Implementation of the Deutsch-Jozsa algorithm with Josephson charge qubits

We investigate the realization of a simple solid-state quantum computer by implementing the Deutsch-Jozsa algorithm in a system of Josephson charge qubits. Starting from a procedure to carry out the one-qubit Deutsch-Jozsa algorithm we show how the N-qubit version of the Bernstein-Vazirani algorithm can be realized. For the implementation of the three-qubit Deutsch-Jozsa algorithm we study in detail a setup which allows to produce entangled states.Comment: accepted for publication in Journal of Modern Optic

Phase diagram of the extended Bose Hubbard model

By means of the Density Matrix Renormalization Group technique, we accurately determine the zero-temperature phase diagram of the one-dimensional extended Bose Hubbard model with on-site and nearest-neighbor interactions. We analyze the scaling of the charge and of the neutral ground-state energy gaps, as well as of various order parameters. In this way we come to an accurate location of the boundaries between the superfluid and the insulating phases. In this last region we are able to distinguish between the conventional Mott insulating and density-wave phases, and the Haldane Insulator phase displaying long-range string ordering, as originally predicted by E.G. Dalla Torre, E. Berg and E. Altman in Phys. Rev. Lett. 97, 260401 (2006).Comment: 13 pages, 6 figures. To appear in NJP, in the focus issue on "Bose Condensation Phenomena in Atomic and Solid State Physics

Entanglement and magnetic order

In recent years quantum statistical mechanics have benefited of cultural interchanges with quantum information science. There is a bulk of evidence that quantifying the entanglement allows a fine analysis of many relevant properties of many-body quantum systems. Here we review the relation between entanglement and the various type of magnetic order occurring in interacting spin systems.Comment: 29 pages, 10 eps figures. Review article for the special issue "Entanglement entropy in extended systems" in J. Phys. A, edited by P. Calabrese, J. Cardy and B. Doyo

Resonant Andreev Tunneling in Strongly Interacting Quantum Dots

We study resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We obtain a formula for the Andreev current and apply it to discuss the linear and non-linear transport in the nonperturbative regime, where the effects of the Kondo resonance on the two particle tunneling arise. In particular we notice an enhancement of the Kondo anomaly in the $I-V$ characteristics due to the superconducting electrode.Comment: 13 pages Revtex, 3 figures .p

Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities

By means of analytical and numerical methods we analyze the phase diagram of polaritons in one-dimensional coupled cavities. We locate the phase boundary, discuss the behavior of the polariton compressibility and visibility fringes across the critical point, and find a non-trivial scaling of the phase boundary as a function of the number of atoms inside each cavity. We also predict the emergence of a polaritonic glassy phase when the number of atoms fluctuates from cavity to cavity.Comment: 4 pages, 5 figures. Published versio

Flux Noise near the Berezinskii-Kosterlitz-Thouless Transition

We study the flux noise in Josephson junction arrays in the critical regime above the Berezinskii-Kosterlitz-Thouless transition. In proximity coupled arrays a local ohmic damping for the phases is relevant, giving rise to anomalous vortex diffusion and a dynamic scaling of the flux noise in the critical region. It shows a crossover from white to $1/f$-noise at a frequency $\omega_\xi\propto\xi^{-z}$ with a dynamic exponent $z=2$.Comment: Revised version to be published in JETP Letter

Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities

By means of analytical and numerical methods we analyze the phase diagram of polaritons in one-dimensional coupled cavities. We locate the phase boundary, discuss the behavior of the polariton compressibility and visibility fringes across the critical point, and find a non-trivial scaling of the phase boundary as a function of the number of atoms inside each cavity. We also predict the emergence of a polaritonic glassy phase when the number of atoms fluctuates from cavity to cavity.Comment: 4 pages, 5 figures. Published versio

Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks

Josephson junction arrays are ideal model systems where a variety of phenomena, phase transitions, frustration effects, vortex dynamics, chaos, to mention a few of them, can be studied in a controlled way. In this review we focus on the quantum dynamical properties of low capacitance Josephson junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated to the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy cost to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single electron effects with the Josephson effect. One example is the (quantum) Superconductor-Insulator phase transition which occurs by varying the ratio between the coupling constants and/or by means of external magnetic/electric fields. We will describe how the phase diagram depends on the various control paramters and the transport properties close to the quantum critical point. The relevant topological excitations on the superconducting side of the phase diagram are vortices. In low capacitance junction arrays vortices behave as massive underdamped particles that can exhibit quantum behaviour. We will report on the various experiments and theoretical treatments on quantum vortex dynamics.Comment: To be published in Physics Reports. Better quality figures can be obtained upon reques

Coulomb-interaction effects in full counting statistics of a quantum-dot Aharonov-Bohm interferometer

We study the effect of Coulomb interaction on the full counting statistics of an Aharonov-Bohm (AB) interferometer with a single-level quantum dot in one arm in the regime of weak dot-lead and lead-lead tunnel couplings. In the absence of Coulomb interaction, the interference processes are of nonresonant nature with an even AB flux dependence and obey bidirectional Poissonian statistics. For large charging energy, the statistic of these processes changes. In addition, processes of resonant nature with an odd flux dependence appear. In the limit of strongly asymmetric tunnel couplings from the dot to the left and right leads, their statistics is found to be strongly super-Poissonian.Comment: 8 pages, 3 figure