Christian J. Bordé

Vibration-rotation molecular constants for the ground and (ν3 = 1) states of 32SF6 from saturated absorption spectroscopy

Abstract An analysis has been made of the vibration-rotation structure of the ν3 band of 32SF6 from measurements, by saturated absorption spectroscopy, of the frequencies for 136 transitions in close coincidence with CO2 and N2O laser lines in the 28-THz region. After deconvolution of the fine structure lines from their hyperfine structures, the centers of vibration-rotation transitions are given with a 5-kHz uncertainty. They are analyzed using the tensor Hamiltonian of Moret-Bailly, developed to the fifth order of approximation. An iterative procedure, using full diagonalization of the Hamiltonian matrices, leads to a very accurate determination of 18 effective molecular constants of the (v3 = 1) excited state, together with 6 constants of the ground state (both for scalar and tensor terms). For instance, the inertial constant of the ground state is β0 = B0 = 0.0910842001(10) cm−1, the vibrational energy is α = ν3 = 948.10252337(40) cm−1, and the Coriolis coupling coefficient is ζ3 = 0.69344341(20). The recorded transitions, ranging from P(84) to R(94), are reproduced with a standard deviation σ d = 28 kHz ⋍ 0.93 × 10 −6 cm −1 . A few transitions remain out of the fit, and the possibility of resonances with close vibrational levels is briefly discussed. We also give the predicted positions for SF6 transitions in close coincidence with laser lines of various isotopic species of CO2.

High stability CW waveguide CO 2 laser for high resolution saturation spectroscopy

We describe a stable waveguide CO 2 laser for spectroscopic applications. The short term spectral width is less than 10 kHz and a 10-12flicker floor is reached for the Allan variance. A study of the oscillation frequency versus resonator length demonstrates the major influence of the anomalous index of refraction of the medium. Saturation resonances with a 20 kHz peak-to-peak width have been obtained with a very good signal-to-noise ratio. A complete spectrum of SF 6 for P (16) at 947.74 cm-1is given as an example to illustrate the 500 MHz bandwidth of the laser.

TOWARDS A NEW ABSOLUTE FREQUENCY REFERENCE GRID IN THE 28 THz RANGE

Abstract We present a grid of absolute reference frequencies based on CO2 (or N2O) lasers locked to saturation peaks of heavy molecules. Frequency differences between OsO4 peaks corresponding to adjacent CO2 laser lines from P(12) to P(22) have been measured with 1 kHz accuracy. This set includes one 192OsO4 resonance whose absolute frequency is known with the same accuracy. This absolute grid is then used to provide an absolute calibration of the ν3 band saturation spectrum of SF6. We also find a 23 kHz average frequency difference between the CO2 grid and the new OsO4 grid which we interpret tentatively as a small extrapolation error from the R to the P branch frequencies of CO2.

Superfine and hyperfine structures in the v3 band of 32SF6

Abstract We present a first detailed account of our theoretical approach to reproduce observed superfine and hyperfine structures in the ν 3 band of SF 6 and we display various observed and calculated patterns of superfine clusters exhibiting hyperfine effects. The main operators of the hamiltonian are derived and the associated constants are related to molecular parameters. We show that, owing to the off-diagonal terms in the hyperfine hamiltonian, a mixing occurs between vibration—rotation states with different point-group symmetry species. As a consequence, superfine and hyperfine structures have to be considered simultaneously and hyperfine hamiltonian matrices connecting several vibration—rotation states need to be diagonalized to reproduce the spectra. We analyse in greater detail a few typical examples from which several molecular constants have been determined (e.g. t 044 , c d ). For the first time, the sign c d is obtained. Also an effective change, Δ c d , is found between upper and lower levels which can be readily interpreted as a manifestation of the tensor spin—vibration interaction.

State-of-the-Art for High Accuracy Frequency Standards in the 28 THz Range Using Saturated Absorption Resonances of OsO4 and CO2

CO2 lasers play an important role in optical frequency metrology. In fact, most infrared frequency synthesis chains implemented up to now, include at least one CO2 laser. In practice, it is possible to measure any frequency from a few GHz to 150THz by means of only two stabilized CO2 lasers and a microwave source. Furthermore, reproducibilities and stabilities now obtained with OsO4 stabilized CO2 lasers allow us to use them as secondary frequency standards for frequency measurements of visible radiation with accuracies approaching 10−12.

Theoretical tools for atom optics and interferometry

Abstract The development of high sensitivity and high accuracy atom interferometers requires new theoretical tools for their modelization: in this article we emphasize specifically a generalized Fresnel–Kirchhoff formula for atom optics in the form of ABCD matrices and covariant wave equations in the form of a Dirac equation for atom optics in the presence of gravito-inertial fields. As examples, we derive the phase shift for the atom gravimeter and the output of an atom laser. Some of the physics of the beam splitters is described. We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background. This theory is used to calculate and discuss relativistic phase shifts in the context of matter-wave interferometry (especially atom or antiatom interferometry). In this way, many effects are introduced in a unified relativistic framework, including spin-gravitation terms: gravitational red shift, Thomas precession, Sagnac effect, spin-rotation effect, orbital and spin Lense–Thirring effects, de Sitter geodetic precession and finally the effect of gravitational waves.

Measurement of the Boltzmann constant by the Doppler broadening technique at a accuracy level

In this article, we describe an experiment performed at the Laboratoire de physique des lasers and dedicated to an optical measurement of the Boltzmann constant kB. With the proposed innovative technique, determining kB comes down to an ordinary frequency measurement. The method consists in measuring as accurately as possible the Doppler absorption profile of a rovibrational line of ammonia in thermal equilibrium. This profile is related to the Maxwell–Boltzmann molecular velocity distribution along the laser beam. A fit of the absorption line shape leads to a determination of the Doppler width proportional to √ kBT and thus to a determination of the Boltzmann constant. The laser source is an ultra-stable CO2 laser with a wavelength λ ≈ 10 µm. The absorption cell is placed in a thermostat, keeping the temperature at 273.15 K within 1.4 mK. We were able to measure kB with a relative uncertainty as small as 3.8 × 10 −5 , which represents an improvement of an order of magnitude for an integration time

Matter-Wave Interferometers: A Synthetic Approach

Publisher Summary This chapter presents a synthetic approach to matter–wave interferometers. The key element of most matter–wave interferometers is a diffractive beam splitter. Ideally, a diffractive beam splitter is a scattering potential for the incident particle. There is a general class of interferometers in which the splitters change, in general, both the external motion and the internal state in a single step. This includes, as a special case, interferometers in which the splitters change only the external motion. In another class of interferometers, the first step is to create a superposition of states (labels), either internal or external, and the second step is to separate these states in the physical space by a diagonal state (label) dependent potential. The chapter discusses the physics of the generalized beam splitter. It explains scattering matrix in the time-dependent approach and propagators among field zones. The chapter also elaborates in detail the architecture of interferometers and its sensitivity to gravitational and electromagnetic fields.

Relativistic Phase Shifts for Dirac Particles Interacting with Weak Gravitational Fields in Matter—Wave Interferometers

We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background. We solve the difficulties which arise from the derivative coupling and we are able to introduce an interaction picture. We derive expressions for the scattering amplitude and for the outgoing spinor to first-order. In several appendices, the link with the canonical approach in General Relativity is established and a generalized stationary phase method is used to calculate the outgoing spinor. We show how our expressions can be used to calculate and discuss phase shifts in the context of matter-wave interferometry (especially atom or antiatom interferometry). In this way, many effects are introduced in a unified relativistic framework, including spin-gravitation terms: gravitational red shift, Thomas precession, Sagnac effect, spin-rotation effect, orbital and spin Lense-Thirring effects, de Sitter geodetic precession and finally the effect of gravitational waves. A new analogy with the electromagnetic interaction is pointed out.

Density Matrix Equations and Diagrams for High Resolution Non-Linear Laser Spectroscopy: Application to Ramsey Fringes in the Optical Domain

We present a semiclassical approach to the line shape problem in high resolution laser spectroscopy which includes,in a unified density matrix formalism, the influences of the beam geometry, of the molecular recoil and of the second-order Doppler effect. A fully covariant second-quantized extension of the formalism is outlined. We give also a general derivation of intensities for all non-linear processes using Racah algebra in Liouville space. We describe diagrammatic representations of the perturbative solutions of the equations suitable for all laser spectroscopy techniques. Simple topological rules characterize Doppler-free processes. The diagrams and their associated diagrammatic rules are illustrated by their applications to the computation of Ramsey fringes in the case of single photon, Doppler-free two-photon and saturation spectroscopies. Finally we show how light-shifts can be calculated by this method and find, as expected, that the shifts for Ramsey fringes are reduced by the ratio of the laser beam radius to the zone separation when compared to the shifts for the single zone signal.