Garally of our numerical simulations

Analysis of the Gross-Pitaevskii equation

  • Driven vortex dynamics of a BEC in a corotating two-dimensional optical lattice

    • We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. The onset of these different phases is described by the force balance of a driving force, a pinning force and vortex-vortex interactions. In particular, when the optical lattice rotates faster than the condensate, an incommensurate effect leads to a vortex liquid phase supported by the competition between the driving force and the dissipation.

    K. Kasamatsu and M. Tsubota, Phys. Rev. Lett. 97, 240404 (2006).
    d \omega = 0.075 d \omega = 0.10,
    where the relative rotation frequency d \omega is defined as omega(optical lattice) - Omega(condensate).

  • Numerical simulation of three-dimensional dynamics of vortex lattice formation in a BEC

    • We study three-dimensional dynamics of vortex lattice formation in a rotating ciger-shaped Bose-Einstein condensate through numerical simulations of the Gross-Pitaevskii equation with a phenomenological dissipation term. The three-dimensional simulation reveals unknown dynamical features of the vortex nucleation process, in which the condensate undergoes strongly turbulent stage and the penetrating vortex lines are highly vibrated. They arise from the spontaneous excitation of Kelvin waves on the proto-vortices during the surface wave instability, caused by the inhomogeneity of the condensate density along the elongated axial direction. The left movie shows the time development of the constant surface density and the right does the time development of the constant surface of the superfluid velocity (i.e., vortex lines themselves).

    　K. Kasamatsu, M. Machida, N. Sasa and M. Tsubota, Phys. Rev. A71, 043611 (2005).

  • Multiple domain formation in two-component BECs

    • The dynamics of multiple domain formation caused by the modulation instability of two-component Bose-Einstein condensates in an axially symmetric trap are studied by numerically integrating the coupled Gross-Pitaevskii equations. The modulation instability induced by the intercomponent mean-field coupling occurs in the out-of-phase fluctuation of the wave function and leads to the formation of multiple domains that alternate from one domain to another. This behavior is analogous to a soliton train formation, which explains the origin of the long lifetime of the spin domains observed by the MIT group.

    　K. Kasamatsu and M. Tsubota, Phys. Rev. Lett. 93, 100402 (2004).

  • Giant vortex formation in a fast rotating BEC

    • A fast rotating Bose-Einstein condensate confined in a quadratic-plus-quartic potential is found to dynamically generate a "giant vortex" that absorbs all phase singularities into a central low density hole, thereby sustaining a quasi-one-dimensional circular superflow at a supersonic speed.（left: condensate density、right: phase）

    K. Kasamatsu, M. Tsubota, and M. Ueda, Phys. Rev. A 66, 053606 (2002)

    　rotation frequency Omega=2.5 \omega (trap frequency)
    　rotation frequency Omega=3.2 \omega (trap frequency)

  • Vortex lattice formation in a rotating Bose-Einstein condensate

    • We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The origin of the peculiar surface-mode excitations is identified to be phase fluctuations at the low-density surface regime. The obtained dependence of a distortion parameter on time and that on the driving frequency agree with the recent experiments by Madison {\it et al.} [Phys. Rev. Lett. {\bf 86}, 4443 (2001)]. （left: condensate density、right: phase）

    M. Tsubota, K. Kasamatsu, and M. Ueda, Phys. Rev. A 65, 023603 (2002)
    K. Kasamatsu, M. Tsubota, and M. Ueda, Phys. Rev. A 67, 033610 (2003)