Thermal Phase Fluctuations in a Quasi-2D Bose-Einstein Condensate

Abstract

Quantum gases are well isolated, highly controllable, and defect-free systems which can simulate many body quantum phenomena that have been studied in condensed matter systems. To study two-dimensional superfluid, we have developed an experimental apparatus that can produce Bose-Einstein condensates (BEC) of Na-23 atoms. The apparatus can generate a pure condensate of 10^7 atoms in an optically plugged magnetic quadrupole trap within 17 s.

The Berezinskii-Kosterlitz-Thouless (BKT) theory provides a general framework of the superfluid phase transition in two dimension, which does not involve spontaneous symmetry breaking and emergence of an order parameter below a critical temperature. Instead, it is the formation of vortex pairs with opposite circulations below the critical temperature that mediates the superfluid phase transition. Recently, it has been demonstrated that degenerate Bose gases confined in highly oblate harmonic potentials undergo the BKT phase transition. This thesis focuses on our experimental research on thermal phase fluctuations (i.e., long-wavelength phonons and vortex pairs) in the superfluid phase of trapped quasi-2D BECs. We have developed a quantitative probe to measure phase fluctuations in the 2D superfluid by free expansion, where the phase fluctuations in the sample were revealed as density modulations in the course of expansion. The power spectrum of the density fluctuations showed an oscillatory shape and the scaling behavior of the peak positions could be understood as a Talbot effect in matter waves. Employing this method, we demonstrated the thermal origin of phase fluctuations. We also investigated relaxation dynamics of nonequilibrium states of the quasi-2D system using the power spectrum.

Thermally excited vortex pairs are the characteristic feature of the 2D superfluid. The quantized vortices are conventionally observed by a density-depleted core after expanding a trapped sample. The method, however, cannot be applied to the 2D sample because the density modulations after free expansion lower the vortex core visibility. We enhanced the core visibility by radial compression of the sample before the expansion so the phonon modes in the 2D sample were relaxed in a 3D environment. Measuring vortex distributions, we revealed the pairing feature by spatial correlations of the vortex positions. We also studied BKT-BEC crossover phenomena in a finite-size sample trapped in a quasi-2D harmonic potential by investigating the vortex profiles at various temperatures.

Condensates of atoms have an internal spin structure so they can host various kinds of topological excitations. The two-dimensional Skyrmion is one of the topological spin textures in the anti-ferromagnetic spinor condensate and we imprinted the structure using the magnetic field sweep technique.

The 2D Skyrmion spin texture has a finite Berry curvature because of the non-coplanar spin configuration. We studied a geometric Hall effect, with condensates trapped in a harmonic potential with the Skyrmion spin texture. Under a linear driving of the spin texture, we observed a condensate dipole motion resonantly developed into a circular motion, which demonstrates the existence of an effective Lorentz force.