Bose-Hubbard models with synthetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Ultracold Atomic Gases

Background:

• Synthetic spin-orbit coupling is experimentally realized in ultracold atoms, enabling novel quantum simulations.
• The Bose-Hubbard model describes interacting bosons on a lattice, crucial for understanding phases like Mott insulator and superfluid.

Purpose of the Study:

• Investigate the phase diagram of the 2D Bose-Hubbard model with synthetic spin-orbit coupling and non-Abelian gauge fields.
• Explore emergent magnetic Hamiltonians and their associated textures in the Mott insulator phase.
• Analyze the influence of these magnetic orders on superfluid phases and charge patterns.

Main Methods:

• Strong coupling expansion to derive effective magnetic Hamiltonians.
• Inhomogeneous mean-field treatment to study superfluid properties.
• Slave-boson theory to understand intertwined spin-charge orders.

Main Results:

• Identified diverse magnetic Hamiltonians in the Mott insulator phase, supporting spin spirals and vortex/Skyrmion crystals.
• Demonstrated that superfluid phases inherit these magnetic orders.
• Observed unusual modulated current patterns in superfluid phases due to intertwined spin-charge orders.

Conclusions:

• The study reveals rich magnetic phases and intertwined spin-charge orders in ultracold atomic systems with synthetic spin-orbit coupling.
• These findings provide a theoretical framework for understanding complex quantum magnetism and superfluidity.
• Proposed experimental signatures in Bragg scattering, microscopy, and dynamic quenches to verify these exotic orders.