Many-Body Cavity QED

Investigations of many-body physics in an AMO context often employ a static optical lattice to create a periodic potential.  Such systems, while capable of exploring, e.g., the Hubbard model, lack the fully emergent crystalline order found in solid state systems whose stiffness is not imposed externally, but arises dynamically.  Our multimode cavity QED experiment introduces fully emergent and compliant optical lattices to the ultracold atom toolbox and provides new avenues to explore beyond mean-field physics and quantum soft matter.  Quantum liquid crystals, superglasses, spin glasses, and Hopfield associative memory may arise due to the oscillatory, frustrated, and tunable-range interactions mediated by the optical cavity modes.  Coherent neural networks based on the quantum phase transtions in these driven, dissipative spin systems may prove powerful for computing solutions to NP-hard combinatorial optimization problems.