Propagation, breathing and transition of matter-wave packet trains

We find a set of new exact solutions of a quantum harmonic oscillator, which describes some wave-packet trains with average energy being proportional to both the quantum level and classical energy of the oscillator. Center of the wave-packet trains may oscillate like a classical harmonic oscillator of frequency $\omega$. Width and highness of the trains may change simultaneously with frequency $2 \omega$ as an array of breathers. Under some perturbations the wave-packet trains could transit between the states of different quantum numbers. We demonstrate analytically and numerically that the wave-packet trains can be strictly fitted to the matter-wave soliton trains observed by Strecher et al. and reported in Nature 417, 150(2002). When the wave-packets breathe with greater amplitudes, they show periodic collapse and revival of the matter-wave.Comment: 15 pages, 7 figure

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.Comment: 12 page

Optical operation of ultracold atomic quasi-clusters

We report several exact solutions of a two-dimensional (2D) Gross-Pitaevskii equation with an optical lattice potential, which describe the motion of an array of ultracold atomic quasi-clusters in a Bose-Einstein condensate. The velocity of the atomic quasi-clusters can be controlled by adjusting the optical potential strength so that one can stop or drive them by the optical brake. The atomic quasi-clusters form a superfluid for the propagation state or a critical insulator for the non-propagation one, and the brake and drive are associated with the quantum phase transitions between the insulator and superfluid. Other topics in quantum fluids and solids; liquid and solid helium