We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.
We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.
Following the recent proposal to create quadrupolar gases [Bhongale et al., Phys. Rev. Lett. 110, 155301 (2013)], we investigate what quantum phases can be created in these systems in one dimension. We consider a geometry of two coupled one-dimensional (1D) systems, and derive the quantum phase diagram of ultracold fermionic atoms interacting via quadrupole-quadrupole interactions within a Tomonaga-Luttinger-liquid framework. We map out the phase diagram as a function of the distance between the two tubes and the angle between the direction of the tubes and the quadrupolar moments. The latter can be controlled by an external field. We show that there are two magic angles ${\ensuremath{\theta}}_{B,1}^{c}$ and ${\ensuremath{\theta}}_{B,2}^{c}$ between 0 and $\ensuremath{\pi}/2$, where the intratube quadrupolar interactions vanish and change signs. Adopting a pseudospin language with regard to the two 1D systems, the system undergoes a spin-gap transition and displays a zigzag density pattern, above ${\ensuremath{\theta}}_{B,2}^{c}$ and below ${\ensuremath{\theta}}_{B,1}^{c}$. Between the two magic angles, we show that polarized triplet superfluidity and a planar spin-density-wave order compete with each other. The latter corresponds to a bond-order solid in higher dimensions. We demonstrate that this order can be further stabilized by applying a commensurate periodic potential along the tubes.
Ultracold Fermi molecules lying in 2D square optical lattices bilayers with its dipole moment perpendicularly aligned to the layers, having interlayer finite range s‐wave interactions, are shown to form superfluid phases, both, in the Bardeen, Cooper and Schrieffer (BCS) regime of Cooper pairs, and in the condensate regime of bound dimeric molecules. We demonstrate this result using a functional integral scheme within the Ginzburg‐Landau theory. For the deep Berezinskii‐Kosterlitz‐Thouless (BKT) phase transition, we predict critical temperatures around 5nK and 20nK for 23Na40K and OH molecules, which are within reach of current experiments [J. W. Park, S. Will and M. Zwierlein, Phys. Rev. Lett. 114, 205302 (2015)]. image
Abstract In this manuscript, we discuss the emergence of p-wave superfluidity in a dipolar Fermi gas confined in a double layer array of parallel optical lattices in two dimensions. The dipole moments of the molecules placed at the sites of the optical lattices, separated a distance L and pointing in opposite directions produce an effective attractive interaction among them, except between those dipoles situated one on top of the other. Such interaction between dipoles is precisely the origin of the non-conventional superfluid state. We present the analysis for the ground state of the many-body system within the mean-field scheme. In particular, we study the stable regions, as a function of the system parameters, namely the effective interaction between dipoles and the filling factor n, for which the superfluid state can exist. Following the BKT scheme, we estimate the critical temperature of the superfluid state.
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.
In a dipolar Fermi gas, the anisotropic interaction between electric dipoles can be turned into an effectively attractive interaction in the presence of a rotating electric field. We show that the topological px+ipy superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a two-dimensional square optical lattice with this attractive interaction at low temperatures. The px+ipy superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. When the interaction is weak, the p-wave superfluid state is stable for most filling factors except near half filling, where phase separation takes place. In the weak-coupling limit, the phase-separation region vanishes. When the interaction strength is above a threshold, the system is phase separated for any filling factor 0<n<1. The transition temperature of the px+ipy superfluid state is estimated and the implication for experiments is discussed.
We show that unconventional spin order arises naturally in two-component dipolar Fermi gases of atoms or molecules, which recently became accessible experimentally, in optical lattices. Using an unbiased functional renormalization-group analysis, we find that dipolar interactions lead to an instability of the gas toward an $\ensuremath{\ell}=1$ spin-density wave state. This phase is the particle-hole analog of spin-triplet, p-wave Cooper pairs. The order parameter for such spin-density waves of p-wave orbital symmetry is a vector in spin space and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half filling on the square lattice as a function of the dipolar orientation and discuss how these exotic spin-density waves emerge amidst competition with superfluid and charge-density wave phases.