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arXiv:1205.1086 · Physical Review A

Antiferrosmectic ground state of two-component dipolar Fermi gases: An analog of meson condensation in nuclear matter

Kenji Maeda, Tetsuo Hatsuda, Gordon Baym

Published Feb 22, 2013• 14 citations
arXivHTMLPDF

Abstract

We show that an antiferrosmectic-$C$ phase has lower energy at high densities than the nonmagnetized Fermi gas and ferronematic phases in an ultracold gas of fermionic atoms, or molecules, with large magnetic dipole moments. This phase, which is analogous to meson condensation in dense nuclear matter, is a one-dimensional periodic structure in which the fermions localize in layers with their pseudospin direction aligned parallel to the layers and staggered layer by layer.

DOI
10.1103/physreva.87.021604

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We show that an antiferrosmectic-CCC phase has lower energy at high densities than the nonmagnetized Fermi gas and ferronematic phases in an ultracold gas of fermionic atoms, or molecules, with large magnetic dipole moments. This phase, which is analogous to meson condensation in dense nuclear matter, is a one-dimensional periodic structure in which the fermions localize in layers with their pseudospin direction aligned parallel to the layers and staggered layer by layer.
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We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive 1/r31/{r}^{3}1/r3 potential. This model can be realized with ultracold atoms or molecules when their dipole moments are aligned in the confinement direction orthogonal to the plane. We characterize the unpolarized mixture by means of the diffusion Monte Carlo technique. Computing the equation of state, we identify the regime of validity for a mean-field theory based on a low-density expansion and compare our results with the hard-disk model of repulsive fermions. At high density, we address the possibility of itinerant ferromagnetism, namely, whether the ground state can be fully polarized in the fluid phase. Within the fixed-node approximation, we show that the accuracy of Jastrow-Slater trial wave functions, even with the typical two-body backflow correction, is not sufficient to resolve the relevant energy differences. By making use of the iterative-backflow improved trial wave functions, we observe no signature of a fully polarized ground state up to the freezing density.
This thesis is devoted to the study of quantum liquid crystal phases in metallic systems and itinerant Fermi systems with dipole-dipole interactions. It is based on published works of Refs. [65, 193, 68, 67, 66]. In the first part of the Thesis, I present the construction of a generalization of the the McMillan- de Gennes theory of nematic-smectic thermal phase transition of classical liquid crystals to describe an analogous quantum phase transition in metallic systems. This theory qualitatively can also describe similar quantum phase transitions in high Tc superconductors. Recent experimental advances in cooling atoms with large electric or magnetic moment[125] make possible the study of novel quantum phases that arise due to the anisotropic and long-range nature of the dipole-dipole interactions. In the next part of the Thesis I present a Landau Fermi liquid theory of one-component Fermi systems with electric or magnetic dipolar interactions. I use this theory to construct an order parameter theory and predict elongated Fermi surface(FS) along the polarization axis. I calculate the temperature and interaction dependence of FS distortions. For a two-component system with magnetic dipole-dipole interactions I predict the existence of “spin textures” in momentum space and of prolate/oblate deformed FS’s. This constitutes a new phase of matter I called ferronematic. Possible observation of this phase in ultracold Fermi gases with large mangnetic moments
Using a combination of results from exact mappings and from mean-field theory we explore the phase diagram of quasi-one-dimensional systems of identical fermions with attractive dipolar interactions. We demonstrate that at low density these systems provide a realization of a single-component one-dimensional Fermi gas with a generalized contact interaction. Using an exact duality between one-dimensional Fermi and Bose gases, we show that when the dipole moment is strong enough, bound many-body states exist, and we calculate the critical coupling strength for the emergence of these states. At higher densities, the Hartree--Fock approximation is accurate, and by combining the two approaches we determine the structure of the phase diagram. The many-body bound states should be accessible in future experiments with ultracold polar molecules.
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