Mode coupling for precise measurements of the electronic g-factor of hydrogen-like ions in Penning traps [Elektronische Ressource] / Tristán Valenzuela Salazar

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Mode coupling for precise measurements ofthe electronic g-factor of hydrogen-likeions in Penning trapsDissertation zur Erlangung des Grades“Doktor der Naturwissenschaften”am Fachbereich Physikder Johannes Gutenberg-Universitätin MainzTristán Valenzuela Salazargeb. in Saint Maurice (Frankreich)Mainz, im Juni 2004BerichterstatterderArbeit:Prof.Dr.Prof.Dr.Datum der mündlichen Prüfung: 05.08.2004A Marisa y BlackContents1 Introduction 11.1 The g-factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The bound state corrections to the electronic g-factor . . . . . . . . . 32 Theoretical aspects 72.1 Trapping of charged particles . . . . . . . . . . . . . . . . . . . . . . 72.1.1 Quantum mechanical description of the motion . . . . . . . . 92.1.2 Open-endcap cylindrical double Penning trap . . . . . . . . . 112.2 Magnetic bottle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Motion of a single ion in a real trap . . . . . . . . . . . . . . . . . . . 142.4 Detection of ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Ion’s equivalent circuit . . . . . . . . . . . . . . . . . . . . . . 162.5 Line-shape of the Larmor resonance . . . . . . . . . . . . . . . . . . . 193 Experimental setup and method 253.1 Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.1 Room temperature electronics . . . . . . . . . . . . . . . . . . 273.1.2 Magnet . . . . . . . . . . . . . .

Sujets

• Physik

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2004
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Mode coupling for precise measurements of the electronic g-factor of hydrogen-like ions in Penning traps

Dissertation zur Erlangung des Grades “Doktor der Naturwissenschaften” am Fachbereich Physik der Johannes Gutenberg-Universität in Mainz

Tristán Valenzuela Salazar geb. in Saint Maurice (Frankreich) Mainz, im Juni 2004

Berichterstatter

Datum

der

der

Arbeit:

mündlichen

Prüfung:

Prof. Dr. Prof. Dr. 05.08.2004

A

Marisa

y

Black

Contents 1 Introduction 1 1.1 Theg-factor 1. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.2 The bound state corrections to the electronicg-factor 3. . . . . . . . . 2 Theoretical aspects 7 2.1 Trapping of charged particles . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Quantum mechanical description of the motion . . . . . . . . 9 2.1.2 Open-endcap cylindrical double Penning trap . . . . . . . . . 11 2.2 Magnetic bottle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Motion of a single ion in a real trap . . . . . . . . . . . . . . . . . . . 14 2.4 Detection of ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.1 Ion’s equivalent circuit . . . . . . . . . . . . . . . . . . . . . . 16 2.5 Line-shape of the Larmor resonance . . . . . . . . . . . . . . . . . . . 19 3 Experimental setup and method 25 3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1.1 Room temperature electronics . . . . . . . . . . . . . . . . . . 27 3.1.2 Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.3 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1.4 Cryoelectronics . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1.5 Double Penning trap . . . . . . . . . . . . . . . . . . . . . . . 30 3.1.6 Ion production . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Single ion preparation and measurement of mode frequencies . . . . . 32 3.2.1 Ion counting and the reduced cyclotron frequency . . . . . . . 33 3.2.2 Cooling of the motional modes . . . . . . . . . . . . . . . . . . 33 3.2.3 Axial motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3 Detection of Spin-flips . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 Results 41 4.1 Motional mode coupling . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.1 Mode splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 Determination of the magnetron frequency . . . . . . . . . . . . . . . 47 4.3 Method to measure the cyclotron frequency . . . . . . . . . . . . . . 48 4.4 Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.5 The electronic g-factor . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.1 Possible uncertainty sources . . . . . . . . . . . . . . . . . . . 51 4.5.2 Comparison of results . . . . . . . . . . . . . . . . . . . . . . . 52 5 Discussion and Outlook 55

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Chapter 1

Introduction

You know, it would be sufficient to really understand the electron. Albert Einstein

1.1 Theg-factor A currentIflowing in a closed loop (fig. 1.1) has an associated magnetic moment in the form of ~µ= I 2 I r~×d`=IA(1.1) ~ ~ ~ ~ whered`is the element of loop,~ris its position’s vector andAis the area vector corresponding to the area enclosed in the loop. According to this definition, for a ~ classical charged particle orbiting with angular momentumLits magnetic moment can be expressed as ~µ l =L q (1.2) ~ 2m whereqandmare the particle’s charge and mass respectively. This can be gener- ~ ~ ~ ~ alized for a quantum particle with total angular momentumJ=L+S, whereS ~ denotes the spin andLthe mechanical angular momentum. In this case, a dimen- sionless constantg J which is a function of the total angularhas to be introduced

Figure 1.1:Elementary magnetic dipolar moment created by an element ~ of current loopd`at a positionr~from the origin of coordinates