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arXiv:1103.1818 · Physical Review A

Nonequilibrium and local detection of the normal fraction of a trapped two-dimensional Bose gas

Iacopo Carusotto, Yvan Castin

Published Nov 29, 2011• 9 citations
arXivHTMLPDF

Abstract

We propose a method to measure the normal fraction of a two-dimensional Bose gas, a quantity that generally differs from the noncondensed fraction. The idea is based on applying a spatially oscillating artificial gauge field to the atoms. The response of the atoms to the gauge field can be read out either mechanically from the deposited energy into the cloud or optically from the macroscopic optical properties of the atomic gas. The local nature of the proposed scheme allows one to reconstruct the spatial profile of the superfluid component; furthermore, the proposed method does not require having established thermal equilibrium in the gas in the presence of the gauge field. The theoretical description of the system is based on a generalization of the Dum-Olshanii theory of artificial gauge fields to the interacting many-body context. The efficiency of the proposed measurement scheme is assessed by means of classical field numerical simulations. An explicit atomic level scheme minimizing disturbing effects such as spontaneous emission and light shifts is proposed for ${}^{87}\mathrm{Rb}$ atoms.

DOI
10.1103/physreva.84.053637

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We propose a method to measure the normal fraction of a two-dimensional Bose gas, a quantity that generally differs from the noncondensed fraction. The idea is based on applying a spatially oscillating artificial gauge field to the atoms. The response of the atoms to the gauge field can be read out either mechanically from the deposited energy into the cloud or optically from the macroscopic optical properties of the atomic gas. The local nature of the proposed scheme allows one to reconstruct the spatial profile of the superfluid component; furthermore, the proposed method does not require having established thermal equilibrium in the gas in the presence of the gauge field. The theoretical description of the system is based on a generalization of the Dum-Olshanii theory of artificial gauge fields to the interacting many-body context. The efficiency of the proposed measurement scheme is assessed by means of classical field numerical simulations. An explicit atomic level scheme minimizing disturbing effects such as spontaneous emission and light shifts is proposed for 87Rb{}^{87}\mathrm{Rb}87Rb atoms.
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 study experimentally and numerically the equilibrium density profiles of a trapped two-dimensional 87Rb^{87}\mathrm{Rb}87Rb Bose gas and investigate the equation of state of the homogeneous system using the local density approximation. We find a clear discrepancy between in situ measurements and quantum Monte Carlo simulations, which we attribute to a nonlinear variation of the optical density of the atomic cloud with its spatial density. However, good agreement between experiment and theory is recovered for the density profiles measured after time of flight, taking advantage of their self-similarity in a two-dimensional expansion.
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We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-fluid--superfluid phase transition point. We establish relations between basic thermodynamic functions: density $n(T,\ensuremath{\mu})$, superfluid density ${n}_{s}(T,\ensuremath{\mu})$, and condensate density ${n}_{\text{cnd}}(T,\ensuremath{\mu})$. Being universal for all weakly interacting ${\ensuremath{\mid}\ensuremath{\psi}\ensuremath{\mid}}^{4}$ systems, these relations are obtained from Monte Carlo simulations of the classical ${\ensuremath{\mid}\ensuremath{\psi}\ensuremath{\mid}}^{4}$ model on a lattice. Comparing with the mean-field results yields a quantitative estimate of the fluctuation region size. Away from the fluctuation region, on the superfluid side, all the data perfectly agree with the predictions of the quasicondensate mean-field theory. This demonstrates that the only effect of the leading above-the-mean-field corrections in the condensate-based treatments is to replace the condensate density with the quasicondensate one in all local thermodynamic relations. Surprisingly, we find that a significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.
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