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arXiv:cond-mat/9711295 · Europhysics Letters (EPL)

Macroscopic angular-momentum states of Bose-Einstein condensates in toroidal traps

Mourad Benakli, S. Raghavan, Augusto Smerzi, Stefano Fantoni, Subodh R. Shenoy

Published May 1, 1999• 32 citations
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Abstract

We study the stability of a rotating repulsive-atom Bose-Einstein condensate in a toroidal trap. The resulting macroscopic angular-momentum states with integer vorticity l spread radially, lowering rotational energies. These states are robust against vorticity-lowering decays, with estimated metastability barriers capable of sustaining large angular momenta ( l ≲10) for typical parameters. We identify the centrifugally squashed l -dependent density profile as a possible signature of condensate rotation and superfluidity.

DOI
10.1209/epl/i1999-00256-8

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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.
Abstract In a harmonically-trapped rotating Bose–Einstein condensate (BEC), a vortex of large angular momentum decays to multiple vortices of unit angular momentum from an energetic consideration. We demonstrate the formation of a robust and dynamically stable giant vortex of large angular momentum in a harmonically trapped rotating BEC with a potential hill at the center, thus forming a Mexican hat like trapping potential. For a small inter-atomic interaction strength, a highly controllable stable giant vortex appears, whose angular momentum slowly increases as the angular frequency of rotation is increased. As the inter-atomic interaction strength is increased beyond a critical value, only vortices of unit angular momentum are formed, unless the strength of the potential hill at the center is also increased: for a stronger potential hill at the center a giant vortex is again formed. The dynamical stability of the giant vortex is demonstrated by real-time propagation numerically. These giant vortices of large angular momentum can be observed and studied experimentally in a highly controlled fashion.
We have studied the ground state configurations of a rotating Bose—Einstein condensation in a toroidal trap as the radius of the central Gaussian potential expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the gaussian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.
In the present work, we consider the problem of a system of few vortices N ≤ 5 as it emerges from its experimental realization in the field of atomic Bose-Einstein condensates. Starting from the corresponding equations of motion for an axially symmetric trapped condensate, we use a two-pronged approach in order to reveal the configuration space of the system's preferred dynamical states. We use a Monte Carlo method parametrizing the vortex particles by means of hyperspherical coordinates and identifying the minimal energy ground states thereof for N=2,...,5 and different vortex particle angular momenta. We then complement this picture with a dynamical system analysis of the possible rigidly rotating states. The latter reveals a supercritical and subcritical pitchfork, as well as saddle-center bifurcations that arise, exposing the full wealth of the problem even for such low-dimensional cases. By corroborating the results of the two methods, it becomes fairly transparent which branch the Monte Carlo approach selects for different values of the angular momentum that is used as a bifurcation parameter.
Abstract Observations of Bose–Einstein condensates—macroscopic populations of ultracold atoms occupying a single quantum state—in dilute alkali-metal and hydrogen gases have stimulated a great deal of research into the statistical physics of weakly interacting quantum degenerate systems1, 2. Recent experiments offer a means of exploring fundamental low-temperature physics in a controllable manner. A current experimental goal in the study of trapped Bose gases is the observation of superfluid-like behaviour, analogous to the persistent currents seen in superfluid liquid helium which flow without observable viscosity. The ‘super’ properties of Bose-condensed systems occur because the macroscopic occupation of a quantized mode provides a stabilizing mechanism that inhibits decay through thermal relaxation3. Here we show how to selectively generate superfluid vortex modes with different angular momenta in a Bose–Einstein condensate. Our approach involves solving the time-dependent equation of motion of a two-component condensate with strongly coupled internal atomic states, as recently investigated experimentally4, 5. The generation of vortices relies on the coupling between the states (achieved by applying an electromagnetic field), combined with mechanical rotation of the trapping potentials which confine the condensate.