Mean-field model for the interference of matter-waves from a three-dimensional optical trap

Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by, Greiner et al. [Nature (London 415 (2002) 39]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three. (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Role of Mie scattering in the seeding of matter-wave superradiance

Matter-wave superradiance is based on the interplay between ultracold atoms coherently organized in momentum space and a backscattered wave. Here, we show that this mechanism may be triggered by Mie scattering from the atomic cloud. We show how the laser light populates the modes of the cloud and thus imprints a phase gradient on the excited atomic dipoles. The interference with the atoms in the ground state results in a grating that in turn generates coherent emission, contributing to the backward light wave onset. The atomic recoil "halos" created by the Mie-scattered light exhibit a strong anisotropy, in contrast to single-atom scattering.

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Dynamical localization of matter-wave solitons in managed barrier potentials

The bright matter-wave soliton propagation through a barrier with a rapidly oscillating position is investigated. The averaged-over rapid oscillations Gross-Pitaevskii equation is derived, where the effective potential has the form of a finite well. Dynamical trapping and quantum tunneling of the soliton in the effective finite well are investigated. The analytical predictions for the effective soliton dynamics is confirmed by numerical simulations of the full Gross-Pitaevskii equation.

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evolutions of matter-wave bright soliton with spatially modulated nonlinearity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Correction of dephasing oscillations in matter-wave interferometry

Vibrations, electromagnetic oscillations, and temperature drifts are among the main reasons for dephasing in matter-wave interferometry. Sophisticated interferometry experiments, e.g., with ions or heavy molecules, often require integration times of several minutes due to the low source intensity or the high velocity selection. Here we present a scheme to suppress the influence of such dephasing mechanisms—especially in the low-frequency regime—by analyzing temporal and spatial particle correlations available in modern detectors. Such correlations can reveal interference properties that would otherwise be washed out due to dephasing by external oscillating signals. The method is shown experimentally in a biprism electron interferometer where a perturbing oscillation is artificially introduced by a periodically varying magnetic field. We provide a full theoretical description of the particle correlations where the perturbing frequency and amplitude can be revealed from the disturbed interferogram. The original spatial fringe pattern without the perturbation can thereby be restored. The technique can be applied to lower the general noise requirements in matter-wave interferometers. It allows for the optimization of electromagnetic shielding and decreases the efforts for vibrational or temperature stabilization.

Optomechanical interface for probing matter-wave coherence

We combine matter-wave interferometry and cavity optomechanics to propose a coherent matter-light interface based on mechanical motion at the quantum level. We demonstrate a mechanism that is able to transfer non-classical features imprinted on the state of a matter-wave system to an optomechanical device, transducing them into distinctive interference fringes. This provides a reliable tool for the inference of quantum coherence in the particle beam. Moreover, we discuss how our system allows for intriguing perspectives, paving the way to the construction of a device for the encoding of quantum information in matter-wave systems. Our proposal, which highlights previously unforeseen possibilities for the synergistic exploitation of these two experimental platforms, is explicitly based on existing technology, available and widely used in current cutting-edge experiments.

Dispersion and uncertainty in multislit matter wave diffraction

We show that single and multislit experiments involving matter waves may be constructed to assess dispersively generated correlations between the position and momentum of a single free particle. These correlations give rise to position dependent phases which develop dynamically as a result of dispersion and may play an important role in the interference patterns. To the extent that initial transverse coherence is preserved throughout the proposed diffraction setup, such interference patterns are noticeably different from those of a classical dispersion free wave. (c) 2007 Published by Elsevier B.V.

Limits to phase resolution in matter-wave interferometry

We study the quantum dynamics of a two-mode Bose-Einstein condensate in a time-dependent symmetric double-well potential using analytical and numerical methods. The effects of internal degrees of freedom on the visibility of interference fringes during a stage of ballistic expansion are investigated varying particle number, nonlinear interaction sign and strength, as well as tunneling coupling. Expressions for the phase resolution are derived and the possible enhancement due to squeezing is discussed. In particular, the role of the superfluid-Mott insulator crossover and its analog for attractive interactions is recognized.

Dynamics of bright matter-wave solitons in a Bose-Einstein condensate with inhomogeneous scattering length

We investigate dynamical effects of a bright soliton in Bose-Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross-Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.

Effective potential of two coupled binary matter wave bright solitons with spatially modulated nonlinearity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)