The capability to create and control strong and coherent matter-light Hamiltonians forms the basis of much of the modern activities in quantum optics and quantum information science (QIS). An important paradigm is found in the setting of the strong coupling regime of cavity QED (cQED), which encompasses and approximates all other forms of quantized atom-field interactions both parametrically and perturbatively. In laymen’s term, this is the regime in which a laser could be operated with just one quanta shared between a gain medium consisting of one atom and threshold energy of one photon. A critical distinction to a conventional laser is that the statistics describing photons leaving and persisting in the optical cavity manifestly differs from that of classical light, in that optical nonlinearity can also be scaled down to single excitations. Remarkable developments in cavity QED have been made in quantum optics and QIS to enlarge our understanding of atom-field interactions but also to formulate framework in which quantum networks and computations can take place (e.g., quantum gates in trapped ions & circuit QED) since its introduction to the strong coherent coupling regime by Jeff Kimble, Serge Haroche, and Herbert Walther. A fundamental problem with cavity QED and all related forms of atom-field quantum systems is that the degree of non-classicality does not scale with the system size, due to the inherent linearization (mean-field) of the original quantum model. That is, the physics describing the atom-field quantum systems generically becomes classical for any reasonable system size.

**Many-body QED**

We have initiated a new regime of atom-light interaction, many-body QED. Taken simply, “many-body” QED can be summarized as the coupling of quantized cavity fields with a quantum many-body system. The “many-body” aspect of our work differentiates from the conventional cavity QED and their siblings in that many-body interactions induce (gauge) constraints as artificial background fields, on top of which dynamics can be introduced by the underlying atom- field interactions. Within the gauge sector of interest, a new Hamiltonian emerges that may depart significantly from the microscopic QED description. For instance, we have developed a framework, where a universal quantum simulator can emerge within the dissipative gauge sector and evolve in “imaginary time.” This implies that it becomes possible to develop a recipe for ground-state cooling of arbitrary quantum materials, without adiabatic evolution. We plan to apply this dissipative gauge fixing of many-body QED to imaginary-time quantum systems that emulates computationally complex Hamiltonians (e.g., spin glasses).