Quantum state control with a superconducting qubit

This thesis explores circuit quantum electrodynamics (circuit QED), an experimental platform for studying fundamental quantum-optics phenomena in the microwave regime. For the realization of a quantum processor, this architecture offers the advantage of scalability and the use of technologies similar to those used in the semiconductor industry. The circuit QED system studied in this thesis is called transmon, and it consists of a superconducting qubit (a tunable artificial atom) coupled to a one-dimensional coplanar waveguide resonator. The qubit can be designed to have a very large electric dipole moment, leading to the strong coupling regime which was hard to reach in optical cavity QED. The main motivation of this thesis is to study the quantum states that can be prepared using this device and how they can be manipulated under various types of modulation. In the early 1980s, Richard Feynman proposed that quantum computers would be useful in performing powerful computational tasks and could perform simulations of interacting quantum many-body systems. In this light, the thesis starts by exploring novel ways of designing gate sequences. The quest to understand if there are fundamental limitations for the speeding-up of standard quantum algorithms prompted us to discover a new quantum impossibility result: the quantum no-reflection theorem. Next, we present our experimental results obtained with the transmon. We discuss the physics of dispersive coupling between the qubit and resonator and we explore the nonlinearities induced by the presence of the qubit when the resonator is strongly driven. Then, the thesis presents the first steps taken in the direction of simulating many-body quantum systems, where the motional averaging observed in NMR based systems was simulated in a circuit QED architecture. By changing the modulation of the qubit from random to periodic latching, we observe a Stückelberg interference spectrum in a strong nonadiabatic regime where the Landau-Zener formula is not valid. Finally, the last chapter of the thesis is devoted to the presentation of our experimental results on quantum state control, from Rabi oscillations to stimulated Raman adiabatic passage.