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

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

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

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

On the existence of Killing vector fields

In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra

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

Two-Photon Doppler cooling of alkaline-earth-metal and ytterbium atoms

A new possibility of laser cooling of alkaline-earth-metal and Ytterbium atoms using a two-photon transition is analyzed. We consider a $^{1}S_{0}$ - $^{1}S_{0}$ transition, with excitation in near resonance with the $^{1}P_{1}$ level. This greatly increases the two-photon transition rate, allowing an effective transfer of momentum. The experimental implementation of this technique is discussed and we show that for Calcium, for example, two-photon cooling can be used to achieve a Doppler limit of 123 microKelvin. The efficiency of this cooling scheme and the main loss mechanisms are analyzed.Comment: 7 pages, 5 figure

Optical frequency measurement of the 1S-3S two-photon transition in hydrogen

This article reports the first optical frequency measurement of the $1\mathrm{S}-3\mathrm{S}$ transition in hydrogen. The excitation of this transition occurs at a wavelength of 205 nm which is obtained with two frequency doubling stages of a titanium sapphire laser at 820 nm. Its frequency is measured with an optical frequency comb. The second-order Doppler effect is evaluated from the observation of the motional Stark effect due to a transverse magnetic field perpendicular to the atomic beam. The measured value of the $1\mathrm{S}_{1/2}(F=1)-3\mathrm{S}_{1/2}(F=1)$ frequency splitting is $2 922 742 936.729 (13) \mathrm{MHz}$ with a relative uncertainty of $4.5\times10^{-12}$. After the measurement of the $1\mathrm{S}-2\mathrm{S}$ frequency, this result is the most precise of the optical frequencies in hydrogen

Symmetries of spacetime and their relation to initial value problems

We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential equations can be deduced from the matter field equations. Second, gravity is supposed to be coupled to the matter fields by requiring that the Ricci tensor is a smooth function of the basic matter field variables and the metric. It is shown then that the ``time'' evolution of these type of gravity-matter systems preserves the symmetries of initial data specifications.Comment: 12 pages, to appear in Class. Quant. Gra

CPT and Lorentz Tests in Hydrogen and Antihydrogen

Signals for CPT and Lorentz violation at the Planck scale may arise in hydrogen and antihydrogen spectroscopy. We show that certain 1S-2S and hyperfine transitions can exhibit theoretically detectable effects unsuppressed by any power of the fine-structure constant.Comment: 4 pages REVTeX, submitted for publicatio