Quantum dynamics of periodically driven superconducting nanocircuits

From the introduction: [...] In this thesis we investigate the effect of a periodic external driving on the transport properties of superconducting nanocircuits. We mainly focus on the properties of the Cooper pair shuttle. We will however consider also quantum dynamics of several superconducting grains connected in series by means of Josephson junctions, i.e. a Josephson junction chain. We will pay a particular attention to the role of a chain in transferring quantum information. The thesis is organized as follows. In Chapter 1 we introduce the relevant physics of superconducting nanocircuits. The main effect we discuss is the coherent transfer of Cooper pairs due to the Josephson effect. We consider the Josephson effect in bulk superconductors and then in mesoscopic systems where charging effects become important. In the rest of the thesis we discuss the effect of the external periodic driving on superconducting nanocircuit. It is divided into two parts. The first part is dedicated to the transport properties of the Cooper pair shuttle. We explore both charge (Chapters 2 and 3) and Josephson (Chapter 4) dominated regimes. In the first regime we are mostly interested in the effect of decoherence on the Josephson current. They are presented in Chapter 2 where we also propose a possible nonmechanical realization of the Cooper pair shuttle’s physics. Charge transfer in the Cooper pair shuttle is achieved as a result of an out of equilibrium process due to the mechanical motion usually associated with dissipation. The role of coherent Cooper pair transfer in presence of dissipation is the key issue in Chapter 3 where we calculate the current noise. We determine the whole current distribution function by means of the formalism of the Full Counting Statistic which is reviewed in Appendix A. The opposite limit, where the Josephson energy dominates over the charging energy, is investigated in Chapter 4. In this case the Cooper pair shuttle behaves like a quantum kicked rotator, which is a chaotic system in the classical limit. We discuss how the Cooper pair shuttle can be used to observe characteristic features of classically chaotic quantum system and we investigate the effect of the chaotic dynamics on the transport properties of the shuttle. In the second part we analyze a Josephson junctions chain as a channel for quantum information transfer. We investigate the transfer of a quantum state between the two ends of the chain and we discuss a protocol to measure the transferred state. We include in the Appendices C, D, E all the technical discussions and calculations. Appendices A and B have a different role: They are extensive introductions to the subject of full counting statistics and quantum dynamics of classically chaotic system respectively. They are not the main topic of this PhD thesis, but turn out to be of some importance for what is discussed in Chapters 3 and 4.