Formation of molecules in an expanding Bose-Einstein condensate

A mean field theory of expanding hybrid atom-molecule Bose-Einstein condensates is applied to the recent MPI experiments on ${}^{87}$Rb that demonstrated the formation of ultracold molecules due to Feshbach resonance. The subsequent dissociation of the molecules is treated using a non-mean-field parametric approximation. The latter method is also used in determining optimal conditions for the formation of molecular BECComment: 5 pages with 5 figure

Formation of molecules from a Cs Bose-Einstein condensate

Conversion of an expanding Bose-Einstein condensate of Cs atoms to a molecular one with an efficiency of more than 30% was observed recently in experiments by M. Mark et al., Europhys. Lett. 69, 706 (2005). The theory presented here describes the experimental results. Values of resonance strength of 8 mG and rate coefficients for atom-molecule deactivation of $1\times 10^{-11}$ cm$^{3}/$s and molecule-molecule one of $1.5\times 10^{-9}$ cm$^{3}/$s are estimated by a fit of the theoretical results to the experimental data. Near the resonance, where the highest conversion efficiency was observed, the results demonstrate strong sensitivity to the magnetic field ripple and inhomogeneity. A conversion efficiency of about 60% is predicted by non-mean-field calculations for the densities and sweep rates lower than the ones used in the experiments.Comment: 9 pages, 10 figure

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

Scale-Free Networks are Ultrasmall

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small world networks which is known to be d ~ lnN, we show, using analytical arguments, that scale free networks with 2<a<3 have a much smaller diameter, behaving as d ~ lnlnN. For a=3, our analysis yields d ~ lnN/lnlnN, as obtained by Bollobas and Riordan, while for a>3, d ~ lnN. We also show that, for any a>2, one can construct a deterministic scale free network with d ~ lnlnN, and this construction yields the lowest possible diameter.Comment: Latex, 4 pages, 2 eps figures, small corrections, added explanation

Atom loss from Bose-Einstein condensates due to Feshbach resonance

In recent experiments on Na Bose-Einstein condensates [S. Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of pairs of atoms belonging to the condensate many-body wavefunction. A mechanism is offered here to account for the observed losses, based on the deactivation of the resonant molecular state by interaction with a third condensate atom.Comment: LaTeX, 4 pages, 4 PostScript figures, uses REVTeX and psfig, submitted to Physical Review A, Rapid Communication

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.

Resilience of the Internet to random breakdowns

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k)=ck^-a. We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p_c, that need to be removed before the network disintegrates. We show that for a<=3 the transition never takes place, unless the network is finite. In the special case of the Internet (a=2.5), we find that it is impressively robust, where p_c is approximately 0.99.Comment: latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett., in pres

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