STATE DETECTION OF A TRAPPED ION QUBIT USING PHOTON ARRIVAL TIMES by Kenneth W ...

63 Pages·2011·7.08 MB·English

STATE DETECTION OF A TRAPPED ION QUBIT USING PHOTON
ARRIVAL TIMES
by
Kenneth W Lee
A senior honors thesis submitted to the Department of Physics of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
High Honors B.S. in Physics
2011
Defense Committee:
Professor Chris Monroe, Chair/Advisor
Professor Steven Anlage, Honors Chair
Professor Dieter Brill
(cid:13)c Kenneth William Lee III
All Rights Reserved
2011
ACKNOWLEDGEMENTS
First and foremost I would like to thank my advisor, Chris Monroe for giving me the wonderful
opportunitytoworkinhisresearchgroupasanundergraduate. Yourguidanceandsupportcoupled
with your enthusiasm for physics has truly been an inspiration. Thank you for being the greatest
advisor ever. I hope my contributions to the lab have proven meaningful.
Secondly,IwouldliketothankDaveHayesforhisseeminglyendlesspatienceandguidanceover
the course of my research here. Thank you for taking me under your wing and teaching me the ins
and outs of experimental physics. Without you, this thesis would not have been possible. You are
a great researcher and friend, and I wish you the best of luck in your future endeavors.
Mycolleagueshaveenrichedmyresearchexperienceinmanywaysanddeserveaspecialmention.
I would like to thank the entire Ion Photon team for their help on this project: David Hucul was
always happy to explain to me anything that confused me and I thank him for helping me through
the more obscure aspects of physics; Shantanu Debnath spent an extraordinary amount of time
helping me with data collection; Susan Clark also was extremely helpful in data collection and ion
trapping, and was a constant source of positive energy. I would also like to thank everyone who
I have worked with in the lab. Although I did not work with all of you directly, I have certainly
learned something important from each and every one of you. I would therefore like to extend my
thankstoWesCampbell, Ming-ShienChang, EmilyEdwards, BrianFields, RajibulIslam, Kihwan
Kim,SimchaKorenblit,AaronLee,LeLuo,AndrewManning,DzmitryMatsukevich,PeterMaunz,
Jonathan Mizrahi, Qudsia Quraishi, Crystal Senko, and Jon Sterk.
I must also thank my friends for keeping me relatively sane throughout this entire process. I
hope that we will all stay in touch wherever life takes us.
And of course, I owe deep thanks to my family. Thank you, Mom, for always supporting me
wherever my interests have carried me. Thank you for giving me the right mindset to succeed in
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life. Thank you, Dad, for always offering to help me when I needed it and keeping my head square
on my shoulders. Thank you, Ethan, for always keeping a rooted interest in my endeavors and
being willing to lend a helping hand. Thank you, Madeline, for always inspiring me, and at the
very least, trying to keep me in good physical shape. Thank you, Kevin, for always helping me to
keep my eyes on the prize. Thank you Caitlyn, for always checking up on me (like a boss, I might
add) and showing interest in my work.
It is impossible to remember all, and I apologize to those I’ve inadvertently left out!
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHAPTER
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
II. Quantum Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 The Quantum Bit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Quantum Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Universal Quantum Computation . . . . . . . . . . . . . . . . . . . . . . . . 6
III. Ion Trapping and Ytterbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
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3.1 Ion Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Photoionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Doppler Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 The Hyperfine Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.5 State Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6 State Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
IV. Methods of State Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1 Discriminator Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 Photon Arrival Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Distributions of Photon Emission . . . . . . . . . . . . . . . . . . . . . . . . 18
4.4 The Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.5 First Photon Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
V. Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.1 Simulating Random Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2 State Detection Error Simulations . . . . . . . . . . . . . . . . . . . . . . . . 28
VI. Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
VII. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
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7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.2 Implications in Larger Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.3 Future Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
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LIST OF TABLES
Table
3.1 Ytterbium Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
6.1 Experimental Fidelities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
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LIST OF FIGURES
Figure
3.1 Four Rod Trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Ytterbium 171 Energy Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1 Theoretical Photon Emission Histograms . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Theoretical Dark State Histogram With Background . . . . . . . . . . . . . . . . . 22
4.3 Theoretical Bright State Distribution With Background . . . . . . . . . . . . . . . 23
5.1 Simulated Photon Emission Histograms . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2 Individual State Detection Error Plot. . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.3 Average Detection Error Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
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LIST OF APPENDICES
Appendix
A. Mathematica Simulation Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
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