Dynamical Stability of Gap Soliton of One-Dimensional Condensate in Optical Lattices with Strong Interatomic Interaction

By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose- Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.     

On a class of quasilinear Schrodinger equations

A type of quasilinear Schrodinger equations in two space dimensions which describe attractive Bose-Einstein condensates in physics is discussed. By establishing the property of the equation and applying the energy method, the blowup of solutions to the equation are proved under certain conditions. At the same time, by the variational method, a sutficient condition of global existence which is related to the ground state of a classical elliptic equation is obtained.     

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 （FIT） 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.     

Generation and control of chaos in a Bose--Einstein condensate

For a Bose--Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k₁\approx k₂ between the two laser wave vectors is kept, the adjustment from k₂1 to k₂\ge k₁ can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.     

Quantum Effects of Many Atoms in Spinor Bose-Einstein Condensates

We have studied the evolutions of the population transfer, tunnelling current and antibunching effects between spin-（＋1） and spin-（-1） in the case of the strong laser pulses. It is found that the population transfer and tunnelling current exhibit periodical oscillation. For the same Rabi frequency, the larger the atom number, the longer the oscillation period is. For the spin-（-1） component, when the atomic numbers are N=4 and 10, the antibunching effect can appear. For different atomic numbers, the appearing regions are very different. For spin component ＋1, the antibunching effect can always appear for different atomic numbers.     

Stability and Chaos of Two Coupled Bose-Einstein Condensates with Three-Body Interaction

We study the dynamics of two Bose-Einstein condensates （BECs） tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time- varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.     

Generation of maximally entangled states in a two-component Bose-Einstein condensate

We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states （SSCS）, may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.     

Effects of the Scattering Length on the Yrast Spectrum for a Two-Component Bose-Einstein Condensates

We study the energy eigenvalue and the yrast states for a harmonically two-component weak-interacting Bose-Einstein condensate (BEC) when the intra-species and interspecies scattering length are different. The energy shift for different energy eigenvalues related to intra-and interspecies scattering lengths is calculated with the perturbation method. The actual yrast spectrum is more complicated than that when intra-species and interspecies scattering length are equal. The degenerated features disappear and so do the perfect symmetric features.     

Small Amplitude Solitons in Bose--Einstein Condensates with External Perturbation

By developing a small amplitude soliton approximation method, we study analytically weak nonlinear excitations in cigar-shaped condensates with repulsive interatomic interaction under consideration of external perturbation potential. It is shown that matter wave solitons may exist and travel over a long distance without attenuation and change in shape by properly adjusting the strength of interatomic interaction to compensate for the effect of external perturbation potential.     

Efimov Superchemistry： Quantum Dynamical Theory for Coherent Atom-Trimer Conversion in a Repulsive Atomic Bose-Einstein Condensate

We show that by making a generalized atom-molecule dark state, coherent creation of triatomic molecules can be enhanced in a repulsive atomic Bose-Einstein condensate. The dynamics of heteronuclear trimer creation is significantly different from the homonuclear case and further enhancement can be realized by controlling its chemical reaction channels. The possibility of manipulating atom-trimer conversion provides an appealing research area for current coherent matter-wave optics.