Many-Body Cavity QED

What is a quantum neural network and how might it exhibit computational advantage? Can we create a spin glass made of atomic spins and photons and use it to resolve longstanding mysteries surrounding spin-glass order? Could BEC matter waves interacting via photons mimic the quantum liquid crystals found in high-Tc superconductors? If so, what might we learn? We are tackling these fundamental and technologically relevant questions using our novel multimode cavity QED-BEC apparatus. The system provides strong, photon-mediated interactions among atoms trapped within the cavity resonator.  Photons virtually scattered among the atoms cause the system to superradiate and self-organize into various exotic forms of quantum matter such as quantum spin glasses---which can be used as quantum neural networks---and quantum liquid crystals. We have recently demonstrated the necessary ingredients needed to realize these exotic systems. Moreover, we are investigating whether quantum neural networks based on these driven-dissipative quantum systems may provide for finding solutions to NP-hard optimization problems.