We have measured the threshold for creating long-lived excitations when a toroidal Bose-Einstein condensate is stirred by a rotating (optical) barrier of variable height. When the barrier height is on the order of or greater than half of the chemical potential, the critical barrier velocity at which we observe a change in the circulation state is much less than the speed for sound to propagate around the ring. In this regime we primarily observe discrete jumps (phase slips) from the noncirculating initial state to a simple, well-defined, persistent current state. For lower barrier heights, the critical barrier velocity at which we observe a change in the circulation state is higher, and approaches the effective sound speed for vanishing barrier height. The response of the condensate in this small-barrier regime is more complex, with vortex cores appearing in the bulk of the condensate. We find that the variation of the excitation threshold with barrier height is in qualitative agreement with the predictions of an effective one-dimensional hydrodynamic model.
We have measured the threshold for creating long-lived excitations when a toroidal Bose-Einstein condensate is stirred by a rotating (optical) barrier of variable height. When the barrier height is on the order of or greater than half of the chemical potential, the critical barrier velocity at which we observe a change in the circulation state is much less than the speed for sound to propagate around the ring. In this regime we primarily observe discrete jumps (phase slips) from the noncirculating initial state to a simple, well-defined, persistent current state. For lower barrier heights, the critical barrier velocity at which we observe a change in the circulation state is higher, and approaches the effective sound speed for vanishing barrier height. The response of the condensate in this small-barrier regime is more complex, with vortex cores appearing in the bulk of the condensate. We find that the variation of the excitation threshold with barrier height is in qualitative agreement with the predictions of an effective one-dimensional hydrodynamic model.
Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase slips are induced by vortex excitations created by a rotating weak link. We analyze the influence of a localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate. We simulate in a three-dimensional dissipative mean-field model the dynamics of the condensate using parameters similar to the experimental conditions. Moreover, we consider the dynamics of the stirred condensate far beyond the experimentally explored region and reveal surprising manifestations of complex vortex dynamics.
We consider the setup employed in a recent experiment (Ramanathan et al 2011 Phys. Rev. Lett. 106 130401) devoted to the study of the instability of the superfluid flow of a toroidal Bose–Einstein condensate in the presence of a repulsive optical barrier. Using the Gross–Pitaevskii mean-field equation, we observe, consistently with what we found in Piazza et al (2009 Phys. Rev. A 80 021601), that the superflow with one unit of angular momentum becomes unstable at a critical strength of the barrier and decays through the mechanism of phase slippage performed by pairs of vortex–antivortex lines annihilating. While this picture qualitatively agrees with the experimental findings, the measured critical barrier height is not very well reproduced by the Gross–Pitaevskii equation, indicating that thermal fluctuations can play an important role (Mathey et al 2012 arXiv:1207.0501). As an alternative explanation of the discrepancy, we consider the effect of the finite resolution of the imaging system. At the critical point, the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, v barr = c l . In particular, in the hydrodynamic regime (not reached in the above experiment), the critical point is determined by applying the Landau criterion inside the barrier region. On the other hand, the Feynman critical velocity v f is much lower than the observed critical velocity. We argue that this is a general feature of the Gross–Pitaevskii equation, where we have v f = c l with being a small parameter of the model. Given these observations, the question still remains open about the nature of the superfluid instability.
Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. A 88, 063633 (2013)], we investigate the microscopic mechanism for excitation of vortices and formation of a persistent current in an annular BEC stirred by a narrow blue-detuned optical beam. In the framework of a two-dimensional mean-field model, we study the dissipative dynamics of the condensate with parameters that reflect realistic experimental conditions. Vortex-antivortex pairs appear near the center of the stirrer in the bulk of the condensate for slow motion of the stirring beam. When the barrier angular velocity is above some critical value, an outer edge surface mode develops and breaks into the vortices entering the condensate annulus. We determine the conditions for creation of vortex excitations in the stirred toroidal condensate and compare our results with experimental observations.
We analyze the nucleation of persistent currents in Bose-Einstein condensates of ultracold gases confined in a ring. This phenomenon has been recently investigated in an experiment [S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature (London) 506, 200 (2014)], where hysteresis loops have been observed in the activation of quantized persistent currents by rotating weak links. In this work, we demonstrate the existence of three-dimensional stationary currents with nonquantized angular momentum. They are generated by families of solitary waves that exhibit a continuous variation in the angular momentum and provide a bridge between different winding numbers. We show that the size of hysteresis loops is determined by the range of existence within the weak link region of solitary waves which configure the energy barrier preventing phase slips. The barrier vanishes when the critical rotation leads winding number and solitonic states to a matching configuration. At this point, Landau and Feynman criteria for phase slips meet: the fluid flow reaches the local speed of sound, and stationary vortex lines (which are the building blocks of multidimensional solitons) can be excited inside the system.
We study superfluid dissipation due to phase slips for a Bose-Einstein condensate flowing through a repulsive barrier inside a torus. The barrier is adiabatically raised across the annulus, while the condensate flows with a finite quantized angular momentum. At a critical height, a vortex moves from the inner region and reaches the barrier to eventually circulate around the annulus. At a higher critical height, an antivortex also enters into the torus from the outer region. Both vortex and antivortex decrease the total angular momentum by leaving behind a $2\ensuremath{\pi}$ phase slip. When they collide and annihilate or orbit along the same loop, the condensate suffers a global $2\ensuremath{\pi}$ phase slip, and the total angular momentum decreases by one quantum. In hydrodynamic regime, the instability sets in when the local superfluid velocity equals the sound speed inside the barrier region.
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.