Biao Wu

Landau and dynamical instabilities of the superflow of Bose-Einstein condensates in optical lattices

The superfluidity of Bose-Einstein condensates (BECs) in optical lattices is investigated. Apart from the usual Landau instability, which occurs when a BEC flows faster than the speed of sound, the BEC can also suffer a dynamical instability, resulting in period doubling and other sorts of symmetry breaking of the system. Such an instability plays a crucial role in the dissipative motion of a trapped BEC in an optical lattice recently observed [Burger et al., Phys. Rev. Lett. 86, 4447 (2001)].

Theory of Nonlinear Landau-Zener Tunneling

We present a comprehensive analysis of the nonlinear Landau-Zener tunneling. We find characteristic scaling or power laws for the critical behavior that occurs as the nonlinear parameter equals to the gap of avoided crossing energy levels. For the nonlinear parameter larger than the energy gap, a closed-form solution is derived for the nonlinear tunneling probability, which is shown to be a good approximation to the exact solution for a wide range of the parameters. Finally, we discuss the experimental realization of the nonlinear model and possible observation of the scaling or power laws using a Bose-Einstein condensate in an accelerating optical lattice.

Superfluidity of Bose?Einstein condensate in an optical lattice: Landau?Zener tunnelling and dynamical instability

Superflow of a Bose–Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau–Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.

Nonlinear evolution of quantum states in the adiabatic regime.

We present a general theory for adiabatic evolution of quantum states as governed by the nonlinear Schrodinger equation, and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our theory not only spells out conditions for adiabatic evolution of eigenstates, but also characterizes the motion of non-eigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that in the adiabatic evolution of non-eigenstates, the Aharonov-Anandan phases play the role of classical canonical actions.

Controlled Generation of Dark Solitons with Phase Imprinting

The generation of dark solitons in Bose-Einstein condensates with phase imprinting is studied by mapping it into the classic problem of a damped driven pendulum. We provide a simple but powerful scheme, designing the phase imprint for various desired outcomes of soliton generation. For a given phase step, we derive a formula for the number of dark solitons traveling in each direction, and examine the physics behind the generation of counterpropagating dark solitons.

Bloch waves and bloch bands of Bose-Einstein condensates in optical lattices

Bloch waves and Bloch bands of Bose-Einstein condensates in optical lattices are studied. We provide further evidence for the loop structure in the Bloch band, and compute the critical values of the mean-field interaction strength for the Landau instability and the dynamical instability.

Quantum Tweezer for Atoms

We propose a quantum tweezer for extracting a desired number of neutral atoms from a reservoir. A trapped Bose-Einstein condensate is used as the reservoir, taking advantage of its coherent nature, which can guarantee a constant outcome. The tweezer is an attractive quantum dot, which may be generated by red-detuned laser light. By moving at certain speeds, the dot can extract a desired number of atoms from the condensate through Landau-Zener tunneling. The feasibility of our quantum tweezer is demonstrated through realistic and extensive model calculations.

Bright solitons in spin-orbit-coupled Bose-Einstein condensates

We study bright solitons in a Bose-Einstein condensate with a spin-orbit coupling that has been realized experimentally. Both stationary bright solitons and moving bright solitons are found. The stationary bright solitons are the ground states and possess well-defined spin-parity, a symmetry involving both spatial and spin degrees of freedom; these solitons are real valued but not positive definite, and the number of their nodes depends on the strength of spin-orbit coupling. For the moving bright solitons, their shapes are found to change with velocity due to the lack of Galilean invariance in the system. DOI: 10.1103/PhysRevA.87.013614

Nonlinear coherent destruction of tunneling

We study theoretically two coupled periodically curved optical waveguides with Kerr nonlinearity. We find that the tunneling between the waveguides can be suppressed in a wide range of parameters. This suppression of tunneling is found to be related to the coherent destruction of tunneling in a linear medium, which in contrast occurs only at isolated parameter points. Therefore, we call this suppression nonlinear coherent destruction of tunneling. This localization phenomenon can be observed readily with current experimental capability; it may also be observable in a different physical system, the Bose-Einstein condensate.

Direct extraction of the Eliashberg function for electron-phonon coupling: A case study of Be(1010)

We propose a systematic procedure to directly extract the Eliashberg function for electron-phonon coupling from high-resolution angle-resolved photoemission measurement. The procedure is successfully applied to the Be(10(-)10) surface, providing new insights into electron-phonon coupling at this surface. The method is shown to be robust against imperfections in experimental data and suitable for wider applications.