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arXiv:1006.2072

Superfluid Phases of Dipolar Fermions in Harmonically Trapped Optical Lattices

Dog̃a Murat Kürkçüog̃lu, Han Li, C. A. R. Sá de Melo

Published Jun 10, 2010• 0 citations

Abstract

We describe the emergence of superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at intermediate and larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally arise in the singlet channel: local s-wave $(sl)$, extended s-wave $(se)$, d-wave $(d)$ or time-reversal-symmetry breaking $(sl + se \pm id)$-wave. We obtain the temperature versus filling factor phase diagram and show that d-wave pairing is favored near half-filling, that $(sl + se)$-wave is favored near zero or full filling, and that time-reversal-breaking $(sl + se \pm id)$-wave is favored in between. The inclusion of a harmonic trap reveals that a sequence of phases can coexist in the cloud depending on the filling factor at the center of the trap. Most notably in the spatial region where the $(sl + se \pm id)$-wave superfluid occurs, spontaneous currents are generated, and may be detected using velocity sensitive Bragg spectroscopy.

DOI: 10.48550/arxiv.1006.2072

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We describe the emergence of superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at intermediate and larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally arise in the singlet channel: local s-wave

(sl)

, extended s-wave

(se)

, d-wave

(d)

or time-reversal-symmetry breaking

(sl + se \pm id)

-wave. We obtain the temperature versus filling factor phase diagram and show that d-wave pairing is favored near half-filling, that

(sl + se)

-wave is favored near zero or full filling, and that time-reversal-breaking

(sl + se \pm id)

-wave is favored in between. The inclusion of a harmonic trap reveals that a sequence of phases can coexist in the cloud depending on the filling factor at the center of the trap. Most notably in the spatial region where the

(sl + se \pm id)

-wave superfluid occurs, spontaneous currents are generated, and may be detected using velocity sensitive Bragg spectroscopy.

In a dipolar Fermi gas, the dipole-dipole interaction between fermions can be turned into a dipolar Ising interaction between pseudospins in the presence of an ac electric field. When trapped in a two-dimensional optical lattice, this dipolar Fermi gas has a very rich phase diagram at zero temperature, due to the competition between antiferromagnetism and superfluidity. At half-filling, the antiferromagnetic state is the favored ground state. The superfluid state appears as the ground state at a smaller filling factor. In between there is a phase-separated region. The order parameter of the superfluid state can display different symmetries depending on the filling factor and interaction strength, including the

d

-wave (

d

), the extended

s

-wave (

xs

), or their linear combination (

xs+id

). Implications for the current experiment are discussed.

We study a system of ultracold fermionic polar molecules in a two-dimensional square lattice interacting via both the long-range dipole-dipole interaction and a short-range on-site attractive interaction. Singlet-superfluid, change density wave, and supersolid phases are found to exist in the system. We map out the zero-temperature phase diagram and find that the supersolid phase is considerably stabilized by the dipole-dipole interaction and thus can exist over a large region of filling factors. We study the melting of the supersolid phase with increasing temperature, map out a finite-temperature phase diagram of the system at fixed filling, and determine the parameter region where the supersolid phase can possibly be observed in experiments.

We examine antiferromagnetic and

d

-wave superfluid phases of cold fermionic atoms with repulsive interactions in a two-dimensional optical lattice combined with a harmonic trapping potential. For experimentally realistic parameters, the trapping potential leads to the coexistence of magnetic and superfluid ordered phases with the normal phase. We study the intriguing shell structures arising from the competition between the magnetic and superfluid order as a function of the filling fraction. In certain cases, antiferromagnetism induces superfluidity by charge redistributions. We furthermore demonstrate how these shell structures can be detected as distinct antibunching dips and pairing peaks in the density-density correlation function probed in expansion experiments.

We consider dipolar fermions in a two-dimensional square lattice and a harmonic trapping potential. The anisotropy of the dipolar interaction combined with the lattice leads to transitions between phases with density order of different symmetries. We show that the attractive part of the dipolar interaction results in a superfluid phase that is suppressed by density order. The trapping potential is demonstrated to make the different phases coexist, forming ring and island structures. The phases with density and superfluid order can overlap, forming regions with supersolid order.

Many-body effects on superfluidity and transition temperatures are calculated for optical lattices and uniform systems with ultracold multi-component Fermi gases. The induced interactions depend sensitively on the interactions between the multi-components and their densities. The s- and d-wave pairing gaps and critical temperatures are calculated for optical lattices at low (dilute) filling as well as near half filling to leading orders in the interaction strength with and without induced interactions. They can deviate strongly from dilute two-component systems and affect the phase diagram. In two dimensional optical lattices the induced interactions are singular at half filling and strongly affect s- and d-wave superfluidity.

We explore in this paper a harmonically trapped asymmetric fermionic superfluid in a two-dimensional optical lattice with pairing interactions between the neighboring sites, by self-consistently solving Bogliubov--de Gennes equations. We find the superfluid generally phase separates into a

d

-wave pairing component and an extended

s

-wave pairing one, mixed with the unpaired normal fermions. For sufficient large number asymmetries, the ground state is found to be a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state without fourfold rotational symmetry. Both the

d

-wave and

s

-wave order parameters show spatially varying novel patterns with nodal points or nodal lines. These features are expected to be checked by the experiments on the repulsive ultracold fermionic atoms.