Ultracold atoms in a square lattice with spin-orbit coupling: Charge order, superfluidity, and topological signatures

Abstract

We present an $\text{ab initio}$, numerically exact study of attractive fermions in square lattices with Rashba spin-orbit coupling. The ground state of this system is a supersolid, with co-existing charge and superfluid order. The superfluid is composed of both singlet and triplet pairs induced by spin-orbit coupling. We perform large-scale calculations using auxiliary-field quantum Monte Carlo to provide the first full, quantitative description of the charge, spin, and pairing properties of the system. In addition to characterizing the exotic physics, our results will serve as essential high-accuracy benchmarks for the intense theoretical and especially experimental efforts in ultracold atoms to realize and understand an expanding variety of quantum Hall and topological superconductor systems.

6 pages, 4 figures

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• Interplay between singlet and triplet pairings in multi-band two-dimensional oxide superconductors
• Ab initio Calculations in Atoms, Molecules, and Solids, Treating Spin-Orbit Coupling and Electron Interaction on Equal Footing
• Nature of the mixed-parity pairing of attractive fermions with spin-orbit coupling in optical lattice
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• Robust Dynamics of Rogue waves, Breathers and Mixed Bound State Solutions in Spin-Orbit and Rabi Coupled Condensates
• Weyl semimetallic, Néel, spiral, and vortex states in the Rashba-Hubbard model
• Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update
• Precision thermodynamics of the strongly interacting Fermi gas in two dimensions
• Spin-orbit coupled periodic Anderson model: Kondo-Dirac semimetal and orbital-selective antiferromagnetic semimetal