Formation of a molecular Bose-Einstein condensate and an entangled atomic gas by Feshbach resonance

Processes of association in an atomic Bose-Einstein condensate, and dissociation of the resulting molecular condensate, due to Feshbach resonance in a time-dependent magnetic field, are analyzed incorporating non-mean-field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long-lived molecular condensate (with lifetimes of 10 ms and more). Entangled atoms in two-mode squeezed states (with noise reduction of about 30 dB) may also be formed by molecular dissociation. A gas of atoms in squeezed or entangled states can have applications in quantum computing, communications, and measurements.Comment: LaTeX, 5 pages with 4 figures, uses REVTeX

Shortcut to a Fermi-Degenerate Gas of Molecules via Cooperative Association

We theoretically examine the creation of a Fermi-degenerate gas of molecules via a photoassociation or Feshbach resonance applied to a degenerate Bose-Fermi mixture of atoms. This problem raises an interest because, unlike bosons, fermions in general do not behave cooperatively, so that the collective conversion of, say, two million atoms into one million molecules is not to be expected. Nevertheless, we find that the coupled Fermi system displays collective Rabi-like oscillations and adiabatic passage between atoms and molecules, thereby mimicking Bose-Einstein statistics. Cooperative association of a degenerate mixture of Bose and Fermi gases could therefore serve as a shortcut to a degenerate gas of Fermi molecules.Comment: 4 pages, 2 figures, submitted to PRL; v2: expanded intro, added discussion on neglect of collisions and when mimicking should occu

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

Two simple systems with cold atoms: quantum chaos tests and nonequilibrium dynamics

This article is an attempt to provide a link between the quantum nonequilibrium dynamics of cold gases and fifty years of progress in the lowdimensional quantum chaos. We identify two atomic systems lying on the interface: two interacting atoms in a harmonic multimode waveguide and an interacting two-component Bose-Bose mixture in a double-well potential. In particular, we study the level spacing distribution, the wavefunction statistics, the eigenstate thermalization, and the ability to thermalize in a relaxation process as such.Comment: 18 pages, 9 figure

Tree-body loss of of trapped ultracold 87^{87}Rb atoms due to a Feshbach resonance

The loss of ultracold trapped atoms in the vicinity of a Feshbach resonance is treated as a two-stage reaction, using the Breit-Wigner theory. The first stage is the formation of a resonant diatomic molecule, and the second one is its deactivation by inelastic collisions with other atoms. This model is applied to the analysis of recent experiments on $^{87}$Rb, leading to an estimated value of $7\times 10^{-11}$ cm$^{3}/$s for the deactivation rate coefficient.Comment: LaTeX, 4 pages with 1 figures, uses REVTeX4, uses improved experimental dat

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

One-dimensional Bose chemistry: effects of non-integrability

Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy dependent strength. The related problem with an energy independent strength (the Lieb-Liniger-McGuire model) has an exact solution and forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev-Lovelace equations. The results demonstrate that as the internal symmetry of the Lieb-Liniger-McGuire model is lifted, the reflection and chemical reactions become allowed and may be observed in experiments.Comment: 5 pages, 4 figure

Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas

We have converted an ultracold Fermi gas of $^6$Li atoms into an ultracold gas of $^6$Li$_2$ molecules by adiabatic passage through a Feshbach resonance. Approximately $1.5 \times 10^5$ molecules in the least-bound, $v = 38$, vibrational level of the X$^1 \Sigma ^+_g$ singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.Comment: Accepted for publication in Phys. Rev. Letter

Production of cold molecules via magnetically tunable Feshbach resonances

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose as well as two spin component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled channels theory provides the rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, as well as the classification in terms of entrance- and closed-channel dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic field sweeps in cold Bose and Fermi gases as well as pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean field as well as beyond mean field approaches are reviewed in detail, including the associated ranges of validity.Comment: 50 pages, 26 figures, to be published in Reviews of Modern Physics, final version with updated reference