Spectroscopic signatures of localization with interacting photons in superconducting qubits

Putting photons to work Interacting quantum particles can behave in peculiar ways. To understand that behavior, physicists have turned to quantum simulation, in which a tunable and clean system can be monitored as it evolves under the influence of interactions. Roushan et al. used a chain of nine superconducting qubits to create effective interactions between normally noninteracting photons and directly measured the energy levels of their system. The interplay of interactions and disorder gave rise to a transition to a localized state. With an increase in the number of qubits, the technique should be able to tackle problems that are inaccessible to classical computers. Science, this issue p. 1175 A many-body spectroscopy technique based on a chain of superconducting qubits gives insight into the localization transition. Quantized eigenenergies and their associated wave functions provide extensive information for predicting the physics of quantum many-body systems. Using a chain of nine superconducting qubits, we implement a technique for resolving the energy levels of interacting photons. We benchmark this method by capturing the main features of the intricate energy spectrum predicted for two-dimensional electrons in a magnetic field—the Hofstadter butterfly. We introduce disorder to study the statistics of the energy levels of the system as it undergoes the transition from a thermalized to a localized phase. Our work introduces a many-body spectroscopy technique to study quantum phases of matter.