Reentrant transition of bosons in a quasiperiodic potential

We investigate the behavior of a two dimensional array of Bose-Einstein condensate tubes described by means of a Bose-Hubbard Hamiltonian. Using a Wannier function expansion for the wavefunction in each tube, we compute the Bose-Hubbard parameters related to two different longitudinal potentials, periodic and quasiperiodic. We predict that - upon increasing the external potential strength along the direction of the tubes - the condensate can experience a reentrant transition between a Mott insulating phase and the superfluid one.Comment: Accepted for publication in EP

Bose-Einstein condensates under a spatially-modulated transverse confinement

We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the usual linear cigar-shaped trap, where the periodic modulation emulates the action of an optical lattice (OL), the model may be also relevant to toroidal traps, where an ordinary OL cannot be created. For either sign of the nonlinearity, extended and localized states are found, in the numerical form (using both the effective NPSE and the full 3D Gross-Pitaevskii equation) and by means of the variational approximation (VA). The latter is applied to construct ground-state solitons and predict the collapse threshold in the case of self-attraction. It is shown that numerical solutions provided by the one-dimensional NPSE are always very close to full 3D solutions, and the VA yields quite reasonable results too. The transition from delocalized states to gap solitons, in the first finite bandgap of the linear spectrum, is examined in detail, for the repulsive and attractive nonlinearities alike.Comment: 10 pages, 10 figures, accepted for publication in Phys. Rev.

Modeling user return time using inhomogeneous poisson process

For Intelligent Assistants (IA), user activity is often used as a lag metric for user satisfaction or engagement. Conversely, predictive leading metrics for engagement can be helpful with decision making and evaluating changes in satisfaction caused by new features. In this paper, we propose User Return Time (URT), a fine grain metric for gauging user engagement. To compute URT, we model continuous inter-arrival times between users’ use of service via a log Gaussian Cox process (LGCP), a form of inhomogeneous Poisson process which captures the irregular variations in user usage rate and personal preferences typical of an IA. We show the effectiveness of the proposed approaches on predicting the return time of users on real-world data collected from an IA. Experimental results demonstrate that our model is able to predict user return times reasonably well and considerably better than strong baselines that make the prediction based on past utterance frequency

Interaction of gravitational waves with matter

We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression for the dispersion of gravitational waves in matter in terms of correlation functions for the matter in flat spacetime. The self energy of a gravitational wave is shown to have contributions analogous to the paramagnetic and diamagnetic contributions to the self energy of an electromagnetic wave. We apply the formalism to some simple systems - free particles, an interacting scalar field, and a fermionic superfluid.Comment: NORDITA-2011-8

Bose-Hubbard model with occupation dependent parameters

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose-Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling the system features a phase-transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background -- instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with 2 particles per site is destroyed completely by particle-hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction, but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a 2D slab, localized along one spatial direction that is spontaneously chosen.Comment: 16 pages, 4 figure

Dynamics of kicked matter-wave solitons in an optical lattice

We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose-Einstein condensate trapped in a optical lattice. The resulting soliton's dynamics is studied within the framework of the time-dependent nonpolynomial Schrodinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice.Comment: 8 pages, 6 figures, to be published in Physica D: Nonlinear Phenomena; special issue on "Nonlinear Phenomena in Degenerate Quantum Gases

Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices

Within the framework of a mean-field description, we investigate atomic Bose-Einstein condensates, with attraction between atoms, under the action of a strong transverse confinement and periodic [optical-lattice (OL)] axial potential. Using a combination of the variational approximation, one-dimensional (1D) nonpolynomial Schrodinger equation, and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation, we show that the ground state of the condensate is a soliton belonging to the semi-infinite band gap of the periodic potential. The soliton may be confined to a single cell of the lattice or extended to several cells, depending on the effective self-attraction strength g (which is proportional to the number of atoms bound in the soliton) and depth of the potential, V-0, the increase of V-0 leading to strong compression of the soliton. We demonstrate that the OL is an effective tool to control the soliton's shape. It is found that, due to the 3D character of the underlying setting, the ground-state soliton collapses at a critical value of the strength, g=g(c), which gradually decreases with the increase of V-0; under typical experimental conditions, the corresponding maximum number of Li-7 atoms in the soliton, N-max, ranges between 8000 and 4000. Examples of stable multipeaked solitons are also found in the first finite band gap of the lattice spectrum. The respective critical value g(c) again slowly decreases with the increase of V-0, corresponding to N-max similar or equal to 5000