We study the thermal fluctuations of vortex positions in small vortex clusters in a harmonically trapped rotating Bose-Einstein condensate. It is shown that the order-disorder transition of two-shell clusters occurs via the decoupling of shells with respect to each other. The corresponding ``melting'' temperature depends strongly on the commensurability between numbers of vortices in shells. We show that melting can be achieved at experimentally attainable parameters and very low temperatures. Also studied is the effect of thermal fluctuations on vortices in an anisotropic trap with small quadrupole deformation. We show that thermal fluctuations lead to the decoupling of a vortex cluster from the pinning potential produced by this deformation. The decoupling temperatures are estimated and strong commensurability effects are revealed.
We study the thermal fluctuations of vortex positions in small vortex clusters in a harmonically trapped rotating Bose-Einstein condensate. It is shown that the order-disorder transition of two-shell clusters occurs via the decoupling of shells with respect to each other. The corresponding ``melting'' temperature depends strongly on the commensurability between numbers of vortices in shells. We show that melting can be achieved at experimentally attainable parameters and very low temperatures. Also studied is the effect of thermal fluctuations on vortices in an anisotropic trap with small quadrupole deformation. We show that thermal fluctuations lead to the decoupling of a vortex cluster from the pinning potential produced by this deformation. The decoupling temperatures are estimated and strong commensurability effects are revealed.
There are many efforts to understand better the dipolar long-range interaction, the shell potential confinement, and the vortices in Bose-Einstein condensates (BECs). Furthermore, combining these three areas suggests that it can give rise to new phenomena. In this thesis, we studied the dynamics of vortices in a shell-trapped dipolar BEC. The long-range dipolar interaction induces an inhomogeneous density distribution on the shell, affecting the vortex velocity field. We analyzed the dynamics of one and two pairs of vortices symmetrically located in the shell to separate the vortex-vortex interaction contribution from that of the density gradient due to the inhomogeneous background. In addition to the numerical studies, a Lagrangian formalism allowed us to derive semi-analytical expressions which are in agreement with the results of the Gross-Pitaevskii equation (GPE) simulations, giving us better insights into the influence of the core in the vortex dynamics outside the validity of the point-vortex model. In the second part of this thesis, we describe an actual experimental implementation of the shell BEC. Using the Stochastic Projected GPE simulations, we determine the configuration of a finite temperature vortex lattice produced in this potential over the action of gravity. More specifically, we studied the transition from a perfectly hexagonal (triangular) lattice to the hexatic and liquid phases by detecting the vortex positions to calculate the angular and pair correlation functions of this system for different values of temperatures and trap rotation frequencies. Our results for the vortex lattice melting are consistent with the hexatic to liquid transition in the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario and can be extended to predict the melting temperature of other finite-size systems.
We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross--Pitaevskii equation, which is the Langevin equation for the Bose--Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.
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 23 Na 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 i 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 densitydepleted 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 ii 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.
We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex-lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex-lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.
Dynamics of vortex clusters is essential for understanding diverse superfluid phenomena. In this paper, we examine the dynamics of vortex quadrupoles in a trapped two-dimensional (2D) Bose-Einstein condensate. We find that the movement of these vortex-clusters fall into three distinct regimes which are fully described by the radial positions of the vortices in a 2D isotropic harmonic trap, or by the major radius (minor radius) of the elliptical equipotential lines decided by the vortex positions in a 2D anisotropic harmonic trap. In the "recombination" and "exchange" regimes the quadrupole structure maintains, while the vortices annihilate each other permanently in the "annihilation" regime. We find that the mechanism of the charge flipping in the "exchange" regime and the disappearance of the quadrupole structure in the "annihilation" regime are both through an intermediate state where two vortex dipoles connected through a soliton ring. We give the parameter ranges for these three regimes in coordinate space for a specific initial configuration and phase diagram of the vortex positions with respect to the Thomas-Fermi radius of the condensate. We show that the results are also applicable to systems with quantum fluctuations for the short-time evolution.
We report the observation of the melting of a vortex lattice in a fast rotating quasi-two dimensional Bose gas, under the influence of thermal fluctuations. We image the vortex lattice after a time-of-flight expansion, for increasing rotation frequency at constant atom number and temperature. We detect the vortex positions and study the order of the lattice using the pair correlation function and the orientational correlation function. We evidence the melting transition by a change in the decay of orientational correlations, associated with a proliferation of dislocations. Our findings are consistent with the hexatic to liquid transition in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario for two-dimensional melting.