Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
Sektion Physik, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 München, Germany
Corresponding author: a Jens.Schneider@mpq.mpg.de
Published online: 15 December 2000
The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of Lz instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples.
PACS: 03.75.Fi – Phase coherent atomic ensembles; quantum condensation phenomena / 05.30.Jp – Boson systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000