Quantum thermalization and optimal control are compatible in a many-body system

We propose a novel protocol for characterizing and ultimately controlling collective matter-radiation effects that emerge when a many-body quantum system is driven through a critical value of the interaction coupling strength. There are many possible ways to use our scheme to achieve quantum computing and information processing, including controlling superconducting qubits or color defects in diamond by means of quantum light in cavities. We show that apparently disparate phenomena such as thermalization, excited state quantum phase transitions and orthogonality catastrophes can be present in the system when subject to a finite pulsed coupling with the light field. In particular, we demonstrate a connection between the thermalization through entanglement of the global quantum pure system reached at the middle of the pulse, and the controlled production of an orthogonal global state at the end of the pulse. Our results should prove useful in a variety of contexts including the preparation of phases of condensed matter in quantum simulators and the engineering of states in quantum protocols.