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Dissertation inPhysics

EuropeanPhD School, XVII Cycle

speciality

QuantumOptics

presented by

TorstenPetelski

to obtain the title of

Docteur de l"Universit´eParis6

Dottore diRicerca

dell"Universit`a degliStudi diFirenze

AtomInterferometers forPrecision

GravityMeasurements

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)

Universit

`a degli studi di Firenze, Dipartimento di Fisica

Polo Scientifico di Sesto Fiorentino

Via Sansone 1, 50019 Sesto Fiorentino - Firenze, Italy

Bureau Nationale de M

´etrologie - Syst`emes de R´ef´erence Temps - Espace (BNM-SYRTE), Observatoire de Paris

61, avenue de l"Observatoire, 75014 Paris, France

Universit

´e Pierre et Marie Curie

4 place Jussieu, 75252 Paris Cedex 05, France

AtomInterferometers forPrecision

GravityMeasurements

Interf´erom`etresAtomiques pour desM´esures

dePr´ecision de laGravitation

InterferometriAtomici perMisure diPrecisione

diGravitazione

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 gwith an absolute precision of 109, whereas the emphasis is placed on the second experiment, a gradiometer for the determination of the gravitational constantGwith a precision of 10

4. Both experiments perform interferometry on a freely falling sample

of cold

87Rb 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- dierential measurement ofG. 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

5m/s2per shot.

Key-words:Atom Interferometer, Atomic fountain, Gravity, Gravitational Constant R

´esum´e

Nous d

´ecrivons dans cette th`ese deux exp´eriences d"interf´erom´etrie atomique. La pre- mi `ere est un gravim`etre qui mesurera l"acc´el´eration de la pesanteur terrestregavec une exactitude relative de 10

9, et qui est d´evelopp´e dans le cadre d"un projet de r´ealisation

d"une Balance du Watt. La deuxi `eme, sur laquelle l"essentiel du travail de cette th`ese a port ´e, est un gradiom`etre pour la d´etermination de la constante de la gravitation univer- selleGavec une exactitude relative de 104. Dans ces deux exp´eriences, des atomes froids de

87Rb en chute libre sont soumis`a une s´equence de trois impulsions laser

Raman, afin de r

´ealiser un interf´erom`etre atomique. Nous d´ecrivons d"abord le prin- cipe de ces exp ´eriences, puis le dispositif exp´erimental que nous avons mis au point.

Nous pr

´esenterons notamment la r´ealisation d"une source intense d"atomes froids, les m ´ethodes de stabilisation en fr´equence et en phase des lasers ainsi que les probl`emes li ´es aux masses sources utilis´ees pour la mesure doublement di´erentielle deG. On porte ici l"accent sur le gradiom `etre, avec lequel nous avons observ´e des premi`eres franges d"interf ´erence r´ecemment, avec une resolution sur la mesure de l"acc´el´eration de l"ordre de 10

5m/s2par coup.

Mots-cl

de la Gravitation i

Riassunto

Nella presente tesi viene illustrato il lavoro eettuato su due distinti esperimenti di interferometria atomica. Il primo `e un gravimetro inserito nel contesto di una nuova bilancia di Watt per misurare l"accelerazione di gravit `a terrestregcon una precisione assoluta di 10

9, ma maggiore enfasi viene riservata per il secondo esperimento, un

gradiometro per la determinazione della costante di gravitazione universaleGcon una precisione di 10

4. Entrambe gli esperimenti si basano su tecniche interferometriche

su un campione di atomi freddi di

87Rb 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-dierenziale diG. 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

5m/s2per lancio.

Parole chiave:Interferometria Atomica, Fontana Atomica, Gravit`a terrestre, Costante di Gravitazione iii

Contents

Abstract, R

´esum´e, Riassunto

i

Introduction

1

Organization of thesis

4

1 The Paris gravimeter and Florence gradiometer

5

1.1 Atom interferometry

5

1.1.1 Past and present devices

6

1.1.2 Future developments and applications

7

1.2 A gravimeter for a new Watt Balance

10

1.2.1 New definition of the Kilogram

10

1.2.2 Watt balance

11

1.2.3 Atom interferometer or falling corner cube

13

1.2.4 Experimental Realization

14

1.3 A gradiometer for the determination ofG

15

1.3.1 Significance of the Gravitational ConstantG

15

1.3.2 PastG-measurements

16

1.3.3Gmeasurement with atom interferometry

18

1.3.4 Experimental realization

19

1.4 Intuitive explanation of gravimeter and gradiometer

20

2 Theory of Raman light pulse interferometry

27

2.1 Atoms and Light

27

2.1.1 Two level atom in a light-field

27

2.1.2 External degrees of freedom

30

2.1.3 Raman transitions

31

2.1.4 Velocity selection

37

2.1.5 Comments on plane-wave approximation

38

2.2 Raman light pulse interferometer

40

2.2.1 Principle

40

2.2.2 Phase contribution of Raman pulses

41

2.2.3 Free evolution

43

2.2.4 TheBord´e method

46

2.2.5 Interferometer phase shift for certain potentials

50

2.3 Sensitivity to noise

51

2.3.1 Definitions

51
v vi Contents

2.3.2 Weighting function

53

2.3.3 Exact calculation of the weighting function

55

2.3.4 Comparison of rough and exact result for the weighting function

58

2.3.5 Dick eect

61

3 Experimental setup

65

3.1 Vacuum System

65

3.1.1 Description of MAGIA apparatus

67

3.1.2 Pressure estimation

71

3.1.3 Sealing with lead and glue

73

3.2 Magnetic fields

76

3.2.1 Coils

76

3.2.2 Magnetic shielding

77

3.3 Laser System

80

3.3.1 Extended cavity diode lasers

81

3.3.2 Laser setup of gradiometer

83

3.3.3 Laser setup of gravimeter

86

3.3.4 Summary and new laser system gradiometer:

88

3.3.5 Fiber system

89

3.4 Masses

92

3.4.1 Double dierential measurement

93

3.4.2 Gravity gradient

94

3.4.3 Best Trajectories

96

3.4.4 Characteristics of Masses

98

4 Laser frequency and phase control

103

4.1 Frequency stabilization

103

4.1.1 Frequency modulation spectroscopy

104

4.1.2 DAVLL

107

4.1.3 Doppler free DAVLL lock

107

4.1.4 Further modulation-free locking techniques

111

4.1.5 Frequency Lock with f-to-V converter

113

4.2 Phase Stabilization

113

4.2.1 Phase-locked-loop

114

4.2.2 Analog Phase Detector

115

4.2.3 Digital Phase and Frequency Detector

116

4.2.4 Digital Phase Dierence Counter

116

4.2.5 Locking bandwidth and capture range

117

4.3 Frequency control for gravimeter

118

4.3.1 Lock Reference Laser on rubidium transition

118

4.3.2 Lock Repumper on Reference

120

4.3.3 Lock Cooling Laser on Repumper

121

4.4 Frequency control for gradiometer

124

4.4.1 Lock Repumper on rubidium transition

124

4.4.2 Lock Reference Laser on rubidium transition

124

4.4.3 Lock Master Raman laser

125
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