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arXiv:0902.0739 · New Journal of Physics

Biaxial nematic phases in ultracold dipolar Fermi gases

Benjamin M. Fregoso, Kai Sun, Eduardo Fradkin, Benjamin Lev

Published Oct 2, 2009• 78 citations
arXivHTMLPDF

Abstract

Ultracold dipolar Fermi gases represent relatively unexplored, strongly correlated systems arising from long-range and anisotropic interactions. We demonstrate the possibility of a spontaneous symmetry breaking biaxial phase in these systems, which may be realized in, e.g., gases of ultracold polar molecules or strongly magnetic atoms. This biaxial nematic phase is manifest in a spontaneous distortion of the Fermi surface perpendicular to the axis of polarization. We describe these dipolar interaction induced phases using Landau Fermi liquid theory.

DOI
10.1088/1367-2630/11/10/103003

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Ultracold dipolar Fermi gases represent relatively unexplored, strongly correlated systems arising from long-range and anisotropic interactions. We demonstrate the possibility of a spontaneous symmetry breaking biaxial phase in these systems, which may be realized in, e.g., gases of ultracold polar molecules or strongly magnetic atoms. This biaxial nematic phase is manifest in a spontaneous distortion of the Fermi surface perpendicular to the axis of polarization. We describe these dipolar interaction induced phases using Landau Fermi liquid theory.
We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the ${d}_{{r}^{2}\ensuremath{-}3{z}^{2}}$ type in three dimensions and of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tridiagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal ppp-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.
Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density-wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x\text{\ensuremath{-}}y$ plane) with dipoles pointing to the zzz direction. We determine the phase diagram using two complementary methods, the Hartree-Fock mean-field theory and the linear-response analysis of compressibility. Both give consistent results. In addition to the staggered $(\ensuremath{\pi},\ensuremath{\pi})$ density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken fourfold (C4)({C}_{4})(C4​) rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the Van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well-defined excitation. Experimental implications of our results are discussed.
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
Long-range anisotropic dipole-dipole interactions between ultracold polar molecules are predicted to drive exotic quantum phases, yet direct many-body signatures of these interactions in degenerate Fermi gases have remained elusive. Here, we report the observation of an interaction-induced controlled deformation of the Fermi surface, providing a clear many-body signature in a deeply degenerate Fermi gas of 23Na40K^{23}\text{Na}^{40}\text{K}23Na40K molecules. Using double microwave (MW) shielding, we prepare 8×1038 \times 10^38×103 molecules at 0.23(1)0.23(1)0.23(1) times the Fermi temperature, achieving a three-fold suppression of inelastic losses compared to single MW shielding while preserving strong elastic dipolar scattering. We observe Fermi surface deformations of up to 7 %7\,\%7%, more than two times larger than those observed in magnetic atoms, despite operating at two orders of magnitude lower densities. Crucially, we demonstrate continuous tuning of the interaction potential from axial U(1) to biaxial C2_{2}2​ symmetry, directly imprinting this geometry onto the Fermi surface. We find excellent agreement between our experimental results and parameter-free Hartree-Fock theory. These results establish MW-shielded polar molecules as a highly tunable platform for exploring strongly correlated dipolar Fermi matter and offer a promising path towards topological superfluidity.
Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: weakly interacting Bose gases, weakly interacting Fermi gases, multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D and quasi-1D geometries. Within each of these topics, purely dipolar effects and connections with experimental realizations are emphasized.
We investigate Fermi liquid states of the ultracold magnetic dipolar Fermi gases in the simplest two-component case including both thermodynamic instabilities and collective excitations. The magnetic dipolar interaction is invariant under the simultaneous spin-orbit rotation but not under either the spin or the orbit one. Therefore, the corresponding Fermi liquid theory is intrinsically spin-orbit coupled. This is a fundamental feature of magnetic dipolar Fermi gases different from electric dipolar ones. The Landau interaction matrix is calculated and is diagonalized in terms of the spin-orbit coupled partial-wave channels of the total angular momentum JJJ. The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with J=1+J={1}^{+}J=1+ and the spin-current mode with $J={1}^{\ensuremath{-}}$, where +++ and $\ensuremath{-}$ represent even and odd parities, respectively. An exotic propagating collective mode is identified as spin-orbit coupled Fermi surface oscillations in which spin distribution on the Fermi surface exhibits a topologically nontrivial hedgehog configuration.