Quantum behavior in mesoscopic systems

In this thesis I present the work done during my PhD. The Thesis is divided into two parts; in the first one I present the study of mesoscopic quantum systems whereas in the second one I address the problem of the definition of Markov regime for quantum system dynamics. The first work presented is the study of vortex patterns in (quasi) two dimensional rotating Bose Einstein condensates (BECs). I consider the case of an anisotropy trapping potential and I shall show that the ground state of the system hosts vortex patterns that are unstable. In a second work I designed an experimental scheme to transfer entanglement from two entangled photons to two BECs. This work is meant to propose a feasible experimental set up to bring entanglement from microscopic to macroscopic systems for both the study of fundamental questions (quantum to classical transition) and technological applications. In the last work of the first part another experimental scheme is presented in order to detect coherences of a mechanical oscillator which is assumed to have been previously cooled down to the quantum regime. In this regime in fact the system can rapidly undergo decoherence so that new techniques have to be employed in order to detect and manipulate their states. In the scheme I propose a micro-mechanical oscillator is coupled to a BEC and the detection is performed by monitoring the BEC with a negligible back-action on the cantilever. In the second part of the thesis I give a definition of Markov regime for open quantum dynamics. The importance of such definition comes from both the mathematical description of the system dynamics and from the understanding of the role played by the environment in the evolution of an open system. In the Markov regime the mathematical description can be simplified and the role of the environment is a passive one.

Creation of a complex butterfly attractor using a novel Lorenz-type system

A novel Lorenz-type system of nonlinear differential equations is proposed. Unlike the original Lorenz system, where the chaotic dynamics remain confined to the positive half-space with respect to the Z state variable due to a limiting threshold effect, the proposed system enables bipolar swing of this state variable. In addition, the classical set of parameters (a, b, c) controlling the behavior of the Lorenz system are reduced to a single parameter, namely a. Two possible modes of operation are admitted by the system; switching between these two modes results in the creation of a complex butterfly chaotic attractor. Numerical simulations and results from an experimental setup are presented

Spatial and energetic mode dynamics of cold atomic systems

In this thesis we relate the formal description of various cold atomic systems in the energy eigenbasis, to the observable spatial mode dynamics. Herein the `spatial mode dynamics' refers to the direction of photon emission following the spontaneous emission of an excited fermion in the presence of a same species and spin ideal anisotropic Fermi sea in its internal ground state. Due to the Pauli principle, the presence of the ground state Fermi sea renders the phase space, anisotropic and only partially accessible, thereby a ecting the direction of photon emission following spontaneous emission. The spatial and energetic mode dynamics also refers to the quantum `tunneling' interaction between localised spatial modes, synonymous with double well type potentials. Here we relate the dynamics of the wavefunction in both the energetic and spatial representations. Using this approach we approximate the relationship between the spatial and energetic representations of a wavefunction spanning three spatial and energetic modes. This is extended to a process known as Spatial Adiabatic Passage, which is a technique to transport matter waves between localised spatial modes. This approach allows us to interpret the transport of matter waves as a signature of a geometric phase acquired by the one of the internal energy eigenstates of the system during the cyclical evolution. We further show that this geometric phase may be used to create spatial mode qubit and qutrit states.

The Rpf/DSF system and the regulation of virulence in the plant pathogen Xanthomonas campestris

The full virulence of Xanthomonas campestris pv. campestris (Xcc) to plants depends upon cell-to-cell signalling mediated by the signal molecule DSF (for diffusible signal factor), that has been characterised as cis-11-methyl-2-dodecenoic acid. DSF-mediated signalling regulates motility, biofilm dynamics and the synthesis of particular virulence determinants. The synthesis and perception of the DSF signal molecule involves products of the rpf (regulation of pathogenicity factors) gene cluster. DSF synthesis is fully dependent on RpfF, which encodes a putative enoyl-CoA hydratase. A two-component system, comprising the complex sensor histidine kinase RpfC and the HD-GYP domain regulator RpfG, is implicated in DSF perception. The HD-GYP domain of RpfG is a phosphodiesterase working on cyclic di-GMP; DSF perception is thereby linked to the turnover of this intracellular second messenger. The full range of regulatory influences of the Rpf/DSF system and of cyclic di-GMP in Xcc has yet to be established. In order to further characterise the Rpf/DSF regulatory network in Xcc, a proteomic approach was used to compare protein expression in the wildtype and defined rpf mutants. This work shows that the Rpf/DSF system regulates a range of biological functions that are associated with virulence and biofilm formation but also reveals new functions mediated by DSF regulation. These functions include antibiotic resistance, detoxification and stress tolerance. Mutational analysis showed that several of these regulated protein functions contribute to virulence in Chinese radish. Interestingly, it was demonstrated that different patterns of protein expression are associated with mutations of rpfF, rpfC and rpfG. This suggests that RpfG and RpfC have broader roles in regulation other than perception and transduction of DSF. Taken together, this analysis indicates the broad and complex regulatory role of Rpf/DSF system and identifies a number of new functions under Rpf/DSF control, which were shown to play a role in virulence.