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Physical Review A

Persistent currents in a toroidal trap

Juha Javanainen, Sun Mok Paik, Sung Mi Yoo

Published Jul 1, 1998• 36 citations
Publisher

Abstract

Using elementary microscopic methods, we theoretically study persistent flow of an alkali-metal vapor Bose-Einstein condensate around a tight toroidal trap. The angular velocity of a persistent current must be smaller than the angular frequency of the lowest condensate excitation. A supercurrent may be excited by rotating a perturbing potential that is strong enough to cut the toroidal condensate.

DOI
10.1103/physreva.58.580

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Using elementary microscopic methods, we theoretically study persistent flow of an alkali-metal vapor Bose-Einstein condensate around a tight toroidal trap. The angular velocity of a persistent current must be smaller than the angular frequency of the lowest condensate excitation. A supercurrent may be excited by rotating a perturbing potential that is strong enough to cut the toroidal condensate.
We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, limited only by experimental factors such as drift and trap lifetime. The quantized rotation was initiated by transferring one unit variant Planck's over 2pi of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply connected, and was observed with a Bose-Einstein condensate fraction as small as 20%. We also created flow with two units of angular momentum and observed its splitting into two singly charged vortices when the trap geometry was changed from multiply to simply connected.
Persistent current, or "flow without friction", as well as quantum vortices are the hallmarks of superfluidity. Recently a very long-lived persistent flow of atoms has been experimentally observed in Bose-Einstein condensates trapped in a ring-shaped potential. This enables fundamental studies of superfluidity and may lead to applications in high-precision metrology and atomtronics. We overview our recent theoretical studies of the generation of the persistent current in a stirred toroidal atomic Bose-Einstein condensate, and discuss our new investigation of the hysteresis in the atomtronic circuit.
We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, and was initiated by transferring one unit, ħ, of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply-connected, and was observed with a BEC fraction as small as 15%. We also created flow with two units of angular momentum, and observed its splitting into two singly-charged vortices when the trap geometry was changed from multiply- to simply-connected.
We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.
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.
The dynamics of toroidal condensates in the presence of condensate flow and dipole perturbation have been investigated. The Bogoliubov spectrum of a condensate is calculated for an oblate torus using a discrete-variable representation and a spectral method to high accuracy. The transition from spheroidal to toroidal geometry of the trap displaces the energy levels into narrow bands. The lowest-order acoustic modes are quantized with the dispersion relation $\ensuremath{\omega}\ensuremath{\sim}|m|{\ensuremath{\omega}}_{s}$ with $m=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,\dots{}.$ A condensate with toroidal current $\ensuremath{\kappa}$ splits the ∣m∣|m|∣m∣ co-rotating and counter-rotating pairs by the amount $\ensuremath{\Delta}E\ensuremath{\approx}2|m|{\ensuremath{\Elzxh}}^{2}\ensuremath{\kappa}〈{r}^{\ensuremath{-}2}〉.$ Radial dipole excitations are the lowest-energy dissipation modes. For highly occupied condensates the nonlinearity creates an asymmetric mix of dipole circulation and nonlinear shifts in the spectrum of excitations so that the center of mass circulates around the axis of symmetry of the trap. We outline an experimental method to study these excitations.