Andrea Trombettoni

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 BECs 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.

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.

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.

Nonlinear tight-binding approximation for Bose-Einstein condensates in a lattice

The dynamics of Bose-Einstein condensates trapped in a deep optical lattice is governed by a discrete nonlinear equation (DNL). Its degree of nonlinearity and the intersite hopping rates are retrieved from a nonlinear tight-binding approximation taking into account the effective dimensionality of each condensate. We derive analytically the Bloch and the Bogoliubov excitation spectra and the velocity of sound waves emitted by a traveling condensate. Within a Lagrangian formalism, we obtain Newtonian-like equations of motion of localized wave packets. We calculate the ground-state atomic distribution in the presence of a harmonic confining potential, the frequencies of small amplitude dipole, and quadrupole oscillations. We finally quantize the DNL, recovering an extended Bose-Hubbard model.

Relativistic Bose-Einstein Condensates: a New System for Analogue Models of Gravity

In this paper we propose to apply the analogy between gravity and condensed matter physics to relativistic Bose?Einstein condensates (RBECs), i.e. condensates composed by relativistic constituents. While such systems are not yet a subject of experimental realization, they do provide us with a very rich analogue model of gravity, characterized by several novel features with respect to their non-relativistic counterpart. Relativistic condensates exhibit two (rather than one) quasi-particle excitations, a massless and a massive one, the latter disappearing in the non-relativistic limit. We show that the metric associated with the massless mode is a generalization of the usual acoustic geometry allowing also for non-conformally flat spatial sections. This is relevant, as it implies that these systems can allow the simulation of a wider variety of geometries. Finally, while in non-RBECs the transition is from Lorentzian to Galilean relativity, these systems represent an emergent gravity toy model where Lorentz symmetry is present (albeit with different limit speeds) at both low and high energies. Hence they could be used as a test field for better understanding the phenomenological implications of such a milder form of Lorentz violation at intermediate energies.

Josephson effect in fermionic superfluids across the BEC-BCS crossover.

Simulating electronic transport with atoms Two superconductors connected by a bridge made out of nonsuperconducting material form a so-called Josephson junction (see the Perspective by Belzig). Valtolina et al. replaced the superconductors with two reservoirs of a superfluid Fermi gas and connected them by a weak link to allow atoms to move from one side to the other. Then they made one reservoir more populated than the other and studied the ensuing dynamics as a function of interaction strength between the atoms. In a related experiment, Husmann et al. kept the interaction strength at its maximum, but varied the temperature and the properties of the link. As temperature increased, the superfluid disappeared and thermal transport took over. Science, this issue p. 1498, p. 1505; see also p. 1470 The effects of interaction strength are studied in a junction composed of two 6Li superfluids. [Also see Perspective by Belzig] The Josephson effect is a macroscopic quantum phenomenon that reveals the broken symmetry associated with any superfluid state. Here we report on the observation of the Josephson effect between two fermionic superfluids coupled through a thin tunneling barrier. We show that the relative population and phase are canonically conjugate dynamical variables throughout the crossover from the molecular Bose-Einstein condensate (BEC) to the Bardeen-Cooper-Schrieffer (BCS) superfluid regime. For larger initial excitations from equilibrium, the dynamics of the superfluids become dissipative, which we ascribe to the propagation of vortices through the superfluid bulk. Our results highlight the robust nature of resonant superfluids.

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.

One-dimensional Lieb-Liniger Bose gas as nonrelativistic limit of the sinh-Gordon model

The repulsive Lieb-Liniger model can be obtained as the nonrelativistic limit of the sinh-Gordon model: all physical quantities of the latter model (S-matrix, Lagrangian, and operators) can be put in correspondence with those of the former. We use this mapping, together with the thermodynamical Bethe ansatz equations and the exact form factors of the sinh-Gordon model, to set up a compact and general formalism for computing the expectation values of the Lieb-Liniger model both at zero and finite temperatures. The computation of one-point correlators is thoroughly detailed and when possible compared with known results in the literature.

(3+1) massive Dirac fermions with ultracold atoms in frustrated cubic optical lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a cubic optical lattice in a frustrating magnetic field which can be realized by rotating the lattice or, alternatively, using a synthetic gauge field. We show that it is possible to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse: the method relies on the peculiar position of the Dirac points in the (magnetic) Brillouin zone, and it would not generally work for other lattices (e.g., for honeycomb lattices). A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. Finally, we also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions.

Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials

We show that non-Abelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with non-Abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: The non-Abelian part of the vector potential makes the Landau levels nondegenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-Abelian quantum Hall states appear: These ground states, including deformed Moore-Read states (characterized by Ising anyons as quasiholes), are studied for both fermionic and bosonic gases.