Trapped-Mg+ Apparatus for Control and Structure Studies

107 Pages·2017·4.48 MB·English

TRAPPED-Me+ APPARATUS FOR CONTROL AND STRUCTURE STUDIES
TRAPPED-MG+ APPARATUS FOR CONTROL AND STRUCTURE STUDIES
By

LAURA A TOPPOZINI, B.Sc.

A Thesis

Submitted to the School of Graduate Studies

in Partial Fulfilment of the Requirements

for the Degree

Masters

McMaster University

@Copyright by Laura Toppozini, November 2006
MASTERS (2006) McMaster University
(Department of Physics and Astronomy) Hamilton, Ontario
TITLE: Trapped-Mg+ Apparatus for Control and Structure Studies

AUTHOR: Laura Toppozini, B.Sc.

SUPERVISOR: Dr. Brian E. King

NUMBER OF PAGES: xii, 94

11
Abstract

Trapped ions can be isolated from external perturbations such as collisions with
other atoms or electric and magnetic field inhomogeneities. For this reason, trapped
ions can be useful in spectral measurements, quantum information technology and
studying quantum behaviour. In this thesis, I discuss a trapped-Mg+ apparatus for
studying the quantum mechanics of atoms. I describe the laser interactions that
allow us to coherently excite our atoms. I go on to discuss the actual apparatus for
trapping ions and making precise measurements, the hyperfine structure of 25 Mg+
and a proposed linewidth measurement.
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Acknowledgernents

I would like to take this opportunity to thank my supervisor, Brian E. King. Your
patience, determination and knowledge are greatly admired and appreciated. I hope, during
my next few years with the group, that I can continue to learn from your example.
I would also like to thank my labmates Jason Nguyen and JiaJia Zhou. I have learned a
lot from you both and you make working in the lab much more fun than it should be. You
guys are great friends.
Finally, I would like to thank my parents, John and Barbara and my brothers and
sisters: William, Johnny, Kimberly and Lisa. Without your support I would have never
been able to start this degree let alone finish it. You all mean the world to me. Thank you.
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Dedicated to William, Johnny, Kimberly and Lisa
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Table of Contents

Abstract iii

Acknowledgements iv

List of Figures ix

Chapter 1 Introduction 1

Chapter 2 Laser Interactions 5

2.1 Linewidth ..... 8

2.2 Power Broadening . 10

2.3 Laser Cooling ... 11

2.3.1 Atomic Structure of Magnesium 11

2.3.2 Cycling 'fransition 14

2.3.3 Doppler cooling . . 14

2.3.4 Hyperfine Optical Pumping 18

2.4 Ionization . . . . . . . . . . . . . . 18

Chapter 3 Apparatus 21

3.1 Dye Laser ... 22

3.1.1 Side Lock 25

3.2 Diagnostics . . . 27

3.3 Doppler-Free Saturated Absorption Spectroscopy 29

3.3.1 Iodine Spectrum . . . . . . 32

VI
3.4 Wavetrain Doubling Cavity ............ .
36
3.4.1 Pound-Drever-Hall Frequency Stabilization . 37
3.4.2 Second Harmonic Generation 41
3.5 Fiber Lasers . . . . . . . . . . . . . . 44
3.5.1 LBO and BBO Doubling Cavities 45
3.5.2 Hansch-Couillaud Frequency Stabilization 48
3.6 Ion Source . . . . . . 49
3.7 Radiofrequency 'frap 51
3.8 Imaging System ... 54
Chapter 4 Hyperfine Interaction 58
4.1 Hyperfine Interactions of Particles . 59
4.1.1 Magnetic Dipole Interaction 60
4.1.2 Electric Quadrupole Interaction 61
4.2 The Hyperfine Structure of Magnesium 63
4.3 Hyperfine Calculation ......... . 65

Chapter 5 Linewidth Measurement of 24Mg 70
5.1 Linewidth in 24Mg ... 70
5.2 Previous Measurements . 72
Chapter 6 Conclusion 74
Appendix A Hyperfine Calculation Code 76
vii
6.1 Matlab Code for the 2S 1 State Energy Level Splitting . ........ 76

2

6.2 Matlab Code for the 2P1 State Energy Level Splitting . . . . . . 80

2 ~
6.3 Matlab Code for the 2P~ State Energy Level Splitting . 85

2
• • • • • ao • •
Bibliography 93

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List of Figures
2PQ states of 24Mg+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2
3.1 Schematic of the optical table and locations of the apparatus. . . . 21
3.2 Schematic of the Coherent 699 dye laser cavity and reference cavity. 22
3.3 'Ifansmission curves for the birefringent filter, thick etalon and thin etalon.
This shows the wavelength selectivity of the dye laser (a). An enlarged
section is seen in (b). Curves by Coherent Inc. . . . . . . . . 24
3.4 Schematic of Doppler-free saturated Iodine Spectroscopy setup. 33
3.5 Representative plot of the screen on the oscilliscope when scanning laser
frequency. Plot is taken with 4.2V applied to PZT. High peaks are the
dye laser and smaller peaks are the fiber laser. . . . . . . . . . . . . . 35
3.6 Representative plot of the screen on the oscilliscope when scanning laser
frequency. Plot is taken with 26.4V applied to PZT. High peaks are
the dye laser and smaller peaks are the fiber laser. . . . . . . . . . . . 36
3.7 Plot of peak separation (fiber laser and reference dye laser) versus voltage
applied to the PZT. The dots represent actual data points and the line
is a quadratic fit: f(V) = aV2 + bV + c = 0.0614898V2 + 38.0281V­
45.3555. Plot and fitting done with Gnuplot; asymptotic standard
error: a =36.53%, b =3.414% and c =34%. 37
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