Bosonic many-body localization and collective phenomena in arrays of transmon devices

Abstract Superconducting circuits are electric devices in which information can be stored and processed on quantum level. The spectrum of these devices is often anharmonic, which means that their two lowest states can be used as a qubit. Moreover, their parameters are highly versatile and their energies are in-situ tunable, they are resistant to thermal noise, and they can be controlled and measured with high accuracy. These properties make superconducting circuits promising candidates for the basic units of a quantum computer. Currently available technology does not yet allow the construction of these machines, partly due to the errors in the qubits caused by external noise. In the meantime, these circuits could be used for simpler tasks such as quantum simulations, where the behavior of a complicated quantum system is studied experimentally using a simpler system. In this thesis we study many-body phenomena in arrays of specific superconducting circuits called transmons, which we model as anharmonic oscillators in contrast to the conventional two-level approximation. In the first part of this thesis, the transmons are embedded inside a waveguide. The electromagnetic field allows the transmons to interact with each other over long distances, which results in collective effects such as correlated decay and coherent exchange interaction. Correlated decay can be observed as superradiant and subradiant states, whose properties are well known in two-level systems. The bosonic nature of transmons distinguishes them from real two-level systems by enhancing the superradiance in this setup. We model the system with a specific master equation, from which we recover a non-Hermitian effective Hamiltonian whose eigenvalues describe the radiative properties of the system. Our model is in good agreement with experimental data, showing the inadequacy of the two-level approximation. In the latter part of this thesis we study how the interplay between many-body interactions and local disorder affects the behavior of transmon arrays. With weak disorder the system obeys the laws of statistical physics, resulting in thermalization of the system. With sufficiently strong disorder the system is instead in the many-body localized phase, characterized by the absence of transport of particles and logarithmic spreading of entanglement. The transition point is probed numerically and the phase diagram for the Bose–Hubbard Hamiltonian is constructed