We report on a superfluid properties of a Bose- Einstein condensate in a rotating harmonic trap. We employ the semiclassical approximation, which is the density of state approach. Our approach provided the finite size effect. The superfluid fraction of bosons and its heat capacity at constant volume are investigated. The calculated results provide a good qualitative agreement with the measured experimental results for superfluid helium 4H. Moreover, furnish useful qualitatively theoretical results for a spectroscopic measurement of the superfluid fraction of an ultracold atomic gas [N. R. Cooper and Z. Hadzibabic, Phys. Rev. Lett. 104, 030401 (2010)]. Our results show that both The superfluid fraction of bosons and its heat capacity depend on the number of the atoms. This significant dependence should be considered when the it in situ widths are used in extracting measurable experimental quantities. Our approach can be extended to consider the rotating condensate in optical potential .
We present a study of phase transition to macroscopic superfluidity for an ultracold bosonic gas confined in a combined trap formed by a one-dimensional optical lattice and a harmonic potential, focusing on the critical temperature of this system and the interference patterns of the Bose gas released from the combined trap. Based on a semiclassical energy spectrum, we develop an analytic approximation for the critical temperature
Tc, and compare the analytic results with that obtained by numerical computations. For finite temperatures below
Tc, we calculate the interference patterns for both the normal gas and the superfluid gas. The total interference pattern shows a feature of ``peak on a peak.'' As a comparison, we also present the experimentally observed interference patterns of
87Rb atoms released from a one-dimensional optical lattice system in accord with our theoretical model. Our observations are consistent with the theoretical results.
We examine antiferromagnetic and
d-wave superfluid phases of cold fermionic atoms with repulsive interactions in a two-dimensional optical lattice combined with a harmonic trapping potential. For experimentally realistic parameters, the trapping potential leads to the coexistence of magnetic and superfluid ordered phases with the normal phase. We study the intriguing shell structures arising from the competition between the magnetic and superfluid order as a function of the filling fraction. In certain cases, antiferromagnetism induces superfluidity by charge redistributions. We furthermore demonstrate how these shell structures can be detected as distinct antibunching dips and pairing peaks in the density-density correlation function probed in expansion experiments.