Probing the Degree of Coherence through the Full 1D to 3D Crossover.

We experimentally study a gas of quantum degenerate ^{87}Rb atoms throughout the full dimensional crossover, from a one-dimensional (1D) system exhibiting phase fluctuations consistent with 1D theory to a three-dimensional (3D) phase-coherent system, thereby smoothly interpolating between these distinct, well-understood regimes. Using a hybrid trapping architecture combining an atom chip with a printed circuit board, we continuously adjust the system's dimensionality over a wide range while measuring the phase fluctuations through the power spectrum of density ripples in time-of-flight expansion. Our measurements confirm that the chemical potential µ controls the departure of the system from 3D and that the fluctuations are dependent on both µ and the temperature T. Through a rigorous study we quantitatively observe how inside the crossover the dependence on T gradually disappears as the system becomes 3D. Throughout the entire crossover the fluctuations are shown to be determined by the relative occupation of 1D axial collective excitations.

Critical Transport and Vortex Dynamics in a Thin Atomic Josephson Junction.

We study the onset of dissipation in an atomic Josephson junction between Fermi superfluids in the molecular Bose-Einstein condensation limit of strong attraction. Our simulations identify the critical population imbalance and the maximum Josephson current delimiting dissipationless and dissipative transport, in quantitative agreement with recent experiments. We unambiguously link dissipation to vortex ring nucleation and dynamics, demonstrating that quantum phase slips are responsible for the observed resistive current. Our work directly connects microscopic features with macroscopic dissipative transport, providing a comprehensive description of vortex ring dynamics in three-dimensional inhomogeneous constricted superfluids at zero and finite temperatures.

Integrable Floquet Hamiltonian for a Periodically Tilted 1D Gas.

An integrable model subjected to a periodic driving gives rise generally to a nonintegrable Floquet Hamiltonian. Here we show that the Floquet Hamiltonian of the integrable Lieb-Liniger model in the presence of a linear potential with a periodic time-dependent strength is instead integrable and its quasienergies can be determined using the Bethe ansatz approach. We discuss various aspects of the dynamics of the system at stroboscopic times and we also propose a possible experimental realization of the periodically driven tilting in terms of a shaken rotated ring potential.

Thermalization processes induced by quantum monitoring in multilevel systems.

We study the heat statistics of a multilevel N-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number M of measurements (M→∞). In this context, the conditions allowing for an infinite-temperature thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the nonequilibrium evolution of the system and its initial state. Exceptions to ITT, which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasicommuting) with the Hamiltonian of the quantum system or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N→∞), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits M→∞ and N→∞ matters: When N is fixed and M diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A nontrivial result is obtained fixing M/N^{2} where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented.

Expectation values in the Lieb-Liniger Bose gas.

We present a novel method to compute expectation values in the Lieb-Liniger model both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas.

Josephson junction arrays with Bose-Einstein condensates.

We report on the direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the interwell barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.

One-dimensional long-range percolation: A numerical study.

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C/r^{d+σ}, where r is the distance length between distinct sites and d=1. We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value C_{c} at which percolation occurs. The critical exponents in the range 0<σ<1 are reported. Our analysis is in agreement, up to a numerical precision ≈10^{-3}, with the mean-field result for the anomalous dimension η=2-σ, showing that there is no correction to η due to correlation effects. The obtained values for C_{c} are compared with a known exact bound, while the critical exponent ν is compared with results from mean-field theory, from an expansion around the point σ=1 and from the ɛ-expansion used with the introduction of a suitably defined effective dimension d_{eff} relating the long-range model with a short-range one in dimension d_{eff}. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with σ>0.

Superfluid flow above the critical velocity.

Superfluidity and superconductivity have been widely studied since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current flow in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are a critical rotation rate and a critical velocity respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be completely restored for specific, arbitrarily large flow velocities above the critical velocity through quantum interference-induced resonances providing a nonlinear counterpart of the Ramsauer-Townsend effect occurring in ordinary quantum mechanics. We illustrate the robustness of this phenomenon through a thorough analysis in one dimension and prove its generality by showing the persistence of the effect in non-trivial 2d systems. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing.

Topological filters and high-pass/low-pass devices for solitons in inhomogeneous networks.

We show that, by inserting suitable finite networks at a site of a chain, it is possible to realize filters and high-pass/low-pass devices for solitons propagating along the chain. The results are presented in the framework of coupled optical waveguides; possible applications to different contexts, such as photonic lattices and Bose-Einstein condensates in optical networks are also discussed. Our results provide a first step in the control of the soliton dynamics through the network topology.

Discrete nonlinear Schrödinger equation with defects.

We investigate the dynamical properties of the one-dimensional discrete nonlinear Schrödinger equation (DNLS) with periodic boundary conditions and with an arbitrary distribution of on-site defects. We study the propagation of a traveling plane wave with momentum k: the dynamics in Fourier space mainly involves two localized states with momenta +/-k (corresponding to a transmitted and a reflected wave). Within a two-mode ansatz in Fourier space, the dynamics of the system maps on a nonrigid pendulum Hamiltonian. The several analytically predicted (and numerically confirmed) regimes include states with a vanishing time average of the rotational states (implying complete reflections and refocusing of the incident wave), oscillations around fixed points (corresponding to quasi-stationary states), and, above a critical value of the nonlinearity, self-trapped states (with the wave traveling almost undisturbed through the impurity). We generalize this treatment to the case of several traveling waves and time-dependent defects. The validity of the two-mode ansatz and the continuum limit of the DNLS are discussed.

Nonlinear self-trapping of matter waves in periodic potentials.

We report the first experimental observation of nonlinear self-trapping of Bose-condensed 87Rb atoms in a one-dimensional waveguide with a superimposed deep periodic potential . The trapping effect is confirmed directly by imaging the atomic spatial distribution. Increasing the nonlinearity we move the system from the diffusive regime, characterized by an expansion of the condensate, to the nonlinearity dominated self-trapping regime, where the initial expansion stops and the width remains finite. The data are in quantitative agreement with the solutions of the corresponding discrete nonlinear equation. Our results reveal that the effect of nonlinear self-trapping is of local nature, and is closely related to the macroscopic self-trapping phenomenon already predicted for double-well systems.

Propagation of discrete solitons in inhomogeneous networks.

In many physical applications solitons propagate on supports whose topological properties may induce new and interesting effects. In this paper, we investigate the propagation of solitons on chains with a topological inhomogeneity generated by inserting a finite discrete network on a chain. For networks connected by a link to a single site of the chain, we derive a general criterion yielding the momenta for perfect reflection and transmission of traveling solitons and we discuss solitonic motion on chains with topological inhomogeneities.

Discrete nonlinear dynamics of weakly coupled Bose-Einstein condensates.

The dynamics of a Bose-Einstein condensate trapped in a periodic potential is governed by a discrete nonlinear equation. The interplay/competition between discreteness (introduced by the lattice) and nonlinearity (due to the interatomic interaction) manifests itself on nontrivial dynamical regimes which disappear in the continuum (translationally invariant) limit, and have been recently observed experimentally. We review some recent efforts on this highly interdisciplinary field, with the goal of stimulating interexchanges among the communities of condensed matter, quantum optics, and nonlinear physics.

Discrete solitons and breathers with dilute Bose-Einstein condensates.

We study the dynamical phase diagram of a dilute Bose-Einstein condensate (BEC) trapped in a periodic potential. The dynamics is governed by a discrete nonlinear Schrödinger equation: intrinsically localized excitations, including discrete solitons and breathers, can be created even if the BEC's interatomic potential is repulsive. Furthermore, we analyze the Anderson-Kasevich experiment [Science 282, 1686 (1998)], pointing out that mean field effects lead to a coherent destruction of the interwell Bloch oscillations.

Superfluidity versus disorder in the discrete nonlinear Schrödinger equation.

We study the discrete nonlinear Schrödinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective nonrigid pendulum Hamiltonian. The different regimes include the complete reflection and refocusing of the initial wave, solitonic structures, and a superfluid state. In the superfluid regime, which occurs above a critical value of nonlinearity, a plane wave travels coherently through the randomly distributed defects. This superfluidity criterion for the DNLS is analogous to (yet very different from) the Landau superfluidity criteria in translationally invariant systems. Experimental implications for the physics of Bose-Einstein condensate gases trapped in optical potentials and of arrays of optical fibers are discussed.

Dynamical superfluid-insulator transition in a chain of weakly coupled bose-Einstein condensates.

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the condensates coherently oscillate in the array. For large displacements, the condensates remain localized on the side of the harmonic trap with a randomization of the relative phases. The superfluid-insulator transition is due to a discrete modulational instability, occurring when the condensate center of mass velocity is larger than a critical value.