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arXiv:1307.2151

Superfluid theory of a gas of polarized dipolar Fermi molecules

Yuki Endo, Daisuke Inotani, Yoji Ohashi

Published Jul 8, 2013• 0 citations
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Abstract

We present a superfluid theory of a polarized dipolar Fermi gas. For two dipolar molecules each of which consists of two atoms with positive charge and negative charge, we derive an effective dipole-dipole pairing interaction. Using this pairing interaction, we show that the resulting BCS gap equation is not suffered from the well-known ultraviolet divergence, so that one can quantitatively predict superfluid properties of a dipolar Fermi gas. Using this cutoff-free superfluid theory, we examine the symmetry of the superfluid order parameter at T=0. We also discuss the deformation of the Fermi surface, originating from the anisotropy of the dipole-dipole interaction.

DOI
10.48550/arxiv.1307.2151

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We present a superfluid theory of a polarized dipolar Fermi gas. For two dipolar molecules each of which consists of two atoms with positive charge and negative charge, we derive an effective dipole-dipole pairing interaction. Using this pairing interaction, we show that the resulting BCS gap equation is not suffered from the well-known ultraviolet divergence, so that one can quantitatively predict superfluid properties of a dipolar Fermi gas. Using this cutoff-free superfluid theory, we examine the symmetry of the superfluid order parameter at T=0. We also discuss the deformation of the Fermi surface, originating from the anisotropy of the dipole-dipole interaction.
We present a superfluid theory of a polarized dipolar Fermi gas with an effective dipole-dipole pairing interaction. Treating each dipole as a molecule consisting of two atoms with opposite charges to each other, we show that the well-known ultraviolet divergence in the theory of dipolar Fermi superfluids can be eliminated without introducing any cutoff prescription. Using this cutoff-free superfluid theory, we discuss how the deformation of the Fermi surface coming from the anisotropic nature of the dipole-dipole interaction affects the superfluid order parameter at T = 0.
We examine the superfluid and collapse instabilities of a quasi-two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipole-dipole interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii-Kosterlitz-Thouless temperature as a function of the dipole angle.
Abstract Advances in semiconductor nanostructures have enabled the creation of ultra-cold dipolar fermions, offering a new frontier for exploring many-body fermionic physics. By manipulating electric dipole interactions in these systems, we demonstrate the possibility of cooling and condensing particles. The anisotropic nature of dipole interactions leads to an anisotropic Fermi liquid state, distinct from the isotropic standard, and supports unconventional Cooper pair symmetries involving both singlet and triplet states. Long-range dipolar interactions foster strong correlations within the system. Employing methods such as Gaussian expansion and random-phase-approximation, we analyze how anisotropy influences the spectrum, collective excitations, and correlation functions. In particular, we derive the screened interaction and the polarization function, and we investigate the pairing instability via the Bethe–Salpeter equation in the ladder approximation. The critical temperature for superfluidity is obtained as function of the effective coupling strength. We discuss the the conditions for attractive pairing, the expected order parameter symmetry, and the role of confinement dimensionality. Our results provide a theoretical framework for understanding dipolar Fermi gases in nanostructures and highlight the possibility of realizing unconventional superfluid phases.
We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with equal density. The interplay of the isotropic sss-wave interaction and anisotropic long-range dipolar interaction reveals rich physics. We find that the single-particle momentum distribution has a characteristic ellipsoidal shape that can be reasonably represented by a deformation parameter $\ensuremath{\alpha}$ defined similarly to the normal phase. Interesting momentum-dependent features of the order parameter are identified. We calculate the critical temperatures of both the singlet and triplet superfluids, suggesting a possible pairing symmetry transition by tuning the sss-wave or dipolar interaction strength.
We present a detailed study of the BCS pairing transition in a trapped polarized dipolar Fermi gas. In the case of a shallow nearly spherical trap, we find a decrease in the transition temperature as a function of the trap aspect ratio and predict the existence of the optimal trap geometry. The latter corresponds to the highest critical temperature of the BCS transition for a given number of particles. We also derive the phase diagram for an ultracold trapped dipolar Fermi gas in the situation where the trap frequencies can be of the order of the critical temperature of the BCS transition in the homogeneous case, and determine the critical value of the dipole–dipole interaction energy below which the BCS transition ceases to exist. The critical dipole strength is obtained as a function of the trap aspect ratio. Alternatively, for a given dipole strength, there is a critical value of the trap anisotropy for the BCS state to appear. The order parameter calculated at criticality exhibits novel non-monotonic behaviour resulting from the combined effect of the confining potential and the anisotropic character of the interparticle dipole–dipole interaction.