Dynamic structure factor of ultracold Bose and Fermi gases in optical lattices

We investigate the dynamic structure factor of atomic Bose and Fermi gases in one-dimensional optical lattices at zero temperature. The focus is on the generic behaviour of S(k,omega) as function of filling and interaction strength with the aim of identifying possible experimental signatures for the different quantum phase transitions. We employ the Hubbard or Bose-Hubbard model and solve the eigenvalue problem of the Hamiltonian exactly for moderate lattice sizes. This allows us to determine the dynamic structure factor and other observables directly in the phase transition regime, where approximation schemes are generally not applicable. We discuss the characteristic signatures of the various quantum phases appearing in the dynamic structure factor and illustrate that the centroid of the strength distribution can be used to estimate the relevant excitation gaps. Employing sum rules, these quantities can be evaluated using ground state expectation values only. Important differences between bosonic and fermionic systems are observed, e.g., regarding the origin of the excitation gap in the Mott-insulator phase.Comment: 15 pages, 7 figure

Creation of macroscopic superposition states from arrays of Bose-Einstein condensates

We consider how macroscopic quantum superpositions may be created from arrays of Bose-Einstein condensates. We study a system of three condensates in Fock states, all with the same number of atoms and show that this has the form of a highly entangled superposition of different quasi-momenta. We then show how, by partially releasing these condensates and detecting an interference pattern where they overlap, it is possible to create a macroscopic superposition of different relative phases for the remaining portions of the condensates. We discuss methods for confirming these superpositions.Comment: 7 pages, 5 figure

Ultracold Bosonic Atoms in Disordered Optical Superlattices

The influence of disorder on ultracold atomic Bose gases in quasiperiodic optical lattices is discussed in the framework of the one-dimensional Bose-Hubbard model. It is shown that simple periodic modulations of the well depths generate a rich phase diagram consisting of superfluid, Mott insulator, Bose-glass and Anderson localized phases. The detailed evolution of mean occupation numbers and number fluctuations as function of modulation amplitude and interaction strength is discussed. Finally, the signatures of the different phases, especially of the Bose-glass phase, in matter-wave interference experiments are investigated.Comment: 4 pages, 4 figures, using REVTEX

The Composition of Cosmic Rays at the Knee

The observation of a small change in spectral slope, or 'knee' in the fluxes of cosmic rays near energies 10^15 eV has caused much speculation since its discovery over 40 years ago. The origin of this feature remains unknown. A small workshop to review some modern experimental measurements of this region was held at the Adler Planetarium in Chicago, USA in June 2000. This paper summarizes the results presented at this workshop and the discussion of their interpretation in the context of hadronic models of atmospheric airshowers.Comment: 36 pages, 10 figure

Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability

Superflow of Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results on the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau-Zener tunneling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.Comment: A new section on tight-binding approximation is added with a new figur

Bogoliubov approach to superfluidity of atoms in an optical lattice

We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter wave interference patterns. We complement these findings by self-consistent Hartree-Fock-Bogoliubov-Popov calculations for one-dimensional lattices including the effects of a parabolic trapping potential.Comment: 25 pages, 8 figure

Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques

The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new references added, fixed typo

Gamma-Ray Emission Concurrent with the Nova in the Symbiotic Binary V407 Cygni

Novae are thermonuclear explosions on a white dwarf surface fueled by mass accreted from a companion star. Current physical models posit that shocked expanding gas from the nova shell can produce X-ray emission but emission at higher energies has not been widely expected. Here, we report the Fermi Large Area Telescope detection of variable gamma-ray (0.1-10 GeV) emission from the recently-detected optical nova of the symbiotic star V407 Cygni. We propose that the material of the nova shell interacts with the dense ambient medium of the red giant primary, and that particles can be accelerated effectively to produce pi0 decay gamma-rays from proton-proton interactions. Emission involving inverse Compton scattering of the red giant radiation is also considered and is not ruled out.Comment: 38 pages, includes Supplementary Online Material; corresponding authors: C.C. Cheung, A.B. Hill, P. Jean, S. Razzaque, K.S. Woo

Fermi-LAT observations of the exceptional gamma-ray outbursts of 3C 273 in September 2009

We present the light curves and spectral data of two exceptionally luminous gamma-ray outburts observed by the Large Area Telescope (LAT) experiment on board Fermi Gamma-ray Space Telescope from 3C 273 in September 2009. During these flares, having a duration of a few days, the source reached its highest gamma-ray flux ever measured. This allowed us to study in some details their spectral and temporal structures. The rise and decay are asymmetric on timescales of 6 hours, and the spectral index was significantly harder during the flares than during the preceding 11 months. We also found that short, very intense flares put out the same time-integrated energy as long, less intense flares like that observed in August 2009.Comment: Corresponding authors: E. Massaro, [email protected]; G. Tosti, [email protected]. 15 pages, 4 figures, published in The Astrophysical Journal Letters, Volume 714, Issue 1, pp. L73-L78 (2010

Swift and Fermi observations of the early afterglow of the short Gamma-Ray Burst 090510

We present the observations of GRB090510 performed by the Fermi Gamma-Ray Space Telescope and the Swift observatory. This is a bright, short burst that shows an extended emission detected in the GeV range. Furthermore, its optical emission initially rises, a feature so far observed only in long bursts, while the X-ray flux shows an initial shallow decrease, followed by a steeper decay. This exceptional behavior enables us to investigate the physical properties of the GRB outflow, poorly known in short bursts. We discuss internal shock and external shock models for the broadband energy emission of this object.Comment: Comments: Submitted to ApJ Letters. Contact Authors: Massimiliano De Pasquale ([email protected]), Mathew Page ([email protected]), Kenji Toma ([email protected]), Veronique Pelassa ([email protected]). Minor change in the authorlis