Quantum phases of quadrupolar Fermi gases in coupled one-dimensional systems

Abstract

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 systems, and derive the quantum phase diagram of ultra-cold fermionic atoms interacting via quadrupole-quadrupole interaction 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 θ c B,1 and θ c B,2 between 0 to π/2, where the intratube quadrupolar interactions vanish and change signs. Adopting a pseudo-spin language with regards to the two 1D systems, the system undergoes a spin-gap transition and displays a zig-zag density pattern, above θ c B,2 and below θ c B,1 . 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.

Triplet superfluidity on a triangular ladder with dipolar fermions

“…In a one dimensional optical lattice, bosonization study has shown triplet superfluid (TSF) phase for dipolar fermions 53 . TSF phase is also found in two coupled one dimensional systems for quadrupolar Fermi gas 54 . Interestingly, mixture of triplet and singlet superfluidity has also been shown in a quasi-one dimensional system with two component fermions 55 .…”

“…It has been found that the external electric and microwave fields on optical lattices can control quantum many body interactions parameters of dipolar systems and polar molecules [6][7][8][9] . It has been argued that the long range and anisotropic characters of the dipolar interactions, in fact, can provide various types of exotic phases like, charge-density wave (CDW; even though the density modulation is produced by charge neutral atoms or molecules, it is called CDW in the literature) [10][11][12] , spin density wave (SDW; spin order for pseudo-spin-1/2 of dipolar fermions, shown in schematic of Fig.2(a)) 13,14 , liquid-crystal 15,16 , conventional and unconventional fermionic superfluids [17][18][19][20][21][22] , to name a few.…”

Simultaneous dipole and quadrupole moment contribution in the Bogoliubov spectrum: Application of the non-integral Gross–Pitaevskii equation

“…Earlier papers on this subject are focused on quantum phases of quadrupolar Fermi gases located in different traps [15], [16]. A nonlinear Schrodinger equation was applied to consider solitons in quantum gases with the long-range quadrupolequadrupole interaction [14].…”

Exotic roton excitations in quadrupolar Bose–Einstein condensates

“…Finally, although the quadrupolequadrupole interactions are of shorter range compared to the dipole-dipole ones [15], particles possessing electric quadrupole moments, such as Cs 2 [23] or Sr 2 [24,25], are readily available in experiments at higher densities, compared to dipolar species. Among the exciting properties of the quadrupole-quadrupole interactions is their peculiar anisotropy, which, combined with their broad tunability, paves the way to observing novel quantum phases in ultracold experiments [19][20][21].…”