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Europhysics Letters (EPL)

Anomalous Angular-Momentum Fluctuations for an Ideal Bose Gas in a Rotating Bucket

Pim Tuyls, M Van Canneyt, André F. Verbeure

Published Jul 1, 1994• 2 citations
Publisher

Abstract

An equilibrium superfluid is usually modelled by a Bose gas below its transition temperature. Here we compute rigorously the deviation from normality of the angular-momentum fluctuations, and prove that the extremal phases, or the extremal equilibrium state components, show normal behaviour, except for special boundary conditions.
DOI
10.1209/0295-5075/27/1/004

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An equilibrium superfluid is defined as a substance whose moment of inertia in thermal equilibrium is less than the classical value. The ideal Bose-Einstein gas below its transition temperature is shown to be an equilibrium superfluid. However, a more detailed analysis of the relation between angular momentum and angular velocity shows that experiments carried out with practical angular momenta and velocities would give an abnormally large apparent moment of inertia in thermal equilibrium, i.e., the gas would appear to be an "infrafluid." Nevertheless, a weakly interacting Bose-Einstein gas can be used as a model of a superfluid, if the superfluid state is assumed to be metastable rather than the thermodynamic equilibrium state.
We have investigated the superfluid properties of a ring of weakly interacting and degenerate 1D Bose gas at thermal equilibrium with a rotating vessel. The conventional definition of superfluidity predicts that the gas has a significant superfluid fraction only in the Bose condensed regime. In the opposite regime, it is found that a superfluid behaviour can still be identified when the probability distribution of the total momentum of the gas has a multi-peaked structure, revealing unambiguously the existence of ‘superfluid’ supercurrent states that did not show up in the conventional definition of superfluidity.
We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for metastable states in finite-size systems. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov--de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist two topologically distinct quantum phases. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is where one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity. The phase of the condensate can therefore be continuously wound and unwound.