means that there exists a violation of Cauchy-Schwartz inequality.The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.     

Analytical method for yrast line states in the interacting two—component Bose—Einstein condensate

The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC),omitting the difference between the two components,has been studied using an analytical method.The energy eigenstates and eigenvalues for L=0,1,2,3 are given,We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions.Except for symmetric states,there are antisymmetric states for the permutation of the two components,which cannot reduce to those in a single condensate case when the value of L is odd.     

The Atomic Tunneling Current in Two—Species Bose—Einstein Condensates

It is shown that the atomic tunneling current and the Shapiro-like steps strongly depend on the initial number of atoms in each condensate and the initial phase difference between the two condensates which are initially in even(odd) coherent states.The nonlinearity of interatomic interactions in the two condensates may lead to the atomic tunneling current and Shapiro-like step between the two condensates.It is found that the interatomic nonlinear interactions can induce the atomic tunneling current and Shapiro-like step between two condensates even though there does not exist the interspecies Josephson-like tunneling coupling.The static atomic tunneling current flows in positive or negative direction,which depends on the phase difference of the two-species condensates.     

Phonon Spectrum and Modulational Instability in a Bose—Einstein Condensate Array

We derive the phonon spectrum and the corresponding modulational instability conditions of an array of traps containing Bose-Einstein condensates with each trap linked to adjacent traps by tunnelling.It is shown that modulational instability regimes always exist regardless of the sign of the two-body interaction.     

Evolution and Collision of Bose—Condensed Gas in One—Dimensional Optical Lattices and a Far—Off Resonant Laser Beam

Evolution of a Bose-condensed gas in one-dimensional optical lattices is investigated in the presence of a potentialbarrier created by a far-off resonant laser beam. After the magnetic trap and optical lattices are switched off,by using the propagator method, the analytical result of the evolution of the density distribution of the Bose-condensed gas is given. In particular, the collision between the condensate and the potential barrier is shown inthis paper.     

Self—Trapping State and Atomic Tunnelling Current of an Atomic Bose—Einstein Condensate Interacting with a Laser Field in a Double—Well Potential

We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting with a single-mode quantized travelling-wave laser field in a double-well potential.When the atom-field system is initially in a coherent state,expressions for the energy exchange between atoms and photons are derived.It is revealed that atoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included.It is found that there is an alternating current with two different sinusoidal oscillations between the two wells,but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field,both the population difference and the atomic tunnelling current are only a single oscillation.But they will respectively become a superposition of two oscillations with different oscillatory frequencies in the presence of the laser field.For the two oscillations of the population difference,one always has an increment in the oscillatory frequency,the other can have an increment or a decrease under different cases.These conclusions are also suitable to those of the atomic tunnelling current.As a possible application,by measurement of the atomic tunnelling current between the two wells,the number of Bose-condensed atoms can be evaluated.By poperly selecting the laser field,the expected atomic tunnelling current can be obtained too.     

Rabi Oscillations in Two－Component Bose－Einstein COndensates with a Coupling Drive

The Rabi oscillations in two-component Bose-Einstein condensates with a coupling drive are studied by means of a pair of bosonic operators.The coupling drive and initial phase difference will affect the amplitude and the period of the Rabi oscillations.The Rabi oscillations will vanish in the evolution of the condensate density for some special initial phase differences(φ=0 or π).Our theory provides not only an analytical framework for quantitiative predictions for two-component condensates,but also gives an intuitive understanding of some mysterious features observed in experiments and numerical simulations.     

Coherent Superposition States of Atoms and Molecules in a Bose—Einstein Condensate with Exactly Bananced Photo—Associations and Photo—Dissociations

We show that there exist a series of coherent superposition states of atoms and molecules in a dilute Bose-Einstein condensate with exactly balanced photo-associations and photo-dissociations,and their analytical expressions are explicitly given.They also correspond to the coherent superposition states of two kinds of hpotons in optical second harmonic generation processes,which shows exactly balaced down-and up-conversions.     

（2＋1）—Dimensional Envelope Solitons in a Disk—Shaped Bose—Einstein Condensate

We show that, due to the nonlinear coupling between a wavepacket superposed by short-wavelength collective modes and a long-wavelength mean field generated by the self-interaction of the wavepacket, the (2 1)-dimensional envelope solitons decaying in all spatial directions, i.e., dromions, are possible nonlinear excitations in a disk-shaped Bose-Einstein condensate with a repulsive interatomic interaction.     

Stimulated Raman Adiabatic Population Transfer of Two Bose—Einstein Condensates

Considering all the ground-state atom interactions,we investigate the population transfer of two Bose-Einstein condensate (BEC) states,which are trapped in diffecent potential wells,or two ground states of the BEC in the same trap using the stimulated Raman adiabatic process.With a proper choice of pulsed geometric parameters,the dark state exists.By simply choosing ground-state detunings,the effects of the interatomic interaction can be suppressed and a high population transfer rate can be obtained.     

Breathing Bright Solitons in a Bose—Einstein Condensate

A Bose-Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross-Pitaeviskii equation are obtained to describe single soliton, bisoliton and N-soliton properties of the matter wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very sinall trap aspect ratio or oscillates with a high frequency, the matter wave preserves its shape nearly like a soliton train in propagation, while the breathing behaviour, which displays the periodic collapse and revival of the matter wave, is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass centre of the matter wave translates and/or oscillates for different trap aspect ratio and trap frequencies.     

Quantum Dynamics of Cooled Atoms in the Presence of Bose—Einstein Condensates

Under the Markov approximation,the quantum dynamics of cooled atoms in the presence of Bose-Einstein condensates is studied.A master equation governing the evolution of such a system is derved.Using this master equation,the distribution of the atoms in the excited states at finite temperature and the dynamics of the excited atom at zero temperature are given and discussed.     

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.