Formation of Two Component Bose Condensate During the Chemical Potential Curve Crossing

In this article we study the formation of the two modes Bose-Einstein condensate and the correlation between them. We show that beyond the mean field approximation the dissociation of a molecular condensate due to the chemical potential curve crossing leads to the formation of two modes condensate. We also show that these two modes are correlated in a two mode squeezed state.Comment: 10 page

Curve crossing in linear potential grids: the quasidegeneracy approximation

The quasidegeneracy approximation [V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne, and Y. B. Band, J. Phys. B {\bf 32}, 1845 (1999)] is used here to evaluate transition amplitudes for the problem of curve crossing in linear potential grids involving two sets of parallel potentials. The approximation describes phenomena, such as counterintuitive transitions and saturation (incomplete population transfer), not predictable by the assumption of independent crossings. Also, a new kind of oscillations due to quantum interference (different from the well-known St\"uckelberg oscillations) is disclosed, and its nature discussed. The approximation can find applications in many fields of physics, where multistate curve crossing problems occur.Comment: LaTeX, 8 pages, 8 PostScript figures, uses REVTeX and psfig, submitted to Physical Review

Counterintuitive transitions in multistate curve crossing involving linear potentials

Two problems incorporating a set of horizontal linear potentials crossed by a sloped linear potential are analytically solved and compared with numerical results: (a) the case where boundary conditions are specified at the ends of a finite interval, and (b) the case where the sloped linear potential is replaced by a piecewise-linear sloped potential and the boundary conditions are specified at infinity. In the approximation of small gaps between the horizontal potentials, an approach similar to the one used for the degenerate problem (Yurovsky V A and Ben-Reuven A 1998 J. Phys. B 31,1) is applicable for both problems. The resulting scattering matrix has a form different from the semiclassical result obtained by taking the product of Landau-Zener amplitudes. Counterintuitive transitions involving a pair of successive crossings, in which the second crossing precedes the first one along the direction of motion, are allowed in both models considered here.Comment: LaTeX 2.09 using ioplppt.sty and psfig.sty, 16 pages with 5 figures. Submitted to J. Phys.

Information extraction and transmission techniques for spaceborne synthetic aperture radar images

Information extraction and transmission techniques for synthetic aperture radar (SAR) imagery were investigated. Four interrelated problems were addressed. An optimal tonal SAR image classification algorithm was developed and evaluated. A data compression technique was developed for SAR imagery which is simple and provides a 5:1 compression with acceptable image quality. An optimal textural edge detector was developed. Several SAR image enhancement algorithms have been proposed. The effectiveness of each algorithm was compared quantitatively

Modeling of gyrosynchrotron radio emission pulsations produced by MHD loop oscillations in solar flares

A quantitative study of the observable radio signatures of the sausage, kink, and torsional MHD oscillation modes in flaring coronal loops is performed. Considering first non-zero order effect of these various MHD oscillation modes on the radio source parameters such as magnetic field, line of sight, plasma density and temperature, electron distribution function, and the source dimensions, we compute time dependent radio emission (spectra and light curves). The radio light curves (of both flux density and degree of polarization) at all considered radio frequencies are than quantified in both time domain (via computation of the full modulation amplitude as a function of frequency) and in Fourier domain (oscillation spectra, phases, and partial modulation amplitude) to form the signatures specific to a particular oscillation mode and/or source parameter regime. We found that the parameter regime and the involved MHD mode can indeed be distinguished using the quantitative measures derived in the modeling. We apply the developed approach to analyze radio burst recorded by Owens Valley Solar Array and report possible detection of the sausage mode oscillation in one (partly occulted) flare and kink or torsional oscillations in another flare.Comment: ApJ, accepte

Feshbach-Stimulated Photoproduction of a Stable Molecular Condensate

Photoassociation and the Feshbach resonance are, in principle, feasible means for creating a molecular Bose-Einstein condensate from an already-quantum-degenerate gas of atoms; however, mean-field shifts and irreversible decay place practical constraints on the efficient delivery of stable molecules using either mechanism alone. We therefore propose Feshbach-stimulated Raman photoproduction, i.e., a combination of magnetic and optical methods, as a viable means to collectively convert degenerate atoms into a stable molecular condensate with near-unit efficiency.Comment: 5 pages, 3 figures, 1 table; v3 includes few-level diagram of scheme, and added discussion; transferred to PR

Generation of macroscopic pair-correlated atomic beams by four-wave mixing in Bose-Einstein condensates

By colliding two Bose-Einstein condensates we have observed strong bosonic stimulation of the elastic scattering process. When a weak input beam was applied as a seed, it was amplified by a factor of 20. This large gain atomic four-wave mixing resulted in the generation of two macroscopically occupied pair-correlated atomic beams.Comment: Please take eps files for best details in figure

Stationary solutions of the one-dimensional nonlinear Schroedinger equation: II. Case of attractive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper has treated the repulsive case. Our solutions take the form of bounded, quantized, stationary trains of bright solitons. Among them are two uniquely nonlinear classes of nodeless solutions, whose properties and physical meaning are discussed in detail. The full set of symmetry-breaking stationary states are described by the $C_{n}$ character tables from the theory of point groups. We make experimental predictions for the Bose-Einstein condensate and show that, though these are the analog of some of the simplest problems in linear quantum mechanics, nonlinearity introduces new and surprising phenomena.Comment: 11 pages, 9 figures -- revised versio

BEC Collapse and Dynamical Squeezing of Vacuum Fluctuations

We analyze the phenomena of Bose Novae, as described by Donley et al [Nature 412, 295 (2001)], by focusing on the behavior of excitations or fluctuations above the condensate, as driven by the dynamics of the condensate (rather than the dynamics of the condensate alone or the kinetics of the atoms). The dynamics of the condensate squeezes and amplifies the quantum excitations, mixing the positive and negative frequency components of their wave functions thereby creating particles which appear as bursts and jets. By analyzing the changing amplitude and particle content of these excitations, our simple physical picture (based on a test field approximation) explains well the overall features of the Bose Novae phenomena and provide excellent quantitative fits with experimental data on several aspects, such as the scaling behavior of the collapse time and the amount of particles in the jet. The predictions of the bursts at this level of approximation is less than satisfactory but may be improved on by including the backreaction of the excitations on the condensate. The mechanism behind the dominant effect -- parametric amplification of vacuum fluctuations and freezing of modes outside of horizon -- is similar to that of cosmological particle creation and structure formation in a rapid quench (which is fundamentally different from Hawking radiation in black holes). This shows that BEC dynamics is a promising venue for doing `laboratory cosmology'.Comment: Latex 36 pages, 6 figure

Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings

We generalize the Brundobler-Elser hypothesis in the multistate Landau-Zener problem to the case when instead of a state with the highest slope of the diabatic energy level there is a band of states with an arbitrary number of parallel levels having the same slope. We argue that the probabilities of counterintuitive transitions among such states are exactly zero.Comment: 9 pages, 5 figure