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arXiv:1503.08302 · Physical Review A

Persistent currents supported by solitary waves in toroidal Bose-Einstein condensates

Antonio Muñoz Mateo, Albert Gallemí, M. Guilleumas, R. Mayol

Published Jun 22, 2015• 52 citations
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Abstract

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.

DOI
10.1103/physreva.91.063625

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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 investigate the rotational properties of a dipolar Bose-Einstein condensate trapped in a toroidal geometry. Studying the ground states in the rotating frame and at fixed angular momenta, we observe that the condensate acts in distinctly different ways depending on whether it is in the superfluid or in the supersolid phase. We find that intriguingly, the toroidal dipolar condensate can support a supersolid persistent current which occurs at a local minimum in the ground state energy as a function of angular momentum, where the state has a vortex solution in the superfluid component of the condensate. The decay of this state is prevented by a barrier that in part consists of states where a fraction of the condensate mimics solid-body rotation in a direction opposite to that of the vortex. Furthermore, we find that superfluid condensates may enter the supersolid phase when forced to take angular momentum. Last, the rotating toroidal supersolid shows hysteretic behavior that is qualitatively different depending on the superfluid fraction of the condensate.
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 analyse the dynamical properties of three-dimensional solitary waves in cylindrically trapped Bose–Einstein condensates. Families of solitary waves bifurcate from the planar dark soliton and include the solitonic vortex, the vortex ring and more complex structures of intersecting vortex lines known collectively as Chladni solitons. The particle-like dynamics of these guided solitary waves provides potentially profitable features for their implementation in atomtronic circuits, and play a key role in the generation of metastable loop currents. Based on the time-dependent Gross–Pitaevskii equation we calculate the dispersion relations of moving solitary waves and their modes of dynamical instability. The dispersion relations reveal a complex crossing and bifurcation scenario. For stationary structures we find that for the solitonic vortex is the only stable solitary wave. More complex Chladni solitons still have weaker instabilities than planar dark solitons and may be seen as transient structures in experiments. Fully time-dependent simulations illustrate typical decay scenarios, which may result in the generation of multiple separated solitonic vortices.
We have observed well-defined phase slips between quantized persistent current states around a toroidal atomic (23Na) Bose-Einstein condensate. These phase slips are induced by a weak link (a localized region of reduced superfluid density) rotated slowly around the ring. This is analogous to the behavior of a superconducting loop with a weak link in the presence of an external magnetic field. When the weak link is rotated more rapidly, well-defined phase slips no longer occur, and vortices enter into the bulk of the condensate. A noteworthy feature of this system is the ability to dynamically vary the current-phase relation of the weak link, a feature which is difficult to implement in superconducting or superfluid helium circuits.
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 propose a simple stirring experiment to generate quantized ring currents and solitary excitations in Bose-Einstein condensates in a toroidal trap geometry. Simulations of the three-dimensional Gross-Pitaevskii equation show that pure ring current states can be generated efficiently by adiabatic manipulation of the condensate, which can be realized on experimental timescales. This is illustrated by simulated generation of a ring current with winding number two. While solitons can be generated in quasi-one-dimensional tori, we show the even more robust generation of hybrid, solitonic vortices (svortices) in a regime of wider confinement. Svortices are vortices confined to essentially one-dimensional dynamics, which obey a similar phase-offset-velocity relationship as solitons. Marking the transition between solitons and vortices, svortices are a distinct class of symmetry-breaking stationary and uniformly rotating excited solutions of the two-dimensional and three-dimensional Gross-Pitaevskii equation in a toroidal trapping potential. Svortices should be observable in dilute-gas experiments.