Shining Light on Bose-Hubbard Models: From Equilibrium Theory to Exotic Steady States

The Bose–Hubbard model is a cornerstone of quantum many-body physics, capturing the interplay between kinetic energy and interactions in lattice boson systems. In equilibrium, effective field-theoretical approaches highlight the role of Berry-phase-like terms and reveal the nature of collective excitations across the superfluid–Mott transition. I will first review these equilibrium insights. I will then turn to discuss a minimal Bose-Hubbard model under a chiral drive implemented by light carrying finite orbital angular momentum. This drive introduces a new control knob, chirality, that qualitatively reshapes the phase diagram. Strikingly, the system evolves toward non-trivial driven-dissipative steady states that exhibit quantum-chaotic dynamics. Together, these two threads bridge insights from equilibrium field theory with the physics of driven steady states, giving insights into the structure of the collective excitations and showing how light can be used to engineer, destabilize, and ultimately control complex quantum phases. Experimental platforms ranging from cold atoms to polariton condensates and superconducting circuits may offer promising routes for realizing these ideas.