Quantum Optical Neural Network with Multimode Cavity QED*

The ability to engineer inter-particle interaction is at the heart of quantum simulation of many-body systems. However, the necessary nonlocal interaction in complex neural networks poses challenges to traditional implementation of ultracold atoms quantum simulators. We present our theoretical and experimental studies of photon-mediated interactions with atoms trapped inside a multimode confocal cavity. Superposition of different photon modes with incommensurate spatial profiles gives rise to a sign-changing and non-local interaction. Through numerical simulations, we show that the connectivity resulting from such non-local interaction will allow us to explore spin models featuring an associative memory to spin glass transition. In addition, the dissipative cavity photon dynamics facilitate more efficient spin relaxation to low energy states than the textbook Glauber dynamics. Combined with our recent experimental demonstration of cavity-mediated spin-spin interaction and characterization of the non-local interaction, a quantum optical neural network is within our reach.