Narrow Results

Developments in the realization and study of ultracold atomic gases inside elongated magnetic traps and atom waveguides have stimulated calculations of equilibrium properties and excitation spectra for mesoscopic clouds of hard-core bosons and of spin-polarized fermions moving under an external harmonic potential in one dimension. A rigorous correspondence exists between the wave functions of these two types of system, allowing a number of exact results to be obtained. The main theoretical techniques and results are reviewed in this article, with emphasis on their relevance in regard to tests of the Thomas–Fermi approximation for confined Fermi fluids and to the foundations of density functional theory for inhomogeneous quantum systems.

The deviation effect of spinor mode from the single-mode for a spin-1 Bose gas of trapped atoms is studied beyond the mean field theory. Based on the effective Hamiltonian with nondegenerated level of the collective spin states, the splitting level of the system energy due to the deviation effect has been calculated. For the large condensates of ⁸⁷Rb and ²³Na with atom number N>10⁵, the splitting fraction of the energy, arising from the magnetization exhibited by the trapped Bose gas, is found to have a typical order of (10^-4~10^-8), decreasing as N^-2 for ⁸⁷Rb and increasing as -N^-2 for ²³Na, respectively.

Recent experimental and theoretical advances in the creation and description of bright matter wave solitons are reviewed. Several aspects are taken into account, including the physics of soliton train formation as the nonlinear Fresnel diffraction, soliton-soliton interactions, and propagation in the presence of inhomogeneities. The generation of stable bright solitons by means of Feshbach resonance techniques is also discussed.

We present studies of the behavior of the permittivity of such liquid systems as pure distilled water, alcohol and 50%-aqueous solutions of alcohol as affected by the inerton field generated by a special signal generator contained within a wrist-watch or bracelet made by so-called Teslar^® technology. It has been found that the changes are in fact significant. The method employed has allowed us to fix the value of frequency of the field generated by the Teslar^® chip. The frequency has been determined to be approximately 8 Hz. The phenomenological consideration and submicroscopic foundations of a significant increase of the permittivity are studied, taking into account an additional interaction, namely, the mass interaction between polar water molecules, which is caused by the inerton field of the Teslar^® chip. This is one more proof of Krasnoholovets' concept regarding the existence of a substructure of the matter waves of moving/vibrating entities, i.e. the inerton field, which has been predicted in a series of his previous works.

We investigate the four-wave mixing of matter wave packets created from a Bose–Einstein condensate, realized experimentally by utilizing light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary condensate. Based on the Gross–Pitaevskii equation, a set of nonlinearly coupled envelope equations including self- and cross-phase modulational effects are derived systematically using a method of multiple-scales. The exact and explicit analytical solutions are provided for the coupled envelope equations and the evolution of the wave packets after turning off trapping potential is discussed and compared with experiment.

We consider several effects of the matter wave dynamics which can be observed in Bose–Einstein condensates embedded into optical lattices. For low-density condensates, we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross–Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models, we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force and lattice defects affect the nonlinear matter waves.

In this brief review we summarize a number of recent developments in the study of vortices in Bose–Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.

In recent paper, Nowak et al. report a charged wire interferometer for atoms, and employ analytical method to explain the interference patterns [Phys. Rev. Lett.81 (1998) 5792]. In this paper, a numerical calculation with semi-classical method is carried out and the experimental patterns are rebuilt very well. The interference patterns are interpreted by path integral. We also calculate the fringe period for different voltages and the agreement with experiment is more rigorous than the analytical expression. Besides, the fringe visibility of the interference patterns at different applied voltages and degrees is also discussed.

A simplified operator correspondence scheme is derived to address nonlinear quantum systems within the framework of the $P$-representation. The simplified method is applied to a general nonlinear quantum oscillator model that has been used in the literature to describe nonlinear quantum optical and matter wave systems. The $P$-representation evolution equation for the model is derived for arbitrary nonlinearity exponents. It is shown that in the high temperature case, the $P$-representation is sufficient to describe the model and its associated systems such that there is no need to use alternative, mathematically more involved representations. Systems with quadratic and cubic nonlinearities are considered in more detail. Distributions for the energy levels and photon and particle numbers are obtained within the framework of the $P$-representation. Moreover, the electrical field oscillation frequency dependency is studied numerically when interpreting the model as model for quantum optical nonlinear oscillators.

We study the quantum dynamics of a material wave packet bouncing off a modulated atomic mirror in the presence of a gravitational field. We find the occurrence of coherent accelerated dynamics for atoms. The acceleration takes place for certain initial phase space data and within specific windows of modulation strengths. The realization of the proposed acceleration scheme is within the range of present day experimental possibilities.

We present a generalized kick rotor model in which the phase of the kick can vary from kick to kick. This additional freedom allows one to control the transport in phase space. For a specific choice of kick-to-kick phases, we predict novel forms of accelerator modes which are potentially of high relevance for future experimental studies.

We analyze the matter wave transmission above a step potential within the framework of the cubic-nonlinear Schrödinger equation. We present a comprehensive analysis of the corresponding stationary problem based on an exact second-order nonlinear differential equation for the probability density. The exact solution of the problem in terms of the Jacobi elliptic sn-function is presented and analyzed. Qualitatively distinct types of wave propagation picture are classified depending on the input parameters of the system. Analyzing the 2D space of involved dimensionless parameters, the nonlinearity and the reflecting potential's height/depth given in the units of the chemical potential, we show that the region of the parameters that does not sustain restricted solutions is given by a closed curve consisting of a segment of an elliptic curve and two line intervals. We show that there exists a specific singular point, belonging to the elliptic curve, which causes a jump from one evolution scenario to another one. The position of this point is determined and the peculiarities of the evolution scenarios (oscillatory, non-oscillatory and diverging) for all the allowed regions of involved parameters are described and analyzed in detail.

Interference of particles is one of the central phenomena of quantum mechanics. The computer program InterferenceSimulator demonstrates two-slit Fresnel interference patterns with one, the other, or both slits open. A magnetic flux situated between the two slits allows the demonstration of the Aharonov–Bohm effect. Simulations with short de Broglie wavelengths illustrate the classical limit of quantum mechanics. Because of the universality of wave phenomena, this program also demonstrates the geometrical-optics limit of wave optics for small wavelengths.

We study the quantum dynamics of a material wave packet bouncing off a modulated atomic mirror in the presence of a gravitational field. We find the occurrence of coherent accelerated dynamics for atoms. The acceleration takes place for certain initial phase space data and within specific windows of modulation strengths. The realization of the proposed acceleration scheme is within the range of present day experimental possibilities.

We discuss different schemes on matter or light generation with unusual properties. First, we shall demonstrate the generation of two-particle entanglement via external field pumping and damping through a squeezed electromagnetic field reservoir. Then, continuous variable entanglement of the generated field of a pumped multi-atom sample will be reported. Further, in a different setup, a particular attention will be devoted to spatial entanglement of matter waves. Various entangled interference patterns will be described and analyzed.