Bifix codes and interval exchanges

We investigate the relation between bifix codes and interval exchange transformations. We prove that the class of natural codings of regular interval echange transformations is closed under maximal bifix decoding.Comment: arXiv admin note: substantial text overlap with arXiv:1305.0127, arXiv:1308.539

Agile low phase noise radio-frequency sine wave generator applied to experiments on ultracold atoms

We report on the frequency performance of a low cost (~500$) radio-frequency sine wave generator, using direct digital synthesis (DDS) and a field-programmable gate array (FPGA). The output frequency of the device may be changed dynamically to any arbitrary value ranging from DC to 10 MHz without any phase slip. Sampling effects are substantially reduced by a high sample rate, up to 1 MHz, and by a large memory length, more than 2.10^5 samples. By using a low noise external oscillator to clock the DDS, we demonstrate a phase noise as low as that of the master clock, that is at the level of -113 dB.rad^2/Hz at 1 Hz from the carrier for an output frequency of 3.75 MHz. The device is successfully used to confine an ultracold atomic cloud of rubidium 87 in a RF-based trap, and there is no extra heating from the RF source.Comment: 10 pages, 6 figure

Coherence-preserving trap architecture for long-term control of giant Rydberg atoms

We present a way to trap a single Rydberg atom, make it long-lived and preserve an internal coherence over time scales reaching into the minute range. We propose to trap using carefully designed electric fields, to inhibit the spontaneous emission in a non resonant conducting structure and to maintain the internal coherence through a tailoring of the atomic energies using an external microwave field. We thoroughly identify and account for many causes of imperfection in order to verify at each step the realism of our proposal.Comment: accepted for publication in PR

Parallel approximation of the exponential of Hermitian matrices

In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the computation reduces to independent resolutions of linear systems. We analyze the effects of rounding errors on the accuracy of our algorithm. We complete this work with numerical tests showing the efficiency of our method and a comparison of its performances with Krylov algorithms

The finite index basis property

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namely the class of tree sets. We prove as a main result that for a uniformly recurrent tree set S, a finite bifix code X on the alphabet A is S-maximal of S-degree d if and only if it is the basis of a subgroup of index d of the free group on

Maximal bifix decoding

International audienceWe consider a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurrent tree sets, where the tree sets are defined by a condition on the possible extensions of bispecial factors. We prove that this class is closed under maximal bifix decoding. The proof uses the fact that the class is also closed under decoding with respect to return words

Source laser intense pour le refroidissement du 87Rb par doublement de fréquence d'un laser fibré télécom

to appear in EPJ-ST; COLOQ11 ProceedingsWe built a frequency-doubled laser for 87Rb laser cooling, from a Telecom fiber laser. Thanks to intense technological development, telecom fiber lasers exhibit outstanding properties regarding relative intensity noise and modulation bandwidth. The enhanced doubling efficiency of periodically poled crystals allowed to obtain up to 1.8 W at 780 nm from 10 W at 1560 nm, with a simple pass configuration in a 50-mm long crystal of ppLN:MgO. This technique can also be applied at the wavelength of potassium (767 nm) (Bourdel, 2009) and could be of great interest for the realization of dipole traps

Responsive Pickering Emulsions Stabilized by Frozen Complex Coacervate Core Micelles

[Image: see text] Frozen complex coacervate core micelles (C3Ms) were developed as a class of particle stabilizers for Pickering emulsions. The C3Ms are composed of a core of electrostatically interacting weak polyelectrolytes, poly(acrylic acid) (pAA) and poly(dimethylaminopropylacrylamide) (pDMAPAA), surrounded by a corona of water-soluble and surface active poly(N-isopropylacrylamide) (pNiPAM). Mixing parameters of the two polymer solutions, including pH, mixing method, charge ratio, and salinity of the medium, were carefully controlled, leading to monodisperse, colloidally stable C3Ms. A combination of dynamic light scattering and proton nuclear magnetic resonance experiments showed that the C3Ms gradually disassembled from a dynamically frozen core state in pure water into free polyelectrolyte chains above 0.8 M NaCl. Upon formulation of dodecane-in-water emulsions, the frozen C3Ms adsorb as particles at the droplet interfaces in striking contrast with most of the conventional micelles made of amphiphilic block copolymers which fall apart at the interface. Eventually, increasing the salt concentration of the system triggered disassembly of the C3Ms, which led to emulsion destabilization