On distribution formulas for complex and ℓ\ell-adic polylogarithms

We study an $\ell$-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a notion of certain universal Kummer-Heisenberg measures that enable interpolating the $\ell$-adic polylogarithmic distribution relations for all degrees.Comment: This article has appeared in the proceedings volume "Periods in Quantum Field Theory and Arithmetic" (J.~Burgos Gil, K.~Ebrahimi-Fard, H.~Gangl eds), [Conference proceedings ICMAT-MZV 2014] Springer Proceedings in Mathematics \& Statistics {\bf 314} (2020), pp.593--61

Du tracé de la ligne dans la Genèse

RÉSUMÉ   Drawing a line implies the ability to separate, to divide up, and to organize (to "rule" or "govern"). We will examine how these three abilities function in one French and one German translation of the Book of Genesis, and how, examined from a linguistic perspective, these texts illustrate a genesis of another kind : the birth of number, perfectivity, and the impersonal construction. Key words : closure ; genesis ; form ; impersonal ; number ; perfectivity.     Mots clés : 

Semiclassical theory of cavity-assisted atom cooling

We present a systematic semiclassical model for the simulation of the dynamics of a single two-level atom strongly coupled to a driven high-finesse optical cavity. From the Fokker-Planck equation of the combined atom-field Wigner function we derive stochastic differential equations for the atomic motion and the cavity field. The corresponding noise sources exhibit strong correlations between the atomic momentum fluctuations and the noise in the phase quadrature of the cavity field. The model provides an effective tool to investigate localisation effects as well as cooling and trapping times. In addition, we can continuously study the transition from a few photon quantum field to the classical limit of a large coherent field amplitude.Comment: 10 pages, 8 figure

Micro-mechanical oscillator ground state cooling via intracavity optical atomic excitations

We predict ground state cooling of a micro-mechanical oscillator, i.e. a vibrating end-mirror of an optical cavity, by resonant coupling of mirror vibrations to a narrow internal optical transition of an ensemble of two level systems. The particles represented by a collective mesoscopic spin model implement, together with the cavity, an efficient, frequency tailorable zero temperature loss channel which can be turned to a gain channel of pump. As opposed to the case of resolved-sideband cavity cooling requiring a small cavity linewidth, one can work here with low finesses and very small cavity volumes to enhance the light mirror and light atom coupling. The tailored loss and gain channels provide for efficient removal of vibrational quanta and suppress reheating. In a simple physical picture of sideband cooling, the atoms shape the cavity profile to enhance/inhibit scattering into higher/lower energy sidebands. The method should be applicable to other cavity based cooling schemes for atomic and molecular gases as for molecular ensembles coupled to stripline cavities

Scaling properties of cavity-enhanced atom cooling

We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.Comment: 7 pages, 5 figure

Ultra-cold atoms in an optical cavity: two-mode laser locking to the cavity avoiding radiation pressure

The combination of ultra-cold atomic clouds with the light fields of optical cavities provides a powerful model system for the development of new types of laser cooling and for studying cooperative phenomena. These experiments critically depend on the precise tuning of an incident pump laser with respect to a cavity resonance. Here, we present a simple and reliable experimental tuning scheme based on a two-mode laser spectrometer. The scheme uses a first laser for probing higher-order transversal modes of the cavity having an intensity minimum near the cavity's optical axis, where the atoms are confined by a magnetic trap. In this way the cavity resonance is observed without exposing the atoms to unwanted radiation pressure. A second laser, which is phase-locked to the first one and tuned close to a fundamental cavity mode drives the coherent atom-field dynamics.Comment: 7 pages, 7 figure

Cold atoms in a high-Q ring-cavity

We report the confinement of large clouds of ultra-cold 85-Rb atoms in a standing-wave dipole trap formed by the two counter-propagating modes of a high-Q ring-cavity. Studying the properties of this trap we demonstrate loading of higher-order transverse cavity modes and excite recoil-induced resonances.Comment: 4 pages, 4 figure

Collective Sideband Cooling in an Optical Ring Cavity

We propose a cavity based laser cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave which acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate travelling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high frequency component, that is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering. Tight confinement in the optical lattice together with the prediction, that more than 50% of the trapped particles can be cooled into the motional ground state, promise high phase space densities.Comment: 4 pages, 1 figur

Observation of Collective-Emission-Induced Cooling inside an Optical Cavity

We report the observation of collective-emission-induced, velocity-dependent light forces. One third of a falling sample containing 3 x 10^6 cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented confocal resonator. We observe decelerations up to 1500 m/s^2 and cooling to temperatures as low as 7 uK, well below the free space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.Comment: 10 pages, 5 figure