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

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

Observation of shock waves in a large Bose-Einstein condensate

We observe the formation of shock waves in a Bose-Einstein condensate containing a large number of sodium atoms. The shock wave is initiated with a repulsive, blue-detuned light barrier, intersecting the BEC, after which two shock fronts appear. We observe breaking of these waves when the size of these waves approaches the healing length of the condensate. At this time, the wave front splits into two parts and clear fringes appear. The experiment is modeled using an effective 1D Gross-Pitaevskii-like equation and gives excellent quantitative agreement with the experiment, even though matter waves with wavelengths two orders of magnitude smaller than the healing length are present. In these experiments, no significant heating or particle loss is observed.Comment: 7 pages, 7 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

Heisenberg-limited metrology with a squeezed vacuum state, three-mode mixing, and information recycling

We have previously shown that quantum-enhanced atom interferometry can be achieved by mapping the quantum state of squeezed optical vacuum to one of the atomic inputs via a beamsplitter-like process [Phys. Rev. A 90, 063630 (2014)]. Here we ask the question: is a better phase sensitivity possible if the quantum state transfer (QST) is described by a three-mode-mixing model, rather than a beamsplitter? The answer is yes, but only if the portion of the optical state not transferred to the atoms is incorporated via information recycling. Surprisingly, our scheme gives a better sensitivity for lower QST efficiencies and with a sufficiently large degree of squeezing can attain near-Heisenberg-limited sensitivities for arbitrarily small QST efficiencies. Furthermore, we use the quantum Fisher information to demonstrate the near optimality of our scheme

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

A Tribute to William S. Geimer

A Tribute to William S. Geimer Meredith Susan Palmer* * Associate Dean for Student Affairs and Admissions, Washington and Lee University School of Law, J.D., 1985, Washington and Lee University. Truly, I say to you, as you did it to one of the least of these my brethren, you did it to me.1 Bill Geimer is not a man of material things. But somehow, in the material things that he chose to have around him - the mementos, the odd souvenirs, the offerings from students, clients, friends - I find the story of the man, the teacher, and the lawyer Bill Geimer is to me. In my mind's eye, I see Bill's office here at Washington and Lee as I first saw it, as a hesitant first-year law student approaching the sanctum sanctorum of a faculty member. There is a desktop name plate, regular Army issue, decorated with grenades or something equally militaristic and intimidating. But next to that is a picture of Dr. Martin Luther King, with his stirring words evoking hope for justice and freedom on earth. And next to that, a membership certificate for the Lawyer's Alliance for Nuclear Arms Control, and a drawing of Quijote, lance raised to a windmill. How could this be? While reconciling the seemingly irreconcilable is the everyday task of the law student, no trick of logic could make these disparate pieces fit; one simply had to get to know the man. That one could do so as a law student is itself part of what defines Bill Geimer. The student who came to know Bill heard a story of a kid from the rural south, off to a small state university to play basketball but who, like countless kids before him, spent a bit more time playing than studying. Come Graduation Day, with no game plan, he joined Uncle Sam's family. A grounding in tanks, guns, and tactics preceded duty with the military police, but something else happened during those years. Assigned to assist with an investigation, he finds an aptitude for the law, an appreciation of justice, and a burning sense of the unfairness of justice denied. The young man who returned from service to go on to a distinguished career as a law student at the University of North Carolina was a man with a game plan, and a mission. It was no surprise that Bill's mission as a lawyer was not in the office towers of Atlanta or the corporate boardrooms of Wall Street, but among the plain folks of Fayetteville, North Carolina, and later in the community of migrant farm labor working and living hard under the hot Carolina sun. I see another memento, this time in Bill's home. It's an odd piece of, well, let's call it folk art. Crudely carved, frankly ugly. Taste is a delicate thing, so one observes diplomatically that it is an "interesting" object. There's a story, of course, a story of a client for whom Bill had worked, putting together the paperwork to get a fledgling arts-and-crafts shop off the ground. This client, like many Bill served, claimed not to have the cash to pay. But, the client said, he could give Bill this valuable piece of work. Barter being a fundamentally more honest exchange and thus appealing to Bill, the transaction was concluded. Not until Bill brought his sculpture home did he discover the price tag stuck to the underside, for something substantially less than the agreed-upon fee. He kept the awkward thing, price tag intact, I think as a reminder of his own fallibility, of the ingenuity of the ordinary man, and of the need to forget neither. Another memento, in some ways the most important to this former student, is a large, faded, well-handled poster on the professor's office door. A young man in Carolina Blue goes up for a shot, stretching for the basket, with seconds left on the clock. Anyone who knows Bill Geimer knows that he is devoted to Carolina basketball. In fact, Bill may have spent so much time watching the Tar Heels play that he began to confuse teaching with coaching. As a former student of Bill's, I'm not sure that was a bad thing.

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

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

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