Sets avoided by Brownian motion

Any fixed cylinder is hit almost surely by a 3-dimensional Brownian motion, but is there a random cylinder that is in the complement? We answer this for cylinders, and then replacing a cylinder with a more general set

Entanglement verification with finite data

Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the second performs a tomographically complete measurement.Comment: 4 pages, 3 pretty picture

Quasi integral of motion for axisymmetric potentials

We present an estimate of the third integral of motion for axisymmetric three-dimensional potentials. This estimate is based on a Staeckel approximation and is explicitly written as a function of the potential. We tested this scheme for the Besancon Galactic model and two other disc-halo models and find that orbits of disc stars have an accurately conserved third quasi integral. The accuracy ranges from of 0.1% to 1% for heights varying from z = 0~kpc to z= 6 kpc and Galactocentric radii R from 5 to 15kpc. We also tested the usefulness of this quasi integral in analytic distribution functions of disc stellar populations: we show that the distribution function remains approximately stationary and that it allows to recover the potential and forces by applying Jeans equations to its moments.Comment: 9 pages, 9 figures, accepted for publication in Astron. and Astrophy

Subradiance in a Large Cloud of Cold Atoms

Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes.Here we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model

Superradiance in a Large and Dilute Cloud of Cold Atoms in the Linear-Optics Regime

Superradiance has been extensively studied in the 1970s and 1980s in the regime of superfluores-cence, where a large number of atoms are initially excited. Cooperative scattering in the linear-optics regime, or "single-photon superradiance" , has been investigated much more recently, and superra-diant decay has also been predicted, even for a spherical sample of large extent and low density, where the distance between atoms is much larger than the wavelength. Here, we demonstrate this effect experimentally by directly measuring the decay rate of the off-axis fluorescence of a large and dilute cloud of cold rubidium atoms after the sudden switch-off of a low-intensity laser driving the atomic transition. We show that, at large detuning, the decay rate increases with the on-resonance optical depth. In contrast to forward scattering, the superradiant decay of off-axis fluorescence is suppressed near resonance due to attenuation and multiple-scattering effects

The rise and fall of early oil field technology: The torsion balance gradiometer

Today elementary physics students take for granted such quantities as "big G," the universal gravitational constant. In fact in the late 1700s the value of this quantity was unknown, and the quest to determine it led to some of the earliest geophysical instrumentation. Just after the Revolutionary War in the United States, Cavendish developed the first system to measure the universal gravitational constant, the familiar "big G." Unfortunately, for geologists (at this time still mostly "gentlemen scientists"), this apparatus produced data which were difficult to interpret geologically, and it was far too large and cumbersome for field use. The geologic limitation was that the system only measured the horizontal derivative of a horizontal component of the gravity field, a quantity which by itself is difficult to interpret. Thus no applications of this elegant yet laboratory-bound instrument emerged