Measuring and controlling radio-frequency quanta with superconducting circuits

In this PhD thesis, we will present the theoretical and experimental work that led to the realization of a radio-frequency circuit quantum electrodynamics system (RFcQED). In chapter 2, we provide a detailed derivation of the Hamiltonian of circuit QED formulated in the context of the Rabi model, and extract expressions for the cross-Kerr interaction. The resulting requirements for the coupling rate in RFcQED are discussed, one of them being the need to dramatically increase the coupling rate compared to typical circuit QED device. In chapter 3 we cover two experimental approaches to increasing the coupling in a circuit QED system, one making use of a high impedance resonator, the second utilizing a large coupling capacitor. In chapter 4, we combine these two approaches to implement RFcQED. Through strong dispersive coupling, we could measure individual photons in a megahertz resonator, demonstrate quantum control by cooling the resonator to the ground state or preparing Fock states, and finally observe with nanosecond resolution the re-thermalization of these states. In chapter 5 we present QuCAT or Quantum Circuit Analyzer Tool in Python, a software package that can be used for the design of circuit QED systems such as the one presented in this thesis. In chapter 6 we discuss how certain interplays between general relativity and quantum mechanics cannot be described using our current laws of physics. In particular, we show how radio-frequency mechanical oscillators are perfect candidates to perform experiments in this regime. In chapter 7 we present the prospects for coupling such mechanical oscillator to weakly anharmonic superconducting circuits such as the transmon qubit or RFcQED systems.