Coherent Nanostructures: Dynamics control and noise

In the last three decades the scienti c community has been attracted by the possibility of controlling quantum system, for example for quantum computing or quantum simulators. Initially this idea was exploited only in microscopic quantum system as atoms and molecules. However these sys-tems present diffi culties on the large scale application due to the extreme laboratory condition that they need, for example ultra low temperature of the order of 1 microKelvin. On the other hand, great progress has been made with superconducting nanodevices, that can be more easily scaled. One of the most important problems that arise in quantum control is decoherence. We will study quantum control for coherent superconducting nanodevices. This devices are aff ected by a Broad Band Colored and Structured (BBCS) noise, which is qualitatively di fferent to what encountered in atomic physics, since it is chatacterized by a strong non-Markovian low-frequency component with a characteristic power spectrum S (f) proportional to 1/f. In this thesis we will present a roundup of physical situations, inolving both undriven and externally driven open quantum systems, which need to be analyzed in the perspective of quantum control. Promising applications to superconducting nanodevices, as the implementation of "Lambda" systems, possibly allowing control of microwawe photons, are discussed in detail. The thesis is structured as follows. Chapter 1 is an overview of the theoretical background of quantum control and quantum computation. In chapter 2 an archetypical problem for driven quantum systems, namely the Rabi problem, is studied in the presence of BBCS low-frequency noise which is not accounted for in standard Master Equation treatments based on the Markovian assumption. In chapter 3 a protocol named STImulated Raman Adiabatic Passage (STIRAP) is studied in the presence of BBCS noise, in view of its implementation in a class of superconducting nanode-vices named Cooper Pair Box. This is done in chapter where Design and control requirements to achieve large e fficiency are discussed, and a new figure of merit is introduced to characterize the tradeoff between effi cient coupling of the control and noise. Actually selection rules due to charge-parity simmetry make impossible operate STIRAP in these device in the regime of maximum protection from noise. Therefore in chapter 5 we propose a new implementation of STIRAP with superconductive device that allows us to circumvent selection rules, based on three-photon coherent processes and suitable crafted pulses compensating the Stark shifts. In chapter 6 we will study the problem of the tunneling of a quantum particle with strongly coupled environment in a bistable pontential. Finally in chapter 7 the study of the motion of a chiral quasiparticle in graphene a ffected by white noise will be presented.