Petelski torsten tino 2005

D  P E PD S, XVII C speciality Q O presented by T P to obtain the title of D  ’U́ P 6 D  R ’U̀  S  F A I  P G M Submitted the 4th February 2005 Guglielmo Tino. Italian principle adviser Christophe Salomon. French principle adviser Robert Pick. Examiner Vincenzo Schettino.

Examiner Tilman Pfau. Referee Ernst Rasel. Referee European Laboratory for Non-linear Spectroscopy (LENS) & Università degli studi di Firenze, Dipartimento di Fisica Polo Scientifico di Sesto Fiorentino Via Sansone 1, 50019 Sesto Fiorentino - Firenze, Italy Bureau Nationale de Métrologie - Systèmes de Référence Temps - Espace (BNM-SYRTE), Observatoire de Paris 61, avenue de l’Observatoire, 75014 Paris, France Université Pierre et Marie Curie 4 place Jussieu, 75252 Paris Cedex 05, France A I  P G M I́̀ A   M́  P́   G I A  M  P  G Abstract The subject of this work is two separate atom-interferometry experiments. The first is a gravimeter in the frame of a new Watt-balance to measure the Earth acceleration g with an absolute precision of 10−9 , whereas the emphasis is placed on the second experiment, a gradiometer for the determination of the gravitational constant G with a precision of 10−4.

Both experiments perform interferometry on a freely falling sample of cold 87 Rb atoms by the application of a sequence of three Raman light-pulses. We describe the idea of the two experiments and report on the details of the apparatus, including a source of an intense flux of cold atoms, frequency and phase stabilization of the lasers and problems related to the source masses that we use for a double- differential measurement of G. Here again, the main weight lies on the gradiometer experiment, where we observed first interference fringes recently with a resolution of the order of 10−5 m/s2 per shot. Key-words: Atom Interferometer, Atomic fountain, Gravity, Gravitational Constant Résumé Nous décrivons dans cette thèse deux expériences d’interférométrie atomique.

La pre- mière est un gravimètre qui mesurera l’accélération de la pesanteur terrestre g avec une exactitude relative de 10−9 , et qui est développé dans le cadre d’un projet de réalisation d’une Balance du Watt. La deuxième, sur laquelle l’essentiel du travail de cette thèse a porté, est un gradiomètre pour la détermination de la constante de la gravitation univer- selle G avec une exactitude relative de 10−4. Dans ces deux expériences, des atomes froids de 87 Rb en chute libre sont soumis à une séquence de trois impulsions laser Raman, afin de réaliser un interféromètre atomique. Nous décrivons d’abord le prin- cipe de ces expériences, puis le dispositif expérimental que nous avons mis au point.

Nous présenterons notamment la réalisation d’une source intense d’atomes froids, les méthodes de stabilisation en fréquence et en phase des lasers ainsi que les problèmes liés aux masses sources utilisées pour la mesure doublement différentielle de G. On porte ici l’accent sur le gradiomètre, avec lequel nous avons observé des premières franges d’interférence récemment, avec une resolution sur la mesure de l’accélération de l’ordre de 10−5 m/s2 par coup. Mots-clés : Interférométrie Atomique, Fontaine Atomique, Pésanteur terrestre, Constante de la Gravitation i Riassunto Nella presente tesi viene illustrato il lavoro effettuato su due distinti esperimenti di interferometria atomica. Il primo è un gravimetro inserito nel contesto di una nuova bilancia di Watt per misurare l’accelerazione di gravità terrestre g con una precisione assoluta di 10−9 , ma maggiore enfasi viene riservata per il secondo esperimento, un gradiometro per la determinazione della costante di gravitazione universale G con una precisione di 10−4.

Entrambe gli esperimenti si basano su tecniche interferometriche su un campione di atomi freddi di 87 Rb in caduta libera mediante l’interazione con una sequenza di tre impulsi Raman. Viene descritta l’idea alla base di tali esperi- menti e vengono riportati i dettagli dei singoli apparati, con particolare riferimento alla sorgente di un flusso intenso di atomi freddi, al sistema per la stabilizzazione in fase e frequenza dei laser ed ai problemi relativi alle masse sorgenti utilizzate per una misura doppio-differenziale di G. Ribadisco che nel lavoro di tesi viene data maggior rilevanza al gradiometro, con il quale si sono di recente osservate le prime frange di interferenza con una risoluzione sull’accelerazione dell’ordine di 10−5 m/s2 per lancio. Parole chiave: Interferometria Atomica, Fontana Atomica, Gravità terrestre, Costante di Gravitazione iii Contents Abstract, Résumé, Riassunto i Introduction 1 Organization of thesis.

4 1 The Paris gravimeter and Florence gradiometer 5 1.1 Past and present devices .2 Future developments and applications .2 A gravimeter for a new Watt Balance .1 New definition of the Kilogram .3 Atom interferometer or falling corner cube .3 A gradiometer for the determination of G .1 Significance of the Gravitational Constant G .3 G measurement with atom interferometry .4 Intuitive explanation of gravimeter and gradiometer. 20 2 Theory of Raman light pulse interferometry 27 2.1 Atoms and Light .1 Two level atom in a light-field .2 External degrees of freedom .5 Comments on plane-wave approximation .2 Raman light pulse interferometer .2 Phase contribution of Raman pulses .4 The Bordé method .5 Interferometer phase shift for certain potentials .3 Sensitivity to noise .3 Exact calculation of the weighting function .4 Comparison of rough and exact result for the weighting function 58 2.1 Description of MAGIA apparatus .3 Sealing with lead and glue .1 Extended cavity diode lasers .2 Laser setup of gradiometer .3 Laser setup of gravimeter .4 Summary and new laser system gradiometer: .1 Double differential measurement .4 Characteristics of Masses. 98 4 Laser frequency and phase control 103 4.1 Frequency modulation spectroscopy .3 Doppler free DAVLL lock .4 Further modulation-free locking techniques .5 Frequency Lock with f-to-V converter .1 Phase-locked-loop .2 Analog Phase Detector .3 Digital Phase and Frequency Detector .4 Digital Phase Difference Counter .5 Locking bandwidth and capture range .3 Frequency control for gravimeter .1 Lock Reference Laser on rubidium transition .2 Lock Repumper on Reference .3 Lock Cooling Laser on Repumper .4 Frequency control for gradiometer .1 Lock Repumper on rubidium transition .2 Lock Reference Laser on rubidium transition .3 Lock Master Raman laser .4 Phase-Lock Slave Raman laser .5 Noise on phase-lock. 127 5 Experimental procedure and first results 133 5.2 Tools to describe a 2D-MOT .3 Characterization of 2D-MOT .4 2D-MOT for gradiometer .2 Sample preparation and analysis gradiometer .1 Velocity insensitive Interferometer .2 Velocity selective Interferometer .1 Summary of work on gravimeter experiment .2 Summary of work on gradiometer experiment .3 Milestones of gravimeter .4 Milestones of gradiometer .1 Rubidium spectroscopy signals .3 Temperature dependence of pressure .4 Further useful numbers on 87 Rb.

177 B Geophysical determination of gravity 179 B.1 Predicted value of g .2 Predicted value of γ, γ0 and γ00. 181 Bibliography 183 Men and machine 193 Introduction ”Gravity is a contributing factor in nearly 73 percent of all accidents involving falling objects. The photo shows a rather unusual example of an accident; but also here the contribution of gravity can hardly be denied. One of the most obvious things in the world is that if you hold a stone in your hand and release it, then the stone falls., Aristotle concludes in his book ’on the heavens’ [1] that a stone falls, because it is driven to its natural place, which is the center of the Earth: .It (a moving body) could not move infinitely; for to traverse an infinite is impossible, and impossibilities do not happen.

So the moving thing must stop somewhere, and there rest not by constraint but naturally. But a natural rest proves a natural movement to the place of rest. For if the natural motion is upward, it will be fire or air, and if downward, water or earth. Hence air and water each have both lightness and weight, and water sinks to the bottom of all things except earth, while air rises to the surface of all things except fire.

1 2 Introduction Natural motion of the heavenly bodies, according to Aristotle, is circular. The ideas of Aristotle imply further that heavy objects fall faster than light things, because their consistence determines the degree of their desire to return to their natural position, the center of the Earth1. Since this ’natural desire’ of objects to fall is the only manifes- tation of gravitation in daily life, we understand that the ideas of Aristotle – although completely wrong – survived for almost 2000 years. In 1632 Galileo published his text ’Dialogo dei massimi sistemi’ [3] and proved those ideas to be wrong.

His experiments together with the celestial mechanics of Kepler [2] delivered a stunningly new description of the motion of objects on Earth as well as of planets, but could not deliver a philosophical description of the origin of the forces that determine this motion. Figure 1: In the so-called ’Principia’ of 1687 [5], Newton published his studies about the gravitational force that he developed during the plague in 1665/66 at the age of 23. This hole was filled for a certain time by the ether theory of Descartes [4] until New- ton in his ’Philosophiae naturalis principia mathematica’ delivered strong arguments against the ether. Newton proposed universal gravitation and the inverse square law of attraction between any two bodies even separated in a vacuum [5]:.

all matter attracts all other matter with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. Newton’s law of gravitation received its definitive analytic form from Euler and is expressed as Mm F =G 2 , r 1 Aristotle concluded a reasoning about the question about the form of the Earth: Its shape must necessarily be spherical. Introduction 3 where F is the absolute value of the force between two bodies of masses m and M at a distance r. G is the universal gravitational constant.

The Earth acceleration g 2 can be written as G · MEarth /rEarth. Newton realized that it is precisely the same force that keeps planets on its orbit that make a stone fall to Earth. Despite the enormous potential of his theory to explain effects of gravitation, it nevertheless did not explain the origin of this attractive force; worse, it is based on some ’magic power’ that attract objects to each other. In the following decades, Newton’s theory became commonly accepted and is fully valid until nowadays, except in the presence of very large gravitational fields, in which case Einstein’s general relativity theory must be applied – that nowadays also fills the philosophical gap by delivering an explanation for the nature of gravity.

Within the past 300 years, Earth gravity acceleration g and the gravitational constant G have been measured to always higher precision. The up-to-date most precise instru- ments for the determination of g use the powerful technique of laser-interferometry to read out changes in the position of a freely falling test mass that are provoked by the Earth acceleration g. The identical technique has been applied for the determination of G, but could not compete with the more precise angular measurements on suspended test masses. Interference of matter waves can offer a much higher sensitivity in the detection of accelerations and the past decade has seen impressive progress in the field of atom interferometry, whose range of applications changed from pure fundamental physics to precision measurements and metrology.

Atom interferometers have already proved their superiority on a g-measurement and they could compete when used to determine G. In my lab, we’ve surpassed the sensitivity of the best absolute-measurement gravimeter, which measures the acceleration due to gravity. So you think that’s kind of crazy, that by dropping atoms you can make the most sensi- tive measurement of gravity, but it’s true. Steven Chu in [6] This thesis contains work on two recently started atom-interferometry experiments for an accurate measurement of g and G, respectively.