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Topological supersolidity of dipolar Fermi gases in a spin-dependent optical lattice

Wang, H Y, Zheng, Z, Lin Zhuang, Tai, Yonghang, Shi, J S, Liu, W M

Published Jun 24, 2026• 7 citations
Publisher

Abstract

We investigate the topological supersolid states of dIPolar Fermi gases trapped in a spin-dependent 2D optical lattice. Our results show that topological supersolid states can be achieved via the combination of topological superfluid states with the strIPe order. Different from the general held belief that supersolid state in fermionic system can only survive with simultaneous coexistence of the repulsive and attractive dIPolar interaction. We demonstrate that it can be maintained when the dIPolar interaction is attractive in both x and y direction. By adjusting the ratio of hopping amplitude between different directions and dIPolar interaction strength U, the system will undergo a phase transition among p x + IP y superfluid state, p y-wave superfluid state, and the topological supersolid state. The supersolid state in the attractive environment is proved to be stable by the positive sign of the inverse compressibility. We also design an experimental protocol to realize the staggered next-next-nearest-neighbor hopping via the laser assisted tunneling technique, which is the key to simulate the spin-dependent potential.

DOI
10.26187/deakin.20706559

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We investigate the topological supersolid states of dIPolar Fermi gases trapped in a spin-dependent 2D optical lattice. Our results show that topological supersolid states can be achieved via the combination of topological superfluid states with the strIPe order. Different from the general held belief that supersolid state in fermionic system can only survive with simultaneous coexistence of the repulsive and attractive dIPolar interaction. We demonstrate that it can be maintained when the dIPolar interaction is attractive in both x and y direction. By adjusting the ratio of hopping amplitude between different directions and dIPolar interaction strength U, the system will undergo a phase transition among p x + IP y superfluid state, p y-wave superfluid state, and the topological supersolid state. The supersolid state in the attractive environment is proved to be stable by the positive sign of the inverse compressibility. We also design an experimental protocol to realize the staggered next-next-nearest-neighbor hopping via the laser assisted tunneling technique, which is the key to simulate the spin-dependent potential.
Abstract We investigate the topological supersolid states of dipolar Fermi gases trapped in a spin-dependent 2D optical lattice. Our results show that topological supersolid states can be achieved via the combination of topological superfluid states with the stripe order. Different from the general held belief that supersolid state in fermionic system can only survive with simultaneous coexistence of the repulsive and attractive dipolar interaction. We demonstrate that it can be maintained when the dipolar interaction is attractive in both x and y direction. By adjusting the ratio of hopping amplitude between different directions and dipolar interaction strength U , the system will undergo a phase transition among p x + i p y superfluid state, p y -wave superfluid state, and the topological supersolid state. The supersolid state in the attractive environment is proved to be stable by the positive sign of the inverse compressibility. We also design an experimental protocol to realize the staggered next-next-nearest-neighbor hopping via the laser assisted tunneling technique, which is the key to simulate the spin-dependent potential.
This work addresses the study of superfluid and supersolid phases of dipolar Fermi molecules lying in a two dimensional space. The prediction of these phases, performed within a mean field analysis, results from proposing a model in which interacting Fermi molecules are confined in a bilayer array of parallel lattices with square symmetry. As a result of the repulsive intralayer and attractive interlayer interactions between dipolar molecules, a checkerboard pattern and a paired superfluid regimes can emerge. The supersolid phase is identified as the spatial coexistence of density ordered and superfluid phases. The model here proposed can be implemented within the current experimental capabilities as a function of the interlayer separation and the application of an external electric field varying the dipolar interaction between molecules.
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{p}_{x}+i{p}_{y}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{p}_{x}+i{p}_{y}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 ppp-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<10<n<10<n<1. The transition temperature of the px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid state is estimated and the implication for experiments is discussed.
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.
We analyze the coexistence of superfluid and density wave (stripe) order in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. Remarkably, the anisotropic nature of the dipolar interaction allows for such a coexistence in a large region of the zero-temperature phase diagram. In this region, the repulsive part of the interaction drives the stripe formation and the attractive part induces the pairing, resulting in a supersolid with ppp-wave Cooper pairs aligned along the stripes. From a momentum space perspective, the stability of the supersolid phase is due to the fact that the stripe order renders the Fermi surface only partially gapped, leaving gapless regions that are most important for ppp-wave pairing. We briefly discuss how this supersolid phase can be detected in time-of-flight experiments.
By means of quantum Monte Carlo simulations we study phase diagrams of dipolar bosons in a square optical lattice. The dipoles in the system are parallel to each other and their orientation can be fixed in any direction in the three-dimensional space. Starting from experimentally tunable parameters like scattering length and dipolar interaction strength, we derive the parameters entering the effective Hamiltonian. Depending on the direction of the dipoles, various types of supersolids (e.g., checkerboard, stripe) and solids (checkerboard, stripe, diagonal stripe, and an incompressible phase) can be stabilized. Remarkably, we find a cluster supersolid characterized by the formation of horizontal clusters of particles. These clusters order along a direction at an angle with the horizontal. Moreover, we find what we call a grain-boundary superfluid. In this phase, regions with solid order are separated by extended defects---grain boundaries---which support superfluidity. We also investigate the robustness of the stripe supersolid against thermal fluctuations. Finally, we comment on the experimental realization of the phases found.