Stabilizing an atom laser using spatially selective pumping and feedback

We perform a comprehensive study of stability of a pumped atom laser in the presence of pumping, damping and outcoupling. We also introduce a realistic feedback scheme to improve stability by extracting energy from the condensate and determine its effectiveness. We find that while the feedback scheme is highly efficient in reducing condensate fluctuations, it usually does not alter the stability class of a particular set of pumping, damping and outcoupling parameters.Comment: 7 figure

Outcoupling from a Bose-Einstein condensate with squeezed light to produce entangled atom laser beams

We examine the properties of an atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light. We model the multimode dynamics of the output field and show that a significant amount of squeezing can be transfered from an optical mode to a propagating atom laser beam. We use this to demonstrate that two-mode squeezing can be used to produce twin atom laser beams with continuous variable entanglement in amplitude and phase.Comment: 11 pages, 14 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

Achieving peak brightness in an atom laser

In this paper we present experimental results and theory on the first continuous (long pulse) Raman atom laser. The brightness that can be achieved with this system is three orders of magnitude greater than has been previously demonstrated in any other continuously outcoupled atom laser. In addition, the energy linewidth of a continuous atom laser can be made arbitrarily narrow compared to the mean field energy of a trapped condensate. We analyze the flux and brightness of the atom laser with an analytic model that shows excellent agreement with experiment with no adjustable parameters.Comment: 4 pages, 4 black and white figures, submitted to Physical Revie

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

Surpassing the Standard Quantum Limit in an Atom Interferometer with Four-mode Entanglement Produced from Four-Wave Mixing

We theoretically investigate a scheme for atom interferometry that surpasses the standard quantum limit. A four-wave mixing scheme similar to the recent experiment performed by Pertot et al. \cite{pertot} is used to generate sub-shot noise correlations between two modes. These two modes are then interfered with the remaining two modes in such a way as to surpass the standard quantum limit, whilst utilising all of the available atoms. Our scheme can be viewed as using two correlated interferometers. That is, the signal from each interferometer when looked at individually is classical, but there are correlations between the two interferometers that allow for the standard quantum limit to be surpassed.Comment: 7 pages, 5 figure

Classical noise and flux: the limits of multi-state atom lasers

By direct comparison between experiment and theory, we show how the classical noise on a multi-state atom laser beam increases with increasing flux. The trade off between classical noise and flux is an important consideration in precision interferometric measurement. We use periodic 10 microsecond radio-frequency pulses to couple atoms out of an F=2 87Rb Bose-Einstein condensate. The resulting atom laser beam has suprising structure which is explained using three dimensional simulations of the five state Gross-Pitaevskii equations.Comment: 4 pages, 3 figure

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

Control of an atom laser using feedback

A generalised method of using feedback to control Bose-Einstein condensates is introduced. The condensates are modelled by the Gross-Pitaevskii equation, so only semiclassical fluctations can be suppressed, and back-action from the measurement is ignored. We show that for any available control, a feedback scheme can be found to reduce the energy while the appropriate moment is still dynamic. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of non-linear controls. If the non-linear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency.Comment: 6 pages, 7 figure