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arXiv:1207.3153 · Physical Review A

Magnetostriction and exchange effects in trapped dipolar Bose and Fermi gases

D. Baillie, P. B. Blakie

Published Aug 6, 2012• 14 citations
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Abstract

We examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. Direct interactions give rise to position space magnetostriction and exchange interactions give rise to momentum space magnetostriction. While the position space magnetostriction is similar in Bose and Fermi systems, the momentum space magnetostriction is markedly different: The Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short-range correlations between the particles we discuss the energetic origin of this difference. Our main calculations are based on Hartree-Fock theory, but we also provide analytic approximations for the magnetostriction effects at zero and finite temperature. Our predictions should be verifiable in current experiments with ultracold polar molecules.

DOI
10.1103/physreva.86.023605

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We examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. Direct interactions give rise to position space magnetostriction and exchange interactions give rise to momentum space magnetostriction. While the position space magnetostriction is similar in Bose and Fermi systems, the momentum space magnetostriction is markedly different: The Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short-range correlations between the particles we discuss the energetic origin of this difference. Our main calculations are based on Hartree-Fock theory, but we also provide analytic approximations for the magnetostriction effects at zero and finite temperature. Our predictions should be verifiable in current experiments with ultracold polar molecules.
We develop and apply meanfield methods to two systems of significant interest in cold atom physics. The first system, and the main subject of this thesis, is a gas of polarized dipoles, in which the particles have a long range anisotropic interaction. The second system is a toroidally trapped gas that interacts via short range interactions. \n \nDipolar gases: We develop accurate techniques for dipolar Bose and Fermi gases accounting for both direct and exchange interactions. We detail an efficient numerical implementation of the meanfield treatment. \n \nWe study the thermodynamic and the first and second order correlation properties of the system. We find that exchange interactions cause the correlation functions to be anisotropic in the low temperature regime. We also find that many uniform gas thermodynamic predictions, for which direct interaction effects vanish, are qualitatively unreliable for trapped systems, most notably for oblate traps. \n \nUsing Hartree-Fock theory and analytic approximations, we examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. The Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short range correlations between the particles we discuss the energetic origin of this difference. \n \nIntroducing local momentum distortion fields, we develop a practical Hartree-Fock theory in which exchange effects are described by a local effective potential. This theory is applicable at zero and finite temperature, and is in excellent agreement with full Hartree-Fock calculations. \n \nContact gases: We show how considerable simplification of numerical results and analytical derivations can be achieved in the local density approximation using a variety of density of states techniques. \n \nWe examine the process of isentropic loading of a Bose or Fermi gas from a harmonic trap into the scale invariant toroidal regime that exhibits a high degree of system invariance when increasing the radius of the toroid. For bosons a regime of cooling is identified and we find that the Fermi gas is subjected to irreducible heating during loading, caused by the loss of one degree of freedom for thermalization.
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 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 calculate the stability diagram for a trapped normal Fermi or Bose gas with dipole-dipole interactions. Our study characterizes the roles of trap geometry and temperature on the stability using Hartree-Fock theory. We find that exchange appreciably reduces stability and that, for bosons, the double instability feature in oblate trapping geometries predicted previously is still predicted by the Hartree-Fock theory. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate or degenerate Fermi gas.
Finite fermion systems are known to exhibit shell structure in the weakly interacting regime, as is well known from atoms, nuclei, metallic clusters, or even quantum dots in two dimensions. All these systems have in common that the particle interactions between electrons or nucleons are spatially isotropic. Dipolar quantum systems as they have been realized with ultracold gases, however, are governed by an intrinsic anisotropy of the two-body interaction that depends on the orientation of the dipoles relative to each other. Here we investigate how this interaction anisotropy modifies the shell structure in a weakly interacting two-dimensional anisotropic harmonic trap. Going beyond Hartree-Fock analysis by applying the so-called importance-truncated configuration-interaction (CI) method as well as quadratic CI with single and double substitutions, we show how the magnetostriction in the system may be counteracted upon by a deformation of the confinement.