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arXiv:1008.0514 · Physical Review A

Anisotropic superfluidity in the two-species polar Fermi gas

Renyuan Liao, Joachim Brand

Published Dec 20, 2010• 13 citations
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Abstract

We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with equal density. The interplay of the isotropic $s$-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 $s$-wave or dipolar interaction strength.

DOI
10.1103/physreva.82.063624

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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 \ensuremathα\ensuremath{\alpha}\ensuremathα 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.
A mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate is considered in which sss-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction long-range and anisotropic in nature and tunable by the dipolar interaction. It is shown that such an interaction can significantly increase the prospect of realizing a superfluid with a gap parameter characterized with a coherent superposition of all odd partial waves. In the spirit of the Hartree-Fock-Bogoliubov mean-field approach, a theory is formulated that allows the estimation of the critical temperature when the anisotropic Fock potential is taken into consideration and the determination of the system parameters that optimize the critical temperature at which such a superfluid emerges before the system begins to phase separate.
It is known from the solution of the two-body problem that an anisotropic dipolar interaction can give rise to s-wave scattering resonances, which are named dipolar interaction induced resonances (DIIR). In this Letter, we study the zero-temperature many-body physics of a two-component Fermi gas across a DIIR. In the low-density regime, it is very striking that the resulting pairing order parameter is a nearly isotropic singlet pairing and the physics can be well described by an s-wave resonant interaction potential with finite range conditions, despite the anisotropic nature of the dipolar interaction. The pairing energy is as strong as a unitary Fermi gas near a magnetic Feshbach resonance. In the high-density regime, the anisotropic effect plays an important role. We find phase transitions from singlet pairing to a state with mixed singlet and triplet pairing and then from mixed pairing to pure triplet pairing. The state with mixed pairing spontaneously breaks the time-reversal symmetry.
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.
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.