Angelo Carollo

Geometric phase in open systems.

We calculate the geometric phase associated with the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main sources of decoherence are considered: dephasing and spontaneous decay. We show that the geometric phase is completely insensitive to the former, i.e., it is independent of the number of jumps determined by the dephasing operator.

Geometric phases and criticality in spin-chain systems

A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that corresponds to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. It is demonstrated that the resulting phase is resilient against the main sources of errors. A physical realization with ultracold atoms in optical lattices is presented.

Vacuum induced spin-1/2 Berry's phase.

We calculate the Berry phase of a spin-1/2 particle in a magnetic field considering the quantum nature of the field. The phase reduces to the standard Berry phase in the semiclassical limit and the eigenstate of the particle acquires a phase in the vacuum. We also show how to generate a vacuum induced Berry phase considering two quantized modes of the field which has an interesting physical interpretation.

Spin-1/2 geometric phase driven by decohering quantum fields.

We calculate the geometric phase of a spin-1/2 system driven by one and two mode quantum fields subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when considering adiabatic and nonadiabatic evolutions. We discuss the implications of our results from both fundamental as well as quantum computational perspectives.

Scaling of Berry's phase close to the Dicke quantum phase transition

We discuss the thermodynamic and finite-size scaling properties of the geometric phase in the adiabatic Dicke model, describing a quantum phase transition for an N qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non-zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading orders in the 1/N expansion of the Berry phase and its critical exponent.

Geometric phase induced by a cyclically evolving squeezed vacuum reservoir.

We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by adiabatically manipulating the environment with which it interacts. As a specific scheme, we analyze a multilevel atom interacting with a broadband squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We also propose a scheme to measure such a geometric phase by means of a suitable polarization detection.

Geometric phases and criticality in spin systems

A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behaviour is presented. This opens up the way for the use of geometric phases as a tool to probe regions of criticality without having to undergo a quantum phase transition. As a concrete example, a spin-1/2 chain with XY interactions is considered and the corresponding geometric phases are analysed. Finally, a generalization of these results to the case of an arbitrary spin system is presented.

Berry's phase in cavity QED: Proposal for observing an effect of field quantization

We propose a feasible experiment to investigate quantum effects in geometric phases, arising when a classical source drives not a single quantum system, but two interacting ones. In particular, we show how to observe a signature of the quantization of the electromagnetic field through a vacuum effect in Berrys phase. To do so, we describe the interaction of an atom and a quantized cavity mode altogether driven by an external quasiclassical field. We also analyze the semiclassical limit recovering the usual Berrys phase results.

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence of Gaussian and correlated fluctuations is calculated, accounting for variations in the the noise source intensity and the bias frequency. Moreover, the transient dynamics of a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian noise sources is investigated. Noise induced phenomena are observed, such as the noise enhanced stability and the stochastic resonant activation. (ii) Second, the electron spin relaxation process in a n-type GaAs bulk driven by a fluctuating electric field is investigated. In particular, by using a Monte Carlo approach, we study the influence of a random telegraph noise on the spin polarized transport. Our findings show the possibility to raise the spin relaxation length by increasing the amplitude of the external fluctuations. Moreover, we find that, crucially, depending on the value of the external field strength, the electron spin depolarization length versus the noise correlation time increases up to a plateau. (iii) Finally, the stabilization of quantum metastable states by dissipation is presented. Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system- bath coupling and the temperature, producing a stabilizing effect.

Stabilization Effects of Dichotomous Noise on the Lifetime of the Superconducting State in a Long Josephson Junction

We investigate the superconducting lifetime of a long overdamped current-biased Josephson junction, in the presence of telegraph noise sources. The analysis is performed by randomly choosing the initial condition for the noise source. However, in order to investigate how the initial value of the dichotomous noise affects the phase dynamics, we extend our analysis using two different fixed initial values for the source of random fluctuations. In our study, the phase dynamics of the Josephson junction is analyzed as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive metastable state as a function of the noise intensity is characterized by nonmonotonic behavior, strongly related to the soliton dynamics during the switching towards the resistive state. The role of the correlation time of the noise source is also taken into account. Noise-enhanced stability is observed in the investigated system.