We quantify the effect of phase fluctuations on atom chip interferometry of Bose-Einstein condensates. At very low temperatures, we observe small phase fluctuations, created by mean-field depletion, and a resonant production of vortices when the two clouds are initially in antiphase. At higher temperatures, we show that the thermal occupation of Bogoliubov modes makes vortex production vary smoothly with the initial relative phase difference between the two atom clouds. We also propose a technique to observe vortex formation directly by creating a weak link between the two clouds. The position and direction of circulation of the vortices are subsequently revealed by kinks in the interference fringes produced when the two clouds expand into one another. This procedure may be exploited for precise force measurement or motion detection.
We quantify the effect of phase fluctuations on atom chip interferometry of Bose-Einstein condensates. At very low temperatures, we observe small phase fluctuations, created by mean-field depletion, and a resonant production of vortices when the two clouds are initially in antiphase. At higher temperatures, we show that the thermal occupation of Bogoliubov modes makes vortex production vary smoothly with the initial relative phase difference between the two atom clouds. We also propose a technique to observe vortex formation directly by creating a weak link between the two clouds. The position and direction of circulation of the vortices are subsequently revealed by kinks in the interference fringes produced when the two clouds expand into one another. This procedure may be exploited for precise force measurement or motion detection.
We show that the decay of a soliton into vortices provides a mechanism for measuring the initial phase difference between two merging Bose-Einstein condensates. At very low temperatures, the mechanism is resonant, operating only when the clouds start in antiphase. But at higher temperatures, phase fluctuations trigger vortex production over a wide range of initial relative phase, as observed in recent experiments at MIT. Choosing the merge time to maximize the number of vortices created makes the interferometer highly sensitive to spatially varying phase patterns and hence atomic movement.
This chapter describes the Bose--Einstein condensate (BEC) interferometry. We first introduce the optical interferometer, briefly discussing the role of fringe contrast in observing interference patterns. Next, we examine a BEC interferometer in a Michelson geometry that consists of a BEC in a trapping potential well. The BEC cloud in the potential well is put into a linear superposition of two clouds that travel along different paths in the trap and are recombined using the same light beams. By studying the population of atoms in the different motional states of the BEC clouds that emerge after recombination, we obtain information about the relative phase shift accumulated by the two traveling superposed condensates during the interferometry. We then characterize the atom distribution that is found in the output of the interferometer by finding the probability density distribution and calculating the features of the probability density such as the mean, the variance, and the interference fringe contrast. Finally, we parameterize the effect of two-body collisional interactions on the observed interference fringes in a way that can be directly controlled in an experiment.
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.
Bose-Einstein condensation, first predicted by Bose and Einstein in 1924, was finally realized in dilute, weakly interacting gases of alkali atoms in 1995. A few years later, quantized vortices - intimately related to the phenomenon of superfluidity - were created and observed in these novel quantum many-body systems.\n\nIn this Thesis, vortices in dilute atomic Bose-Einstein condensates are studied theoretically and computationally using microscopic mean-field theory formalisms. Special emphasis is on the structure and the stability of vortices at finite temperatures. The formation of quantized circulation in Bose-Einstein condensates is investigated, as well as multiply quantized vorticity and the adiabaticity of the precessing motion of a vortex.\n\nThis research strongly relies on numerically solving the Gross-Pitaevskii equation for the macroscopic condensate wavefunction and the coupled Bogoliubov equations and their variants for the collective quasiparticle excitation eigenmodes. The computed elementary excitation spectra are used, for instance, in determining the local stability of various condensate states. The vortex formation process is studied at finite temperatures in terms of the surface modes of the condensate providing the Landau critical velocities for the breakdown of superfluidity. Free energy calculations are used for determining the thermodynamic equilibrium states.\n\nSingly quantized, axisymmetric vortex states are found to be locally energetically stable even in the zero-temperature limit within the self-consistent finite-temperature approximations. This would imply for the vortex a precession direction opposite to that observed in the experiment. Adiabatic approximation of quantum mechanics is formulated for Bose-Einstein condensed systems and is applied to a case of a moving vortex line. The experimentally observed precessing motion of the vortex is found to be nonadiabatic. A method to create stable multiply quantized vortices using an additional pinning potential is presented. The computed critical trap rotation frequencies for vortex nucleation at finite temperatures are in agreement with experiments and the predictions of zero-temperature field theories.
We study the dynamics of vortices in finite temperature atomic Bose-Einstein condensates, focusing on decay rates, precession frequencies, and core brightness, motivated by a recent experiment [Science 329, 1182 (2010)] in which real-time dynamics of a single vortex was observed. Using the Zaremba, Nikuni, and Griffin (ZNG) formalism based on a dissipative Gross-Pitaevskii equation for the condensate coupled to a semiclassical Boltzmann equation for the thermal cloud, we find a rapid nonlinear increase of both the decay rate and precession frequency with increasing temperatures. The increase, which is dominated by the dynamical condensate-thermal coupling is also dependent on the intrinsic thermal cloud collisional dynamics; the precession frequency also varies with the initial radial coordinate. The integrated thermal cloud density in the vortex core is for the most part independent of the position of the vortex (except when it is near the condensate edge), with its value increasing with temperature. This could potentially be used as a variant to the method of Coddington et al. [Phys. Rev. A 70, 063607 (2004)] for experimentally determining the temperature.
We investigate the effects of interatomic interactions and expansion on the distortion of interference fringes of a pair of initially well-separated, but coherent, condensate clouds trapped in a harmonic trap. The distortion of interference fringes, which can lead to the spontaneous formation of vortices in the atom clouds, depends crucially on two relevant parameters: the center-of-mass velocity and peak density of the initial state. We identify three qualitatively distinct regimes for the interfering condensates: collision, expansion, and merging, by the spatial and temporal features of the fringe spacings. Using a comprehensive set of numerical simulations based on the Gross-Pitaevskii equation, we specify the crossovers between these regimes and propose the optimal system parameters required for dynamical instabilities and vortex creation.