Fast and dense magneto-optical traps for Strontium

We improve the efficiency of sawtooth-wave-adiabatic-passage (SWAP) cooling for strontium atoms in three dimensions and combine it with standard narrow-line laser cooling. With this technique, we create strontium magneto-optical traps with $6\times 10^7$ bosonic $^{88}$Sr ($1\times 10^7$ fermionic $^{87}$Sr) atoms at phase-space densities of $2\times 10^{-3}$ ($1.4\times 10^{-4}$). Our method is simple to implement and is faster and more robust than traditional cooling methods.Comment: 9 pages, 6 figure

On a conjecture by Boyd

The aim of this note is to prove the Mahler measure identity $m(x+x^{-1}+y+y^{-1}+5) = 6 m(x+x^{-1}+y+y^{-1}+1)$ which was conjectured by Boyd. The proof is achieved by proving relationships between regulators of both curves

Asymptotic Stability, Instability and Stabilization of Relative Equilibria

In this paper we analyze asymptotic stability, instability and stabilization for the relative equilibria, i.e. equilibria modulo a group action, of natural mechanical systems. The practical applications of these results are to rotating mechanical systems where the group is the rotation group. We use a modification of the Energy-Casimir and Energy-Momentum methods for Hamiltonian systems to analyze systems with dissipation. Our work couples the modern theory of block diagonalization to the classical work of Chetaev

Paraphysial Cysts of the Third Ventricle

The radiographic appearances of the third ventricle in 26 patients with colloid cysts, have been reviewed. The constant radiographic features and the invectigations in which the diagnostic yield is good are stressed

Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator

We experimentally demonstrate electromagnetically induced transparency and light storage with ultracold 87Rb atoms in a Mott insulating state in a three dimensional optical lattice. We have observed light storage times of about 240 ms, to our knowledge the longest ever achieved in ultracold atomic samples. Using the differential light shift caused by a spatially inhomogeneous far detuned light field we imprint a "phase gradient" across the atomic sample, resulting in controlled angular redirection of the retrieved light pulse.Comment: 4 pages, 4 figure

Pfaffian-like ground state for 3-body-hard-core bosons in 1D lattices

We propose a Pfaffian-like Ansatz for the ground state of bosons subject to 3-body infinite repulsive interactions in a 1D lattice. Our Ansatz consists of the symmetrization over all possible ways of distributing the particles in two identical Tonks-Girardeau gases. We support the quality of our Ansatz with numerical calculations and propose an experimental scheme based on mixtures of bosonic atoms and molecules in 1D optical lattices in which this Pfaffian-like state could be realized. Our findings may open the way for the creation of non-abelian anyons in 1D systems

State-Dependent Optical Lattices for the Strontium Optical Qubit

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than four orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks.Comment: 6 pages, 4 figures + 6 pages supplemental materia

A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page