A dynamic scheme for generating number squeezing in Bose-Einstein condensates through nonlinear interactions

We develop a scheme to generate number squeezing in a Bose-Einstein condensate by utilizing interference between two hyperfine levels and nonlinear atomic interactions. We describe the scheme using a multimode quantum field model and find agreement with a simple analytic model in certain regimes. We demonstrate that the scheme gives strong squeezing for realistic choices of parameters and atomic species. The number squeezing can result in noise well below the quantum limit, even if the initial noise on the system is classical and much greater than that of a poisson distribution.Comment: 4 pages, 3 figure

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments

Optically trapped atom interferometry using the clock transition of large Rb-87 Bose-Einstein condensates

We present a Ramsey-type atom interferometer operating with an optically trapped sample of 10^6 Bose-condensed Rb-87 atoms. The optical trap allows us to couple the |F =1, mF =0>\rightarrow |F =2, mF =0> clock states using a single photon 6.8GHz microwave transition, while state selective readout is achieved with absorption imaging. Interference fringes with contrast approaching 100% are observed for short evolution times. We analyse the process of absorption imaging and show that it is possible to observe atom number variance directly, with a signal-to-noise ratio ten times better than the atomic projection noise limit on 10^6 condensate atoms. We discuss the technical and fundamental noise sources that limit our current system, and outline the improvements that can be made. Our results indicate that, with further experimental refinements, it will be possible to produce and measure the output of a sub-shot-noise limited, large atom number BEC-based interferometer. In an addendum to the original paper, we attribute our inability to observe quantum projection noise to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross-Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions account for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 \times 10^4 atoms, we observe a coherence time of {\tau} = (1.0+0.5-0.3) s.Comment: 22 pages, 6 figures Addendum: 11 pages, 6 figure

Self-induced spatial dynamics to enhance spin squeezing via one-axis twisting in a two component Bose-Einstein condensate

We theoretically investigate a scheme to enhance relative number squeezing and spin squeezing in a two- component Bose-Einstein condensate (BEC) by utilizing the inherent mean-field dynamics of the condensate. Due to the asymmetry in the scattering lengths, the two components exhibit large density oscillations where they spatially separate and recombine. The effective nonlinearity responsible for the squeezing is increased by up to 3 orders of magnitude when the two components spatially separate. We perform a multimode simulation of the system using the truncated Wigner method and show that this method can be used to create significant squeezing in systems where the effective nonlinearity would ordinarily be too small to produce any significant squeezing in sensible time frames, and we show that strong spatial dynamics resulting from large particle numbers aren’t necessarily detrimental to generating squeezing. We develop a simplified semianalytic model that gives good agreement with our multimode simulation and will be useful for predicting squeezing in a range of different systems

Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz-Ladik hierarchy

Adler and van Moerbeke \cite{AVM} described a reduction of 2D-Toda hierarchy called Toeplitz lattice. This hierarchy turns out to be equivalent to the one originally described by Ablowitz and Ladik \cite{AL} using semidiscrete zero-curvature equations. In this paper we obtain the original semidiscrete zero-curvature equations starting directly from the Toeplitz lattice and we generalize these computations to the matrix case. This generalization lead us to the semidiscrete zero-curvature equations for the non-abelian (or multicomponent) version of Ablowitz-Ladik equations \cite{GI}. In this way we extend the link between biorthogonal polynomials on the unit circle and Ablowitz-Ladik hierarchy to the matrix case.Comment: 23 pages, accepted on publication on J. Phys. A., electronic link: http://stacks.iop.org/1751-8121/42/36521

On the nature and variability of the east Greenland Spill Jet : a case study in Summer 2003

Author Posting. © American Meteorological Society, 2011. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 41 (2011): 2307–2327, doi:10.1175/JPO-D-10-05004.1.Results from a high-resolution (~2 km) numerical simulation of the Irminger Basin during summer 2003 are presented. The focus is on the East Greenland Spill Jet, a recently discovered component of the circulation in the basin. The simulation compares well with observations of surface fields, the Denmark Strait overflow (DSO), and the hydrographic structure of typical sections in the basin. The model reveals new aspects of the circulation on scales of O(0.1–10) days and O(1–100) km. The model Spill Jet results from the cascade of dense waters over the East Greenland shelf. Spilling can occur in various locations southwest of the strait, and it is present throughout the simulation but exhibits large variations on periods of O(0.1–10) days. The Spill Jet sometimes cannot be distinguished in the velocity field from surface eddies or from the DSO. The vorticity structure of the jet confirms its unstable nature with peak relative and tilting vorticity terms reaching twice the planetary vorticity term. The average model Spill Jet transport is 4.9 ±1.7 Sv (1 Sv ≡ 106 m3 s−1) equatorward, about 2½ times larger than has been previously reported from a single ship transect in August 2001. Kinematic analysis of the model results suggests two different types of spilling events. In the first case (type I), a local perturbation results in dense waters descending over the shelf break into the Irminger Basin. In the second case (type II), surface cyclones associated with DSO deep domes initiate the spilling process. During summer 2003, more than half of the largest Spill Jet transport values are of type II.The research is supported by the National Science Foundation Grants OCE-0726393 and OCI-0904640 (MGM and TWNH) and OCE-0726640 (RSP).2012-06-0

Generating quadrature squeezing in an atom laser through self-interaction

We describe a scheme for creating quadrature- and intensity-squeezed atom lasers that do not require squeezed light as an input. The beam becomes squeezed due to nonlinear interactions between the atoms in the beam in an analogue to optical Kerr squeezing. We develop an analytic model of the process which we compare to a detailed stochastic simulation of the system using phase space methods. Finally we show that significant squeezing can be obtained in an experimentally realistic system and suggest ways of increasing the tunability of the squeezing

qq-analogue of modified KP hierarchy and its quasi-classical limit

A $q$-analogue of the tau function of the modified KP hierarchy is defined by a change of independent variables. This tau function satisfies a system of bilinear $q$-difference equations. These bilinear equations are translated to the language of wave functions, which turn out to satisfy a system of linear $q$-difference equations. These linear $q$-difference equations are used to formulate the Lax formalism and the description of quasi-classical limit. These results can be generalized to a $q$-analogue of the Toda hierarchy. The results on the $q$-analogue of the Toda hierarchy might have an application to the random partition calculus in gauge theories and topological strings.Comment: latex2e, a4 paper 15 pages, no figure; (v2) a few references are adde

Lie point symmetries and first integrals: the Kowalevsky top

We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is essential. Noether's theorem is neither necessary nor considered. The most striking example we present is the relationship between Lie group analysis and the famous first integral of the Kowalevski top.Comment: 23 page

Comparisons of host mitochondrial, nuclear and endosymbiont bacterial genes reveal cryptic fig wasp species and the effects of Wolbachia on host mtDNA evolution and diversity

Background Figs and fig-pollinating wasp species usually display a highly specific one-to-one association. However, more and more studies have revealed that the "one-to-one" rule has been broken. Co-pollinators have been reported, but we do not yet know how they evolve. They may evolve from insect speciation induced or facilitated by Wolbachia which can manipulate host reproduction and induce reproductive isolation. In addition, Wolbachia can affect host mitochondrial DNA evolution, because of the linkage between Wolbachia and associated mitochondrial haplotypes, and thus confound host phylogeny based on mtDNA. Previous research has shown that fig wasps have the highest incidence of Wolbachia infection in all insect taxa, and Wolbachia may have great influence on fig wasp biology. Therefore, we look forward to understanding the influence of Wolbachia on mitochondrial DNA evolution and speciation in fig wasps. Results We surveyed 76 pollinator wasp specimens from nine Ficus microcarpa trees each growing at a different location in Hainan and Fujian Provinces, China. We found that all wasps were morphologically identified as Eupristina verticillata, but diverged into three clades with 4.22-5.28% mtDNA divergence and 2.29-20.72% nuclear gene divergence. We also found very strong concordance between E. verticillata clades and Wolbachia infection status, and the predicted effects of Wolbachia on both mtDNA diversity and evolution by decreasing mitochondrial haplotypes. Conclusions Our study reveals that the pollinating wasp E. verticillata on F. microcarpa has diverged into three cryptic species, and Wolbachia may have a role in this divergence. The results also indicate that Wolbachia strains infecting E. verticillata have likely resulted in selective sweeps on host mitochondrial DNA