Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate regardless of parameter values\,? The energy spectrum of a system can answer this question and reveal the nature of the underlying phases. However, most experimental techniques only indirectly probe the many-body energy spectrum. Using a chain of nine superconducting qubits, we implement a novel technique for directly resolving the energy levels of interacting photons. We benchmark this method by capturing the intricate energy spectrum predicted for 2D electrons in a magnetic field, the Hofstadter butterfly. By increasing disorder, the spatial extent of energy eigenstates at the edge of the energy band shrink, suggesting the formation of a mobility edge. At strong disorder, the energy levels cease to repel one another and their statistics approaches a Poisson distribution - the hallmark of transition from the thermalized to the many-body localized phase. Our work introduces a new many-body spectroscopy technique to study quantum phases of matter.
Pedram Roushan received his PhD in 2011 from Princeton University, performing the first scanning tunneling microscopy on the surface of topological insulators in the lab of A. Yazdani. After three years of post-doctoral studies in the J. Martinis lab at the University of California, Santa Barbara, in 2014 he joined the Google quantum hardware lab aiming on making a quantum computer. The current focus of his research is on simulating condensed matter systems with engineered quantum platforms and controlling dynamics in quantum systems.