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Journal of the Physical Society of Japan

Statistical Difference in the Normal Phase of the Dipolar Ultracold Gases at Finite Temperatures

Yuki Endo, Takahiko Miyakawa, Tetsuro Nikuni

Published Apr 12, 2011• 4 citations
Publisher

Abstract

We study the equilibrium properties of dipolar Bose and Fermi gases at finite temperatures. We have recently developed a variational ansatz for the phase-space distribution function of a dipolar Fermi gas at finite temperatures. We extend the variational formalism to a Bose gas and discuss the effect of dipolar interactions with different statistics on thermal equilibrium, with particular emphasis on deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and dipole moment. In addition, we discuss how deformation in both real and momentum spaces can be observed in the high-temperature regime, which is relevant for the current experiments at JILA [Ni et al. : Science 322 (2008) 231] and at the University of Tokyo [Aikawa et al. : New J. Phys. 11 (2009) 055035].

DOI
10.1143/jpsj.80.044006

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We study the equilibrium properties of dipolar Bose and Fermi gases at finite temperatures. We have recently developed a variational ansatz for the phase-space distribution function of a dipolar Fermi gas at finite temperatures. We extend the variational formalism to a Bose gas and discuss the effect of dipolar interactions with different statistics on thermal equilibrium, with particular emphasis on deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and dipole moment. In addition, we discuss how deformation in both real and momentum spaces can be observed in the high-temperature regime, which is relevant for the current experiments at JILA [Ni et al. : Science 322 (2008) 231] and at the University of Tokyo [Aikawa et al. : New J. Phys. 11 (2009) 055035].
We study the equilibrium properties of dipolar Bose and Fermi gases at finite temperatures. We recently developed a variational ansatz for the phase-space distribution function of a dipolar Fermi gas at finite temperatures. We extend the variational formalism to a Bose gas and discuss the effect of dipolar interactions with different statistics on the thermal equilibrium, with particular emphasis on the deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio and the dipole moment. In addition, we discuss how deformation in both real and momentum space can be observed in the high-temperature regime, which is relevant for the current experiments at JILA [Ni et al. Science 322, 231 (2008)] and at University of Tokyo [Aikawa et al. New. J. Phys. 11, 055035 (2009)].
We study the equilibrium properties of dipolar Fermi gases at finite temperatures. We introduce a variational ansatz for the phase-space distribution function that can describe the deformation in both real and momentum space. The effect of dipole-dipole interactions on thermal equilibrium is discussed, with particular emphasis on the deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and dipole moment. In addition, we discuss how the deformation in both real and momentum space can be observed in the high-temperature regime, which is relevant to the current experiment at JILA (Institute for Laboratory Astrophysics) [K. K. Ni et al., Science 322, 231 (2008)].
Based on the semiclassical theory, we investigate the thermodynamic properties of a dipolar Fermi gas. Through a self-consistent procedure, we numerically obtain the phase-space distribution function at finite temperature. We show that the deformations in both momentum and real space become smaller and smaller as the temperature is increased. For the homogeneous case, we also calculate pressure, entropy, and heat capacity. In particular, at the low-temperature limit and in the weak interaction regime, we obtain an analytic expression for the entropy which agrees qualitatively with our numerical result. The stability of a trapped gas at finite temperature is also explored.
We investigate the dynamical properties of a trapped finite-temperature normal Fermi gas with dipole-dipole interaction. For the free-expansion dynamics, we show that the expanded gas always becomes stretched along the direction of the dipole moment. In addition, we present the temperature and interaction dependences of the asymptotic aspect ratio. We further study the collapse dynamics of the system by suddenly increasing the dipolar interaction strength. We show that, in contrast to the anisotropic collapse of a dipolar Bose-Einstein condensate, a dipolar Fermi gas always collapses isotropically when the system becomes globally unstable. We also explore the interaction and temperature dependences for the frequencies of the low-lying collective excitations.
Under the framework of the semiclassical theory, we investigate the equilibrium-state properties of a spin polarized dipolar Fermi gas through full numerical calculation. We show that the Fermi surfaces in both real and momentum spaces are stretched along the attractive direction of dipolar interaction. We further verify that the deformed Fermi surfaces can be well approximated by ellipsoids. In addition, the deformation parameters slightly depend on the local real- and momentum-space densities. We also study the interaction strength dependence of the energy and real- and momentum-space densities. By comparing them with variational results, we find that the ellipsoidal ansatz usually generates accurate results for weak dipolar interaction, while under strong dipolar interaction limit, notable discrepancy can be observed. Finally, we map out the stability boundary of the system.