A multi-mode model of a non-classical atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light

We examine the properties of an atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light. We introduce a method which allows us to model the full multimode dynamics of the squeezed optical field and the outcoupled atoms. We show that for experimentally reasonable parameters that the quantum statistics of the optical field are almost completely transferred to the outcoupled atoms, and investigate the robustness to the coupling strength and the two-photon detuning.Comment: 6 pages, 4 figures. Accepted to Laser physics letter

Askey-Wilson Type Functions, With Bound States

The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of some instances of the Askey-Wilson difference operator, we can generate functions that satisfy a doubly infinite three-term recursion relation and are also eigenfunctions of $q$-difference operators of arbitrary orders. Our result provides a discrete analogue of the solutions of the purely differential version of the bispectral problem that were discovered in the pioneering work [8] of Duistermaat and Gr\"unbaum.Comment: 42 pages, Section 3 moved to the end, minor correction

Fates and Travel Times of Denmark Strait Overflow Water in the Irminger Basin*

The Denmark Strait Overflow (DSO) supplies about one-third of the North Atlantic Deep Water and is critical to global thermohaline circulation. Knowledge of the pathways of DSO through the Irminger Basin and its transformation there is still incomplete, however. The authors deploy over 10 000 Lagrangian particles at the Denmark Strait in a high-resolution ocean model to study these issues. First, the particle trajectories show that the mean position and potential density of dense waters cascading over the Denmark Strait sill evolve consistently with hydrographic observations. These sill particles transit the Irminger Basin to the Spill Jet section (65.25°N) in 5–7 days and to the Angmagssalik section (63.5°N) in 2–3 weeks. Second, the dense water pathways on the continental shelf are consistent with observations and particles released on the shelf in the strait constitute a significant fraction of the dense water particles recorded at the Angmagssalik section within 60 days (~25%). Some particles circulate on the shelf for several weeks before they spill off the shelf break and join the overflow from the sill. Third, there are two places where the water density following particle trajectories decreases rapidly due to intense mixing: to the southwest of the sill and southwest of the Kangerdlugssuaq Trough on the continental slope. After transformation in these places, the overflow particles exhibit a wide range of densities

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

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

On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models

We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The duality symplectomorphism between these two integrable models, that was constructed by Ruijsenaars using direct methods, can be then interpreted geometrically simply as a gauge transformation connecting two cross sections of the orbits of the reduction group.Comment: 16 pages, v2: comments and references added at the end of the tex

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

Mesoscale mixing of the Denmark Strait Overflow in the Irminger Basin

Highlights: • Water mass transformation in Denmark Strait Overflow is localized in space/time • High transformation co-locates with maxima in eddy velocity variance and shear • Overflow eddies modulate the transformation, eddy heat flux divergence and shear Abstract: The Denmark Strait Overflow (DSO) is a major export route for dense waters from the Nordic Seas forming the lower limb of the Atlantic Meridional Overturning Circulation, an important element of the climate system. Mixing processes along the DSO pathway influence its volume transport and properties contributing to the variability of the deep overturning circulation. They are poorly sampled by observations however which hinders development of a proper DSO representation in global circulation models. We employ a high resolution regional ocean model of the Irminger Basin to quantify impact of the mesoscale flows on DSO mixing focusing on geographical localization and local time–modulation of water property changes. The model reproduces the observed bulk warming of the DSO plume 100–200 km downstream of the Denmark Strait sill. It also reveals that mesoscale variability of the overflow (‘DSO-eddies’, of 20-30 km extent and a time scale of 2–5 day) modulates water property changes and turbulent mixing, diagnosed with the vertical shear of horizontal velocity and the eddy heat flux divergence. The space–time localization of the DSO mixing and warming and the role of coherent mesoscale structures should be explored by turbulence measurements and factored into the coarse circulation models

Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation