Ultracold Atoms in a Square Lattice with Spin-Orbit Coupling: Charge Order, Superfluidity, and Topological Signatures

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Ultracold Atomic Gases

Background:

• Investigating exotic quantum phases in fermionic systems is crucial for understanding novel states of matter.
• Spin-orbit coupling in lattice systems can lead to complex emergent phenomena, including supersolidity.

Purpose of the Study:

• To perform an ab initio, numerically exact study of attractive fermions in square lattices with Rashba spin-orbit coupling.
• To characterize the charge, spin, and pairing properties of the system's ground state.
• To provide high-accuracy benchmarks for theoretical and experimental research in ultracold atoms.

Main Methods:

• Employed the auxiliary-field quantum Monte Carlo (AFQMC) method for large-scale, numerically exact calculations.
• Focused on systems with attractive interactions and Rashba spin-orbit coupling in a square lattice.

Main Results:

• Identified the ground state as a supersolid, exhibiting simultaneous charge and superfluid order.
• Determined that the superfluid component consists of both singlet and triplet pairs, induced by spin-orbit coupling.
• Provided a quantitative description of the system's charge, spin, and pairing characteristics.

Conclusions:

• The study elucidates the exotic physics of attractive fermions in lattices with spin-orbit coupling.
• Results offer crucial benchmarks for ongoing experimental efforts in ultracold atoms.
• The findings are relevant for realizing and understanding quantum Hall and topological superconductor systems.