Precision spectroscopy of the molecular ion HD+: control of Zeeman shifts

Precision spectroscopy on cold molecules can potentially enable novel tests of fundamental laws of physics and alternative determination of some fundamental constants. Realizing this potential requires a thorough understanding of the systematic effects that shift the energy levels of molecules. We have performed a complete ab initio calculation of the magnetic field effects for a particular system, the heteronuclear molecular hydrogen ion HD+. Different spectroscopic schemes have been considered, and numerous transitions, all accessible by modern radiation sources and exhibiting well controllable or negligible Zeeman shift, have been found to exist. Thus, HD+ is a perspective candidate for determination of the ratio of electron-to-nuclear reduced mass, and for tests of its time-independence.Comment: A Table added, references and figures update

The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge also satisfies the full Einstein equations. We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum case.Comment: 83 pages, 1 figur

Doppler cooling to the recoil limit using sharp atomic transitions

In this paper, we develop an analytical approach to Doppler cooling of atoms by one- or two-photon transitions when the natural width of the excited level is so small that the process leads to a Doppler temperature comparable to the recoil temperature. A ``quenching'' of the sharp line is introduced in order to allow control of the time scale of the problem. In such limit, the usual Fokker-Planck equation does not correctly describe the cooling process. We propose a generalization of the Fokker-Planck equation and derive a new model which is able to reproduce correctly the numerical results, up to the recoil limit. Two cases of practical interest, one-photon Doppler cooling of strontium and two-photon Doppler cooling of hydrogen are considered.Comment: 5 pages, RevTex 4, submitted to JOSA B (special issue "laser cooling of atoms"

Continuous-wave Doppler-cooling of hydrogen atoms with two-photon transitions

We propose and analyze the possibility of performing two-photon continuous-wave Doppler-cooling of hydrogen atoms using the 1S-2S transition. "Quenching" of the 2S level (by coupling with the 2P state) is used to increase the cycling frequency, and to control the equilibrium temperature. Theoretical and numerical studies of the heating effect due to Doppler-free two-photon transitions evidence an increase of the temperature by a factor of two. The equilibrium temperature decreases with the effective (quenching dependent) width of the excited state and can thus be adjusted up to values close to the recoil temperature.Comment: 11 pages, 4 figures in eps forma

Non-linear spectroscopy of rubidium: An undergraduate experiment

In this paper, we describe two complementary non-linear spectroscopy methods which both allow to achieve Doppler-free spectra of atomic gases. First, saturated absorption spectroscopy is used to investigate the structure of the $5{\rm S}_{1/2}\to 5{\rm P}_{3/2}$ transition in rubidium. Using a slightly modified experimental setup, Doppler-free two-photon absorption spectroscopy is then performed on the $5{\rm S}_{1/2}\to 5{\rm D}_{5/2}$ transition in rubidium, leading to accurate measurements of the hyperfine structure of the $5{\rm D}_{5/2}$ energy level. In addition, electric dipole selection rules of the two-photon transition are investigated, first by modifying the polarization of the excitation laser, and then by measuring two-photon absorption spectra when a magnetic field is applied close to the rubidium vapor. All experiments are performed with the same grating-feedback laser diode, providing an opportunity to compare different high resolution spectroscopy methods using a single experimental setup. Such experiments may acquaint students with quantum mechanics selection rules, atomic spectra and Zeeman effect.Comment: 16 pages, 8 figure

Conformal scattering for a nonlinear wave equation on a curved background

The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities. The proof is achieved in three steps. A priori linear estimates are obtained via an adaptation of the Morawetz vector field in the Schwarzschild spacetime and a method used by H\"ormander for the Goursat problem. A well-posedness result for the characteristic Cauchy problem on a light cone at infinity is then obtained. This requires a control of the nonlinearity uniform in time which comes from an estimates of the Sobolev constant and a decay assumption on the nonlinearity of the equation. Finally, the trace operators on conformal infinities are built and used to define the conformal scattering operator

Reducing the first-order Doppler shift in a Sagnac interferometer

4p(5)p[1/2](0) transition in Kr at lambda = 212 nm. The achieved precision of 6 x 10(-10) is limited by the characteristics of the laser system. (c) 2007 Optical Society of America

An Improved Experimental Limit on the Electric Dipole Moment of the Neutron

An experimental search for an electric-dipole moment (EDM) of the neutron has been carried out at the Institut Laue-Langevin (ILL), Grenoble. Spurious signals from magnetic-field fluctuations were reduced to insignificance by the use of a cohabiting atomic-mercury magnetometer. Systematic uncertainties, including geometric-phase-induced false EDMs, have been carefully studied. Two independent approaches to the analysis have been adopted. The overall results may be interpreted as an upper limit on the absolute value of the neutron EDM of |d_n| < 2.9 x 10^{-26} e cm (90% CL).Comment: 5 pages, 2 figures. The published PRL is slightly more terse (e.g. no section headings) than this version, due to space constraints. Note a small correction-to-a-correction led to an adjustment of the final limit from 3.0 to 2.9 E-26 e.cm compared to the first version of this preprin