Christian Borde - Academia.edu (original) (raw)

Books by Christian Borde

Papers by Christian Borde

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Jan 15, 2005

Over the past 40 years, a number of discoveries in quantum physics have completely transformed ou... more Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light c. Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light c, the Planck constant h, the Boltzmann constant k B or the electron mass m e can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant a or its gravitational analogue a G . This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.

Laser Frequency Stabilization, Standards, Measurement, and Applications, 2001

A series of two searches of a frequency difference in the vibrational spectrum of the enantiomers... more A series of two searches of a frequency difference in the vibrational spectrum of the enantiomers of CHFClBr by using Fabry-Perot cavities is presented. No difference is observed within the present sensitivity of 10-13. This experiment is limited by pressure shifts induced by uncontrolled impurities of the samples. We propose to use a two-photon Ramsey fringes scheme with a molecular

We present a strong field theory of matter wave splitting in the presence of various gravitationa... more We present a strong field theory of matter wave splitting in the presence of various gravitational, inertial and trapping potentials. The effect of these potentials on the resonance condition (between the splitting potential and the considered effective two-level system) and on the atomic Borrmann effect is investigated in detail. The dispersive structuring of an incident atomic wave packet - due to such generalized beam splitters - is studied and modeled, and several important dynamical features of the solutions are detailed (generalized Rabi oscillations, velocity selection, anomalous dispersion, generalized Borrmann effect and anomalous gravitational bending). Finally, we show how to express this triple interaction "matter - splitting potential - gravito-inertial and trapping potentials" as an equivalent instantaneous interaction which turns out to be a very efficient tool for the modeling of atom interferometers.

Comptes Rendus Physique, 2004

Osmium tetroxide offers the beautiful example of a central particle, the osmium nucleus, with sev... more Osmium tetroxide offers the beautiful example of a central particle, the osmium nucleus, with several possible spin values (1/2 for 187 Os and 3/2 for 189 Os), interacting with the very symmetric and well-defined electromagnetic environment created by a tetrahedron of spinless oxygen nuclei. Among other nuclear hyperfine interactions, the magnetic field generated by the vibrations of these oxygen nuclei orientates this central spin. To study specifically this spin-vibration interaction, the magnetic dipole contributions to the hyperfine structures observed in the ν 3 band of 189 OsO 4 and 187 OsO 4 have been analyzed in detail. Besides the spin-rotation constants already deduced in a previous paper, we have obtained the spin-vibration constant, A, and a small change of the spin-rotation constant δc a in the upper vibrational level. We have verified the speculated relation A = ζ 3 c a at the 1% level (ζ 3 is the Coriolis coupling constant, which multiplies the internal vibrational angular momentum to turn it into a physical angular momentum comparable to the pure rotation angular momentum). Starting from first principles, we have rederived the expressions of the magnetic dipole constants for any semi-rigid polyatomic molecule. When these are applied to OsO 4 , they justify the previous approximate relationship between A and c a and give values for the correction terms which account for the 1% difference. To cite this article: C. Chardonnet et al., C. R. Physique 5 (2004).  2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.

European Physical Journal D, 1999

Excited states of the Z = 102 nuclide 254No have been studied in the reaction 208Pb(48Ca,2n) by m... more Excited states of the Z = 102 nuclide 254No have been studied in the reaction 208Pb(48Ca,2n) by means of in-beam γ -ray spectroscopy in combination with recoil gating and recoil decay tagging. A Ge detector array, consisting of four clover detectors, and a gas-filled separator were used. Six γ-ray lines were observed and associated with E2 transitions in the ground state band of 254No, the highest-lying of these being the 16+→ 14+ transition. Based on global systematics and the extrapolated 2+ 1 excitation energy, the value β2= 0.27 ± 0.03 was extracted for the quadrupole deformation. An improved value for the half-life of 254No, T1/2= (48 ± 3) s, was determined.

Nature, 2010

In a recent paper, H. Mueller, A. Peters and S. Chu [A precision measurement of the gravitational... more In a recent paper, H. Mueller, A. Peters and S. Chu [A precision measurement of the gravitational redshift by the interference of matter waves, Nature 463, 926-929 (2010)] argued that atom interferometry experiments published a decade ago did in fact measure the gravitational redshift on the quantum clock operating at the very high Compton frequency associated with the rest mass of the Caesium atom. In the present Communication we show that this interpretation is incorrect.

IEEE Journal of Quantum Electronics - IEEE J QUANTUM ELECTRON, 2001

ABSTRACT We show that the lineshape and size of the detected signal in ultra-high-resolution stim... more ABSTRACT We show that the lineshape and size of the detected signal in ultra-high-resolution stimulated Raman spectroscopy computed from a general expression of the modulated signal are in good agreement with the experimental results. Using the theoretical expression of the signal, we analyze the resolving power and the sensitivity of our Raman spectrometer. We show that a second harmonic detection in high-frequency transfer modulation generates a lineshape without modulation broadening. A 2.6-kHz-wide resonance has been obtained with iodine, mainly limited by both the transit time and collisions

Comptes Rendus Physique - C R PHYS, 2004

Métrologie fondamentale : unités de base et constantes fondamentales Ce dossier des Comptes-Rendu... more Métrologie fondamentale : unités de base et constantes fondamentales Ce dossier des Comptes-Rendus est destiné à faire un point sur une métrologie fondamentale aujourd'hui en pleine mutation. Une dizaine de contributions y sont réunies sur des domaines frontières où se joue l'avenir de cette discipline. Le lecteur pourra découvrir à travers ces contributions que se dessine une tendance forte à rattacher les unités de base à des constantes fondamentales et le débat est ouvert quant à la pertinence, l'opportunité et la formulation de nouvelles définitions.

, Class. Quant. Grav. 28, 145017, (2011)], to which the reader is referred for more details.

International Journal of Thermophysics, 2010

In this paper, the latest results on the measurement of the Boltzmann constant k B, by laser spec... more In this paper, the latest results on the measurement of the Boltzmann constant k B, by laser spectroscopy of ammonia at 10μm are presented. The Doppler absorption profile of a rovibrational line of an NH3 gas sample at thermal and pressure equilibrium is measured as accurately as possible. The absorption cell is placed inside a large 1 m3 thermostat filled with an ice–water mixture, which sets the temperature very close to 273.15 K. Analyzing this profile, which is related to the Maxwell–Boltzmann molecular speed distribution, leads to a determination of the Boltzmann constant via a measurement of the Doppler width (proportional to \({\sqrt{k_{\rm B} T})}\) . A spectroscopic determination of the Boltzmann constant with an uncertainty as low as 37 ppm is obtained. Recent improvements with a new passive thermostat lead to a temperature accuracy, stability, and homogeneity of the absorption cell of 1 ppm over a day.

Comptes Rendus Physique, 2009

... of the Boltzmann constant by the Doppler broadening technique at a 3.8 10 5 accuracy level Kh... more ... of the Boltzmann constant by the Doppler broadening technique at a 3.8 10 5 accuracy level Khelifa Djerroud a , Cyril Lemarchand a , Alexandre Gauguet a ... d absorption est plac e dans un thermostat qui permet de contr ler la temp rature autour de 273,15 K avec une incertitude ...

Comptes Rendus Physique, 2009

A detailed theory of the line shape in linear absorption spectroscopy of low-pressure gases is de... more A detailed theory of the line shape in linear absorption spectroscopy of low-pressure gases is developed. The goal is to take into account all effects that come into play in the determination of Boltzmann's constant from measurements of the Doppler width. We demonstrate that there is no additional broadening from finite transit time across the laser beams. The molecular recoil and the second-order Doppler effect are included in the line shape thanks to a complete quantum treatment. The Mössbauer–Lamb–Dicke narrowing of Doppler lines by collisions is also included and the special cases of Galatry and Nelkin–Ghatak profiles are presented. To cite this article: C.J. Bordé, C. R. Physique 10 (2009).Une théorie détaillée de la forme des raies d'absorption linéaire des gaz à basse pression est développée. L'objectif est de mieux cerner tous les effets susceptibles d'intervenir dans la détermination de la constante de Boltzmann à partir d'une mesure de la largeur Doppler. On démontre en particulier qu'il n'y a pas d'élargissement supplémentaire lié au temps fini de traversée du faisceau laser par les molécules. Les effets de recul et Doppler du deuxième ordre sont intégrés dans la forme de raie grâce à un traitement quantique complet. L'effet Mössbauer–Lamb–Dicke de rétrécissement des raies Doppler par les collisions est lui aussi incorporé dans la théorie avec comme cas particuliers les profils de Galatry et de Nelkin–Ghatak. Pour citer cet article : C.J. Bordé, C. R. Physique 10 (2009).

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Jan 15, 2005

Over the past 40 years, a number of discoveries in quantum physics have completely transformed ou... more Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light c. Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light c, the Planck constant h, the Boltzmann constant k B or the electron mass m e can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant a or its gravitational analogue a G . This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.

Laser Frequency Stabilization, Standards, Measurement, and Applications, 2001

A series of two searches of a frequency difference in the vibrational spectrum of the enantiomers... more A series of two searches of a frequency difference in the vibrational spectrum of the enantiomers of CHFClBr by using Fabry-Perot cavities is presented. No difference is observed within the present sensitivity of 10-13. This experiment is limited by pressure shifts induced by uncontrolled impurities of the samples. We propose to use a two-photon Ramsey fringes scheme with a molecular

We present a strong field theory of matter wave splitting in the presence of various gravitationa... more We present a strong field theory of matter wave splitting in the presence of various gravitational, inertial and trapping potentials. The effect of these potentials on the resonance condition (between the splitting potential and the considered effective two-level system) and on the atomic Borrmann effect is investigated in detail. The dispersive structuring of an incident atomic wave packet - due to such generalized beam splitters - is studied and modeled, and several important dynamical features of the solutions are detailed (generalized Rabi oscillations, velocity selection, anomalous dispersion, generalized Borrmann effect and anomalous gravitational bending). Finally, we show how to express this triple interaction "matter - splitting potential - gravito-inertial and trapping potentials" as an equivalent instantaneous interaction which turns out to be a very efficient tool for the modeling of atom interferometers.

Comptes Rendus Physique, 2004

Osmium tetroxide offers the beautiful example of a central particle, the osmium nucleus, with sev... more Osmium tetroxide offers the beautiful example of a central particle, the osmium nucleus, with several possible spin values (1/2 for 187 Os and 3/2 for 189 Os), interacting with the very symmetric and well-defined electromagnetic environment created by a tetrahedron of spinless oxygen nuclei. Among other nuclear hyperfine interactions, the magnetic field generated by the vibrations of these oxygen nuclei orientates this central spin. To study specifically this spin-vibration interaction, the magnetic dipole contributions to the hyperfine structures observed in the ν 3 band of 189 OsO 4 and 187 OsO 4 have been analyzed in detail. Besides the spin-rotation constants already deduced in a previous paper, we have obtained the spin-vibration constant, A, and a small change of the spin-rotation constant δc a in the upper vibrational level. We have verified the speculated relation A = ζ 3 c a at the 1% level (ζ 3 is the Coriolis coupling constant, which multiplies the internal vibrational angular momentum to turn it into a physical angular momentum comparable to the pure rotation angular momentum). Starting from first principles, we have rederived the expressions of the magnetic dipole constants for any semi-rigid polyatomic molecule. When these are applied to OsO 4 , they justify the previous approximate relationship between A and c a and give values for the correction terms which account for the 1% difference. To cite this article: C. Chardonnet et al., C. R. Physique 5 (2004).  2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.

European Physical Journal D, 1999

Excited states of the Z = 102 nuclide 254No have been studied in the reaction 208Pb(48Ca,2n) by m... more Excited states of the Z = 102 nuclide 254No have been studied in the reaction 208Pb(48Ca,2n) by means of in-beam γ -ray spectroscopy in combination with recoil gating and recoil decay tagging. A Ge detector array, consisting of four clover detectors, and a gas-filled separator were used. Six γ-ray lines were observed and associated with E2 transitions in the ground state band of 254No, the highest-lying of these being the 16+→ 14+ transition. Based on global systematics and the extrapolated 2+ 1 excitation energy, the value β2= 0.27 ± 0.03 was extracted for the quadrupole deformation. An improved value for the half-life of 254No, T1/2= (48 ± 3) s, was determined.

Nature, 2010

In a recent paper, H. Mueller, A. Peters and S. Chu [A precision measurement of the gravitational... more In a recent paper, H. Mueller, A. Peters and S. Chu [A precision measurement of the gravitational redshift by the interference of matter waves, Nature 463, 926-929 (2010)] argued that atom interferometry experiments published a decade ago did in fact measure the gravitational redshift on the quantum clock operating at the very high Compton frequency associated with the rest mass of the Caesium atom. In the present Communication we show that this interpretation is incorrect.

IEEE Journal of Quantum Electronics - IEEE J QUANTUM ELECTRON, 2001

ABSTRACT We show that the lineshape and size of the detected signal in ultra-high-resolution stim... more ABSTRACT We show that the lineshape and size of the detected signal in ultra-high-resolution stimulated Raman spectroscopy computed from a general expression of the modulated signal are in good agreement with the experimental results. Using the theoretical expression of the signal, we analyze the resolving power and the sensitivity of our Raman spectrometer. We show that a second harmonic detection in high-frequency transfer modulation generates a lineshape without modulation broadening. A 2.6-kHz-wide resonance has been obtained with iodine, mainly limited by both the transit time and collisions

Comptes Rendus Physique - C R PHYS, 2004

Métrologie fondamentale : unités de base et constantes fondamentales Ce dossier des Comptes-Rendu... more Métrologie fondamentale : unités de base et constantes fondamentales Ce dossier des Comptes-Rendus est destiné à faire un point sur une métrologie fondamentale aujourd'hui en pleine mutation. Une dizaine de contributions y sont réunies sur des domaines frontières où se joue l'avenir de cette discipline. Le lecteur pourra découvrir à travers ces contributions que se dessine une tendance forte à rattacher les unités de base à des constantes fondamentales et le débat est ouvert quant à la pertinence, l'opportunité et la formulation de nouvelles définitions.

, Class. Quant. Grav. 28, 145017, (2011)], to which the reader is referred for more details.

International Journal of Thermophysics, 2010

In this paper, the latest results on the measurement of the Boltzmann constant k B, by laser spec... more In this paper, the latest results on the measurement of the Boltzmann constant k B, by laser spectroscopy of ammonia at 10μm are presented. The Doppler absorption profile of a rovibrational line of an NH3 gas sample at thermal and pressure equilibrium is measured as accurately as possible. The absorption cell is placed inside a large 1 m3 thermostat filled with an ice–water mixture, which sets the temperature very close to 273.15 K. Analyzing this profile, which is related to the Maxwell–Boltzmann molecular speed distribution, leads to a determination of the Boltzmann constant via a measurement of the Doppler width (proportional to \({\sqrt{k_{\rm B} T})}\) . A spectroscopic determination of the Boltzmann constant with an uncertainty as low as 37 ppm is obtained. Recent improvements with a new passive thermostat lead to a temperature accuracy, stability, and homogeneity of the absorption cell of 1 ppm over a day.

Comptes Rendus Physique, 2009

... of the Boltzmann constant by the Doppler broadening technique at a 3.8 10 5 accuracy level Kh... more ... of the Boltzmann constant by the Doppler broadening technique at a 3.8 10 5 accuracy level Khelifa Djerroud a , Cyril Lemarchand a , Alexandre Gauguet a ... d absorption est plac e dans un thermostat qui permet de contr ler la temp rature autour de 273,15 K avec une incertitude ...

Comptes Rendus Physique, 2009

A detailed theory of the line shape in linear absorption spectroscopy of low-pressure gases is de... more A detailed theory of the line shape in linear absorption spectroscopy of low-pressure gases is developed. The goal is to take into account all effects that come into play in the determination of Boltzmann's constant from measurements of the Doppler width. We demonstrate that there is no additional broadening from finite transit time across the laser beams. The molecular recoil and the second-order Doppler effect are included in the line shape thanks to a complete quantum treatment. The Mössbauer–Lamb–Dicke narrowing of Doppler lines by collisions is also included and the special cases of Galatry and Nelkin–Ghatak profiles are presented. To cite this article: C.J. Bordé, C. R. Physique 10 (2009).Une théorie détaillée de la forme des raies d'absorption linéaire des gaz à basse pression est développée. L'objectif est de mieux cerner tous les effets susceptibles d'intervenir dans la détermination de la constante de Boltzmann à partir d'une mesure de la largeur Doppler. On démontre en particulier qu'il n'y a pas d'élargissement supplémentaire lié au temps fini de traversée du faisceau laser par les molécules. Les effets de recul et Doppler du deuxième ordre sont intégrés dans la forme de raie grâce à un traitement quantique complet. L'effet Mössbauer–Lamb–Dicke de rétrécissement des raies Doppler par les collisions est lui aussi incorporé dans la théorie avec comme cas particuliers les profils de Galatry et de Nelkin–Ghatak. Pour citer cet article : C.J. Bordé, C. R. Physique 10 (2009).