Quantum engineering of continuous variable quantum states [Elektronische Ressource] = Gezielte Beeinflussung von Quantenzustaenden mit kontinuierlichen Variablen / vorgelegt von Metin Sabuncu

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• Publié par: friedrich-alexander-universitat_erlangen-nurnberg
• Publié le: 01 janvier 2010
• Nombre de lectures: 36
• Langue: English
• Poids de l'ouvrage: 1 Mo

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Quantum Engineering of Continuous Variable
Quantum States
Gezielte Beeinflussung von Quantenzust¨anden mit
kontinuierlichen Variablen
Der Technischen Fakult¨at der
Universit¨at Erlangen-Nurn¨ berg
zur Erlangung des Grades
DOKTOR-INGENIEUR
vorgelegt von
Metin Sabuncu
Erlangen, 2010Als Dissertation genehmigt von
der Technischen Fakult¨at der
Universit¨at Erlangen-Nurn¨ berg
Tag der Einreichung: 08-06-2009
Tag der Promotion: 29-10-2009
Dekan: Prof. Dr.-Ing. habil. Reinhard German
Berichterstatter: Prof. Dr.-Ing. Bernhard Schmauss
Prof. Dr. Gerd LeuchsAbstract
Quantum information with continuous variables is a field attracting increasing at-
tention recently. In continuous variable quantum information one makes use of the
continuous information encoded into the quadrature of a quantized light field instead
of binary quantities such as the polarization state of a single photon. This brand
new research area is witnessing exciting theoretical and experimental achievements
such as teleportation, quantum computation and quantum error correction. The
rapid development of the field is mainly due higher optical data rates and the avail-
ability of simple and efficient manipulation tools in continuous-variable quantum
information processing. We in this thesis extend the work in continuous variable
quantum information processing and report on novel experiments on amplification,
cloning, minimal disturbance and noise erasure protocols. The promising results
we obtain in these pioneering experiments indicate that the future of continuous
variable quantum information is bright and many advances can be foreseen.Zusammenfassung
Quanteninformation mit kontinuierlichen Variablen ist ein Gebiet, das in der let-
zten Zeiten grosses Interesse auf sich zieht. Auf dem Gebiet der Quanteninforma-
tion mit kontinuierlichen Variablen nutzt man die kontinuierliche Information, die
in der Quadratur eines quantisierten Licht Feldes kodiert ist anstelle von binaeren
Parametern wie z.B. den Polarisationszustand eines einzelnen Photons. Dieses
neue Forschungsgebiet erlebt derzeit interessante theoretische und experimentelle
Fortschritte wie Teleportation, Quanten-Berechnung und Quanten-Fehlerkorrektur.
Die rasche Entwicklung auf diesem Gebiet ist in erster Linie bedingt durch die
Moeglichkeit hohe optische Datenraten zu Verwenden sowie durch die Verfueg-
barkeit einfacher und effizienter Werkzeuge zur Quanten-Informationsverarbeitung.
In dieser Arbeit wird die gezielte Beeinflussung der Quantenzustaende mit kon-
tinuierlichen Variablen untersucht und ueber neuartige Experimente zur Verstaerkung,
zum Klonen, zur Messung mit minimalen Stoerungen und zur Loeschung des Rau-
schens von Quantenzustaenden berichtet. Dazu wurde insbesondere die sog. feed
forward Methode eingesetzt. Die vielversprechenden Ergebnisse der beschriebenen
Experimente weisen auf eine bedeutende zukuenftige Entwicklung dieses Forschungs-
gebiets hin.Acknowledgments
This work is maybe a small step (not even a step actually) for mankind though has
been a giant leap for me. I am grateful to many people who helped me in this hard
and challenging path, without their help it would have been absolutely impossible to
accomplish any of the work carried out in my PhD.
I would like to express my sincere thanks to Professor Bernhard Schmauss, who
has always helped me and given me continuous support throughout my PhD thesis. I
owe a great debt of thanks to Professor Gerd Leuchs for giving me the opportunity to
complete my thesis at the Institute of Optics, Information and Photonics, the brand new
Max Planck Institute for the Science of Light.
Special thanks go to Professor Ulrik L. Andersen, the head of the Quantum Infor-
mation Processing Group for being an excellent group leader, and being very hospitable
throughout my stay in Denmark. I would like to express my great gratitude to Ulrik
for his excellent supervision of my work and for his enthusiasm for the subject. I am
particularly grateful to Vincent Josse who introduced me to the cloning machine and
taught me all the tricks with the optic and electronic components. Merci beaucoup
Vincent, without your help I wouldn’t have been able to achieve any of the results I got
in my PhD. I must not forget to thank Dr. Radim Filip who was always very friendly to
me and helped me with the theoretical aspects of quantum optics and for inviting me
to Olomouc. I am most grateful to my roommates Jessica, Josip and later on Alex who
apart from the fruitful scientific discussions always created a friendly atmosphere in the
office. I enjoyed discussing over a Kebab and tea in Norrebronx with you Alex! I owe
thanks to Dr. Haim Abitan who always had something interesting to talk about during
thetimewewereinthesameofficeinLyngby.Emir,Darko,StefanandMartinmade
DTU a better place to be at.
Leonid Krivitsky, Jiri Janousek and Martin Andersen, thanks for the fun times at
the Physics Department at DTU. I thank Julien Niset and Ladislav Mista for providing
excellent theoretical proposals which resulted in fruitful collaborations.
I would also like to thank the other members of the QIP Group: Oliver Gloeckl,
Christoph Marquardt, Carlos Wiechers, Mario A. Usuga, Christopher Wittmann for shar-
ing their experience in Quantum Optics with me and always being friendly. Spasibbo to
Denis Sych, I will never forget the conference in Calgary Mr. Einstein! I enjoyed working
together in the lab with Mikael Lassen and playing pool in building 306 or Stefanshus.
Pavel Marchenko, spassibo, thanks to you I am now a famous film star! Pasha I will
never forget the time we spent together and the deep discussions we had.
Xie xie to Ruifang Dong for always being friendly to me and allowing me to borrow
any kind of equipment that I needed, even when sometimes I was taking the equipment
more than 1000 km away!
Alessandro Villar and Katiuscia Cassemiro: Obrigado, it is always a pleasure to spendtimewithyouguys.FilouRaynal,JanSchae fer, Peter Panzer (one of the most helpful
and positive persons I have met), Jochen Mueller, Dominique Elser, and Wenjia Zhong
made the insititute and Erlangen a place I always would like to be at. Dominique and
Wenjia always remember the DPG conference in Frankfurt ok? Many thanks to Vishal
Vaibhav and Rashit Sharma who were always smiling and emiting positive energy.
I owe many thanks to Eva who has always been willing to help with any kind of beau-
rocratic problem I had and made life easier. I faced administrative hurdles when I started
my thesis in Erlangen and thanks to secretaries Frau Dollinger and Frau Schwender, it
was easy to overcome problems related to paperwork. Thanks to the other members
of the Institute and our Project Coordinator Dr. Sabine Koenig who have always been
friendly and supportive. Without Bruno and Adam from the electronics workshop I
couldn’t have performed any of the measurements. To Seckin Sefi my fellow country-
man: Yolun acik olsun dostum! Nebi Unlenen the computer specialist who brought my
laptop back to life again deserves a big thank you. Cagdas followed me around from
Copenhagen to Nuremberg, every now and then it was great to go out and have fun
together.
My Somalian students/friends in Copenhagen helped me figure out who I am in life:
Waad mahadsan tahay Said, Ahmed, Edmond, Abdifatah, Gulled, Aydarus and Ismail.
Erdem my special friend from Vesterbro, I learnt a lot from you, and am looking forward
to our next encounter already! Millions of aciu go to Milda who diverted me from my
daytodayproblemsandtookmymindawayfromwork,over!
My true friends who were always with me on this journey Savaskan Bulek and Murat
Isikhan, I can‘t thank you enough for your support: Kartallar sonsuz tesekkurler!
There are surely many other people that I should have thanked and maybe forgot,
thank you all!
Lastly, and most importantly, I would like to thank my parents and brother for their
years of love and devotion, I dedicate this work to them.Contents
1 Introduction 1
2 Quantum Optics Formalism 7
2.1 TheQuantizedElectromagneticField.................. 7
2.2 QuantumStatesoftheField............. 9
2.2.1 Thephotonnumberstate .......... 9
2.2.2 Thecoherentstate...10
2.2.3 Squeezed states ...............13
2.3 GausianStates....................13
2.4 ExperimentalConsiderations..17
2.4.1 Experimentalgenerationofcoherentstates.18
2.4.2 LinearOpticsComponents....................20
2.4.3 Stablemeasurements.............24
2.5 Detectionschemes........29
2.5.1 SinglePhotonDetection29
2.5.2 DirectDetection ..............30
2.5.3 HomodyneDetection.............31
2.5.4 HeterodyneDetection .32
2.6 Summary ............35
3 The Quantum Amplifier 37
3.1 TheBasics......................37
3.2 TheScheme...........40
3.3 TheExperimentalDemonstrationandResults...43
3.4 Conclusion.48
4 The Quantum Cloner 49
4.1 Introduction................................49
4.2 AuniversalCVcloner.....51
4.3 Towardsasuperiorcloningmachine.........5
4.4 Asuperiorcloningmachine ..60
4.5 Cloningofpartialquantuminformation.................68
4.6 Conclusion.......................7
5 Minimal Disturbance Measurements 79
5.1 Introduction..........79
5.2 Gausianminimaldisturbancemeasurements....825.3 Quantumteleportationasaminimaldisturbancemeasurement....85
5.4