Controlled Manipulation with a Bose--Einstein Condensates N-Soliton Train under the Influence of Harmonic and Tilted Periodic Potentials

A model of the perturbed complex Toda chain （PCTC） to describe the dynamics of a Bose-Einstein condensate （BEC） N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.     

Stability Diagrams of a Bose-Einstein Condensate in Excited Bloch Bands

Landau and dynamical instabilities o/a Bose-Einstein condensate （BEC） in the excited bands of a one-dimensional optical lattice are investigated by the Gross Pitaevskii theory. Our results show that there always exists Landau instability for a BEC in the whole region of excited bands. We also map out the dangerous zones of the dynamical instability. The experimental implications of the stability diagram are discussed.     

The dynamics and stabilities of Bose-Einstein condensates in deep optical lattices

The dynamics and stabilities of Bose-Einstein condensate (BEC) trapped in a deep one-dimensional periodic optical lattices with three-body interactions are investigated. By using the tight-binding approximation, the Bloch and the Bogoliubov excitation stabilities and the dynamics of the BEC wavepacket with the effects of the three-body interactions are studied. The critical conditions for occurrence of the dynamical/Landau instabilities, self-trapping/diffusion/breather of wavepacket, and localized soliton are obtained analytically. The results show that the boundaries of the dynamical instability and Landau instability are modified significantly due to the presence of the three-body interactions. It is also revealed that, the initial wavepacket width, the initial momentum, especially, the strength of the three-body force have strong effect on the critical conditions which are used to describe the dynamics of the wavepacket. It is shown that the regions of self-trapping, diffusion, and breather for BEC wavepacket in the parameter space are modified dramatically by the three-body interactions. The analytical results are confirmed by the direct numerical solutions of the discrete GPE.     

Stability Diagrams of a Bose-Einstein Condensate in a Periodic Array of Quantum Wells

With the help of a set of exact closed-form solutions to the stationary Gross Pitaevskii equation, we compre-hensively investigate Landau and dynamical instabilities of a Bose-Einstein condensate in a periodic array of quantum wells. In the tight-binding limit, the anaiyticai expressions for both Landau and dynamical instabilities are obtained in terms of the compressibility and effective mass of the BEC system. Then the stability phase diagrams are shown to be similar to the one in the case of the sinusoidal optical lattice.     

Nonlinear Landau--Zener Tunnelling with Two and Three-Body Interactions

We investigate the nonlinear Landau-Zener tunnelling of Bose-Einstein condensate （BEC） in an accelerating optical lattice with two- and three-body interactions between the particles. The influence of the three-body interaction on the eigenstates and the transition probability are discussed both anaJytically and numerically. The analytical eigenstates and the tunnelling probability are obtained, which are verified by numerical methods. It is shown that the eigenstates and the tunnelling probability are modified dramatically by three-body interaction.     

Stabilities of one-dimensional stationary states of Bose-Einstein condensates

We explore the dynamical stabilities of a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) consisting of fixed N atoms with time-independent external potential. For the stationary states with zero flow density the general solution of the perturbed time evolution equation is constructed, and the stability criterions concerning the initial conditions and system parameters are established. Taking the lattice potential case as an example, the stability and instability regions on the parameter space are found. The results suggest a method for selecting experimental parameters and adjusting initial conditions to suppress the instabilities.     

Superfluid properties of a Bose-Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose-Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.     

Dynamics of kicked matter-wave solitons in an optical lattice

We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose-Einstein condensate trapped in an optical lattice. The resulting soliton’s dynamics is studied within the framework of the time-dependent nonpolynomial Schrödinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice.     

Oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

In this work, we study parametric excitations in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric excitations (oscillations of the BEC width). Regular oscillations disappear when one of the competing factors, i.e. the strength of harmonic trap or the strength of optical lattice, dominates. Parametric instabilities (chaotic dynamics) arise for large variations in the strength of the optical lattice.     

Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice

We study the exact Bloch states of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) held in an optical lattice. Under a natural condition of the symmetry between the two species, we obtain two different forms of exact solutions corresponding to different existing conditions. Then, we analytically demonstrate that (a) the average atomic number per well can enlarge the region area (consisting of instability and stability parameter regions) existing exact solutions; (b) the sizes of the instability and stability parameter regions exhibit opposite variation trend with the increase in Rabi coupling strength, and the results of different solutions are just opposite. Besides, we find that spin-orbit coupling (SOC) results in the generation of spin-motion entanglement for the Bloch states, the SOC strength and lattice depth can influence the population transfer between two BEC components, and varying the SOC strength and lattice depth can also reveal the dynamical superfluid-insulator transition from the superfluid state to the critical insulating state. These results present a feasible scheme to manipulate the stable superfluid currents, which will be useful to control quantum transport of BEC.

     

Bose-Einstein condensates in optical lattices: Spontaneous emission in the presence of photonic band gaps

An extended Bose-Einstein condensate (BEC) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it. We examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the BEC, and whether they can lead to a self-stabilization of the BEC against spontaneous emission. We find that self-stabilization is not possible for BECs with a density in the order of 10¹⁴ cm^-3. However, the corresponding non-Markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous BEC interacting with a weak laser beam. These effects are caused by the occurrence of an avoided crossing in the photon (or rather polariton) spectrum. We also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes. This new channel should also occur in ordinary periodic dielectrics. Received 27 March 2000     

Periodic spin domains of spinor Bose-Einstein condensates in an optical lattice

The periodic spin domains of spinor Bose-Einstein condensates confined in a one-dimensional optical lattice are studied in terms of the equation of motion of the spinor which is reduced to the nonlinear Schrödinger equation with the help of Holstein-Primakoff transformation. It is shown that the spin domains obtained analytically can be easily controlled by adjusting the light-induced dipole-dipole interaction, which is realizable in optical lattice created by red-detuned laser beams with modulating intensity. The dynamical stability of the spin domains is also demonstrated.     

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.     

Suppression of Chaos in a Bose-Einstein Condensate Loaded into a Moving Optical Superlattice Potential

We have shown that the application of modulating the secondary lattice is an efficient route to suppressing the generation of chaotic traveling waves of a Bose-Einstein Condensate with attractive interatomic interaction loaded into a moving optical superlattiee consisting of two lattices. With the Melnikov method, we obtain the optimal value of the relative phase between the two lattice harmonics for the control of chaos. We also find that the regularization route as the potential depth of the secondary lattice is varied and fairly rich, including the period-doubling bifurcations.     

Interferometric precision measurements with Bose–Einstein condensate solitons formed by an optical lattice

We propose the precision measurement of both angular rotation and of the gradient magnetic of a field based on the use of matter wave interferometers with soliton states of a Bose-Einstein condensate (BEC). We consider the formation of these soliton states in a BEC with negative scattering length by an optical lattice produced by two counterpropagating laser beams. We determine the parameters of both the initial condensate and the optical radiation necessary for the formation of coherent solitons. We demonstrate that this interferometer can be used to measure magnetic field gradient with a precision of 10^-2 pT/cm. Our calculations show that the sensitivity of a gyroscope based on a ring, two-port matter wave interferometer can achieve 2.6×10^-7 rad s^-1. The precision of this method is more than ten times greater than in that of rotating interferometer with cooled atoms.     

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau-Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate (BEC) with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters (i.e., the modulation amplitude and frequency) and the strength of periodic potential.     

Ground Band and Excited Band of Spin-1 BEC in Cigar Shaped Laser Trap

The wavefunctions that conserve the total spin are constructed for the fully condensed states and the states with one particle excited. A set of equations are deduced for the spatial longitudinal wavefunctions and the chemical potentials. These equations are solved numerically for ^23Na and ^87Rb condensates. The deformed trap shows significant effects on the spectrum. This implies that the spin effect of the spinor BEC are more easily detected in an optical trap of larger aspect ratio.     

Photo-induced dynamics of Bose-Einstein condensates in optical superlattice

The photo-induced dynamics of cold atoms in a one-dimensional optical superlattice is observed. Steady state distribution of the probability amplitudes and the site population in a one-dimensional optical superlattice is found. It is shown that this solution of the equations, which describes the temporal behavior of a Bose-Einstein condensate in a superlattice, is unstable at the sufficiently high level of boson density. The expression for the increment of modulational instability is obtained on the basis of the linear stability analysis. The numerical examples of non-stationary solutions for boson density in a superlattice for the general model are discussed as applied to both the attraction and repulsion potentials of boson interaction.     

Bose-Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

We study the phase coherence property of Bose-Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza-Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.