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arXiv:0910.4767 · Physical Review Letters

Measuring the Superfluid Fraction of an Ultracold Atomic Gas

Nigel R. Cooper, Zoran Hadzibabic

Published Jan 19, 2010• 71 citations
arXivHTMLPDF

Abstract

We propose a method to measure the superfluid fraction of an atomic gas. The method involves the use of a vector potential generated by optical beams with nonzero angular momenta to simulate uniform rotation. The induced change in angular momentum of the atomic gas can be measured spectroscopically. This allows a direct determination of the superfluid fraction.

DOI
10.1103/physrevlett.104.030401

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We propose a method to measure the superfluid fraction of an atomic gas. The method involves the use of a vector potential generated by optical beams with nonzero angular momenta to simulate uniform rotation. The induced change in angular momentum of the atomic gas can be measured spectroscopically. This allows a direct determination of the superfluid fraction.
We perform detailed analytical and numerical studies of a recently proposed method 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)]. Previous theoretical work is extended by explicitly including the effects of nonzero temperature and interactions, and assessing the quantitative accuracy of the proposed measurement for a one-component Bose gas. We show that for suitably chosen experimental parameters the method yields an experimentally detectable signal and a sufficiently accurate measurement. This is illustrated by explicitly considering two key examples: First, for a weakly interacting three-dimensional Bose gas it reproduces the expected result that below the critical temperature the superfluid fraction closely follows the condensate fraction. Second, it allows a clear quantitative differentiation of the superfluid and the condensate density in a strongly interacting Bose gas.
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 propose a method to directly measure the complex phase distribution, superfluid density and velocity field in an ultracold atomic superfluid. The method consists of mapping the momentum distribution of the gas to real space using matterwave focusing, and manipulating the amplitude and phase by means of tailor made optical potentials. This makes it possible to find analogues of well-known techniques in optical microscopy such as Zernike phase contrast imaging, dark field imaging and schlieren imaging. Applying these ideas directly at the level of the macroscopic wavefunction of the superfluid will allow visualization of interesting effects such as phase fluctuations and topological defects, and enable measurements of transport properties such as vorticity.