Vortex lattices in Bose-Einstein condensates: from the Thomas-Fermi to the lowest Landau level regime

We study a harmonically-confined Bose-Einstein condensate under rotation. Vortex lattice configurations are investigated through a variational approach. Vortices with more than a unit of angular momentum are not stable. We explicitly show that the critical rotational frequency is quite small, as was reported in the MIT experiment. The width of the condensate in the xy plane and along z, and the vortex density are determined as functions of the rotational frequency. The aspect...

We characterize several equilibrium vortex effects in a rotating Bose-Einstein condensate. Specifically we attempt precision measurements of vortex lattice spacing and the vortex core size over a range of condensate densities and rotation rates. These measurements are supplemented by numerical simulations, and both experimental and numerical data are compared to theory predictions of Sheehy and Radzihovsky [17] (cond-mat/0402637) and Baym and Pethick [25] (cond-mat/0308325). ...

We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2-dimensional Bose-Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas-Fermi regime. Our starting point is the Gross-Pitaevskii energy functional in the rotating frame. By estimating lower and upper bounds for this energy, we show that the leading order in energy and density can be described by the corresponding Thomas-Fermi quantitie...

We study the fast rotation limit for a Bose-Einstein condensate in a quadratic plus quartic confining potential within the framework of the two dimensional Gross-Pitaevskii energy functional. As the rotation speed tends to infinity with a proper scaling of the other parameters in the model, a linear limit problem appears for which we are able to derive precise energy estimates. We prove that the energy and density asymptotics of the problem can be obtained by minimizing a sim...

We directly image Tkachenko waves in a vortex lattice in a dilute-gas Bose-Einstein condensate. The low (sub-Hz) resonant frequencies are a consequence of the small but nonvanishing elastic shear modulus of the vortex-filled superfluid. The frequencies are measured for rotation rates as high as 98% of the centrifugal limit for the harmonically confined gas. Agreement with a hydrodynamic theory worsens with increasing rotation rate, perhaps due to the increasing fraction of th...

We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP) theory and investigate the properties of the ground state of the theory for rotational speeds close to the critical speed for vortex nucleation. While one could expect that the vortex distribution should be homogeneous within the condensate we prove by means of an asymptotic analysis in the strongly interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously derive a formula due to Sh...

We theoretically examine the rotation of an atomic Bose-Einstein condensate in an elliptical trap, both in the absence and presence of a quantized vortex. Two methods of introducing the rotating potential are considered - adiabatically increasing the rotation frequency at fixed ellipticity, and adiabatically increasing the trap ellipticity at fixed rotation frequency. Extensive simulations of the Gross-Pitaevskii equation are employed to map out the points where the condensat...

The effects of a sudden increase and decrease of the interatomic interaction and harmonic-oscillator trapping potential on vortices in a quasi two-dimensional rotating Bose-Einstein condensate are investigated using the mean-field Gross-Pitaevskii equation. Upon increasing the strength of interaction suddenly the condensate enters a nonstationary oscillating phase which starts to develop more vortices. The opposite happens if the strength is reduced suddenly. Eventually, the ...

We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by the quasiparticle projection method. A simple recurrence oscillation of surface mode populations is broken in the quadrupole resonance region that depends on the trap anisotropy, causing stochastization of...

After delineating the physical regimes which vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate, $\Omega$, increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature. Taking into account effects of the finite compressibility, we find an inertial mode of frequency $\ge 2\Omega$, and a primarily transverse Tkachenko mode, whose frequency goes from being linear in the wave vector in the slowly rotating regi...