Superfluid properties of Bose-Einstein condensates (BEC) in toroidal quasi-one-dimensional traps are investigated in the presence of periodic scattering length modulations along the ring. The existence of several types of stable periodic waves, ranging from almost uniform to very fragmented chains of weakly interacting and equally spaced solitons, is demonstrated. We show that these waves may support persistent atomic currents and sound waves with spectra of Bogoliubov type. Fragmented condensates can be viewed as arrays of Josephson junctions and the current as a BEC manifestation of the dc-Josephson effect. The influence of linear defects on BEC superfluidity has been also investigated. We found that for subcritical velocities, linear defects that are static with respect to the lattice (while the condensate moves in respect to both the optical lattice and the defect) preserve the BEC superfluidity.
Superfluid properties of Bose-Einstein condensates (BEC) in toroidal quasi-one-dimensional traps are investigated in the presence of periodic scattering length modulations along the ring. The existence of several types of stable periodic waves, ranging from almost uniform to very fragmented chains of weakly interacting and equally spaced solitons, is demonstrated. We show that these waves may support persistent atomic currents and sound waves with spectra of Bogoliubov type. Fragmented condensates can be viewed as arrays of Josephson junctions and the current as a BEC manifestation of the dc-Josephson effect. The influence of linear defects on BEC superfluidity has been also investigated. We found that for subcritical velocities, linear defects that are static with respect to the lattice (while the condensate moves in respect to both the optical lattice and the defect) preserve the BEC superfluidity.
We investigate, both analytically and numerically, the quasisuperfluidity properties of periodic Bose-Einstein condensates (BECs) in a quasi-one-dimensional (1D) ring with optical lattices (OL) of different kinds (linear and nonlinear) and with a moving defect of an infinite mass inside. To study the dynamics of the condensate we used a mean-field approximation describing the condensate by use of the Gross-Pitaevskii equation for the order parameter. We show that the resonant scattering of sound Bloch waves with the defect profoundly affect BEC superfluidity. In particular, a moving defect always leads to the breakdown of superfluidity independently of the value of its velocity. For weak periodic potentials the superfluidity breakdown may occur on a very long time scale (quasisuperfluidity) but the breakdown process can be accelerated by increasing the strength of the OL. Quite remarkably, we find that when the length of the ring is small enough to imply the discreteness of the reciprocal space, it becomes possible to avoid the resonant scattering and to restore quasi-superfluidity.
Compacton matter waves are considered in Bose-Einstein condensates (BEC) and in binary BEC mixtures, trapped in deep optical lattices in the presence of strong and rapid periodic time modulations of the atomic scattering length, are considered.For this, we derive vector averaged discrete nonlinear Schrödinger equations (DNLSE) and show that compacton solutions of different types can exist as stable excitations.Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system.
Bose-Einstein condensates (BECs) have proven to be remarkable systems with which to study some of the foundational models of condensed matter physics. The observation of a critical velocity for the breakdown of superfluidity in a BEC and the superfluid to Mott insulator transition observed in a BEC trapped by an optical lattice are but two examples of the, by now, dozens of exciting results in this field, which combines theoretical tools from condensed matter physics with state-of-the-art experimental techniques from ultra-cold atomic physics. However, any real condensed matter system has to contend with the effects of disorder, a phenomena notably absent in the inherently clean BEC systems. We have developed and implemented a way to add well characterized disorder in a controlled way to the otherwise clean BEC system using the light field from a laser speckle pattern. Using this system, we have investigated the effects of disorder or a single Gaussian defect, on the collective dipole motion of a BEC of 7Li in an optical trap. In addition, we perform transport experiments on a weakly interacting BEC expanding in a disordered one-dimensional atom wave-guide. We have observed that in such a system, the wave nature of matter can lead to spectacular and counterintuitive phenomena. Specifically, we verify that this system exhibits Anderson localization, a phenomena fundamentally resulting from the interference of multiply scattered matter waves. In such a state, the localized gas behaves as an insulator in a regime where it is classically expected to be conducting.\nWe also present results of experiments regarding a repulsive BEC scattering from a semi-permeable, single defect potential. We investigate the transport properties of such a system with special emphasis on the velocity and defect strength dependent dissipation of the collective dipole motion of the BEC. Finally, we present the results of our experiments on the scattering properties of bright matter wave solitons. We have observed fragmentation of the soliton in a disordered potential as well as both splitting and recombination of a soliton after interacting with a single repulsive defect potential.
Superfluidity is a remarkable phenomenon. Superfluidity was initially characterized by flow without friction, first seen in liquid helium in 1938, and has been studied extensively since. Superfluidity is believed to be related to, but not identical to Bose-Einstein condensation, a statistical mechanical phenomena predicted by Albert Einstein in 1924 based on the statistics of Satyendra Nath Bose, where bosonic atoms make a phase transition to form a Bose-Einstein condensate (BEC), a gas which has macroscopic occupation of a single quantum state. Developments in laser cooling of neutral atoms and the subsequent realization of Bose-Einstein condensates in ultracold gases have opened a new window into the study of superfluidity and its relation to Bose-Einstein condensation. In our atomic sodium BEC experiment, we studied superfluidity and dissipationless flow in an all-optical toroidal trap, constructed using the combination of a horizontal ``sheet''-like beam and vertical ``ring''-like beam, which, like a circuit loop, allows flow around the ring. On inducing a single quantum of circulation in the condensate, the smoothness and uniformity of the toroidal BEC enabled the sustaining of a persistent current lasting 40 seconds, limited by the lifetime of the BEC due to background gas pressure. This success set the stage for further experiments studying superfluidity. In a first set of experiments, we studied the stability of the persistent current by inserting a barrier in the flow path of the ring. The superflow stopped abruptly at a barrier strength such that the local flow velocity at the barrier exceeded a critical velocity, which supported decay via the creation of a vortex-antivortex pair. Our precise control in inducing and arresting superflow in the BEC is a first step toward studying other aspects of superfluidity, such as the effect of temperature and dimensionality. This thesis discusses these experiments and also details partial-transfer absorption imaging, an imaging technique developed in the course of this work.
We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov--de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime, three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state, and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.