Multi-photon entanglement [Elektronische Ressource] : experimental observation, characterization, and application of up to six-photon entangled states / vorgelegt von Witlef Wieczorek

Witlef Wieczorek

Sujets

• Physik

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2009
• Nombre de lectures: 32
• Poids de l'ouvrage: 7 Mo

Extrait

Multi-Photon Entanglement
Experimental Observation, Characterization, and
Application of up to Six-Photon Entangled States
Witlef Wieczorek
Munchen˜ 2009Multi-Photon Entanglement
Experimental Observation, Characterization, and
Application of up to Six-Photon Entangled States
Witlef Wieczorek
Dissertation
an der Fakult˜at fur˜ Physik
der Ludwig{Maximilians{Universit˜at
Munc˜ hen
vorgelegt von
Witlef Wieczorek
aus Berlin
Munc˜ hen, den 03.11.2009Erstgutachter: Prof. Dr. Harald Weinfurter
Zweitgutachter: Prof. Dr. Stefien Glaser
Tag der mundlic˜ hen Prufung:˜ 17.12.2009Nicht die Notwendigkeit,
sondern der Zufall ist voller Zauber.
Milan Kundera, Die unertr˜agliche
Leichtigkeit des SeinsviContents
Abstract xv
Zusammenfassung xvi
1 Introduction 1
2 Multi-partite entanglement 5
2.1 Classiflcations of quantum states . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Qubit notation and entanglement . . . . . . . . . . . . . . . . . . . 6
2.1.2 Classiflcations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Entanglement detection and measures of entanglement . . . . . . . . . . . 13
2.2.1 Entanglement detection . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Ent measures . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Experimental observation using photons . . . . . . . . . . . . . . . . . . . 22
2.3.1 Photon sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2 processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Observation of a family of four-photon entangled states 33
3.1 Multi-photon interference . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Entanglement detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Ent properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
P3.1 Experimental Observation of an Entire Family of Four-Photon En-
tangled States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
P3.2 Multi-Photon Interference as a Tool to Observe Families of Multi-
Photon Entangled States . . . . . . . . . . . . . . . . . . . . . . . . 53
4 Four-qubit entanglement for revealing anyonic features 63
4.1 Anyons, the quantum Hall efiect, topological quantum computation . . . . 64
4.2 Toric code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Minimal implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Publication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
P4.1 Revealing anyonic features in a toric code quantum simulation . . . 75viii Contents
5 Symmetric entangled Dicke states of up to six photons 85
5.1 High power SPDC photon source based on a femtosecond UV cavity . . . . 86
5.2 Entanglement detection, properties, and applications . . . . . . . . . . . . 91
5.3 Phase estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
P5.1 Experimental Entanglement of a Six-Photon Symmetric Dicke State 102
P5.2 Multiqubit ent engineering via projective measurements . 106
P5.3 Practical methods for witnessing genuine multi-qubit entanglement
in the vicinity of symmetric states . . . . . . . . . . . . . . . . . . . 114
P5.4 Ultraviolet enhancement cavity for ultrafast nonlinear optics . . . . 132
6 Conclusions and outlook 139
Appendix 142
A SPDC photon state 143
A.1 Non-collinear type II SPDC . . . . . . . . . . . . . . . . . . . . . . . . . . 143
A.2 Collinear type II SPDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
B Measurement settings and counting statistics 149
B.1t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
B.2 Counting statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
C SPDC higher order noise 157
C.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
C.2 Higher order noise in the four-photon family experiment . . . . . . . . . . 160
C.3 order noise in the six-photon Dicke experiment . . . . . . . . . . . . 162
D FPGA controlled coincidence logic 167
Publication list 171
Bibliography 173
Acknowledgements 198
Curriculum vitae 201List of Figures
2.1 Bloch sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Separability and classiflcation of two- and three-qubit states . . . . . . . . 10
2.3 Graph states and Dicke states . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Entanglement witness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Type II SPDC sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Beam splitter and polarization analysis . . . . . . . . . . . . . . . . . . . . 29
3.1 Schematic layouts for SPDC experiments . . . . . . . . . . . . . . . . . . . 36
3.2 Setup for the observation of the family of four-photon entangled states . . 37
3.3 Two- and four-photon HOM-type interference . . . . . . . . . . . . . . . . 40
3.4 Detection of entanglement for the states j“ (fi)i . . . . . . . . . . . . . . 434
3.5 3-tangle and concurrence for states obtained of j“ (fi)i . . . . . . . . . . 474
4.1 Braiding of particles in three and two dimensions . . . . . . . . . . . . . . 65
4.2 Quantum Hall efiect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Toric code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 Correlation function for demonstrating anyonic features and statistics . . . 73
5.1 Time and frequency domain picture of ultrashort pulses . . . . . . . . . . . 88
(3)5.2 Experimental setup of femtosecond UV cavity and jD i state . . . . . . 896
5.3 Calculated power enhancement for the implemented UV cavity . . . . . . . 90
(3)
5.4 Telecloning with jD i . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966
(3) +5.5 Correlation function of the states jD i and jGHZ i . . . . . . . . . . 9866
(3)5.6 Measured correlation functions for jD i . . . . . . . . . . . . . . . . . . 996
(3)5.7 Improved phase sensitivity using the state jD i . . . . . . . . . . . . . . 1006
C.1 Model of the setup for the family j“ (fi)i experiment . . . . . . . . . . . 1594
C.2 Modeled fldelity and count rate for the family j“ (fi)i experiment . . . . 1614
(3)C.3 Modeled two-, four- and six-photon counts for the state jD i . . . . . . 1636
C.4 Fitted ¿ and · for difierent pump powers . . . . . . . . . . . . . . . . . . 165det
D.1 Diagram for the FPGA realizing a coincidence unit . . . . . . . . . . . . . 169x List of Figures