Decoherence and measurement of charge qubits in double quantum dots [Elektronische Ressource] / vorgelegt von Udo Hartmann

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Decoherence and Measurementof Charge Qubitsin Double Quantum DotsUdo HartmannMunchen 2005˜Decoherence and Measurementof Charge Qubitsin Double Quantum DotsUdo HartmannDissertationan der Fakultat˜ fur˜ Physikder Ludwig{Maximilians{Universitat˜Munchen˜vorgelegt vonUdo Hartmannaus Bruhl˜ / ErftkreisMunc˜ hen, den 11.08.2005Erstgutachter: PD Dr. Frank K. WilhelmZweitgutachter: Prof. Dr. Erwin FreyTag der mundlichen Prufung: 13.10.2005˜ ˜vFor my teachers and my parentsFur˜ meine Lehrer und meine ElternIhr mu…t mal was zu Dots machen. (You should do something about dots.)˜{ Prof. Dr. J˜org P. KotthausScience is like collecting and recycling garbage.{ Prof. Dr. Yuli V. NazarovThe harder you work, the more trouble you have.{ Dr. Alexander V. KhaetskiiviContentsAbstract xvKurzzusammenfassung xviOutline 1I Introduction to qubits and quantum dots 31 Introduction to quantum computation and qubits 51.1 History and algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Hardware requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Elementary qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Solid-state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Introduction to quantum dots 132.1 Deflnition of quantum dots . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Transport through a single quantum dot . . . . . . . . . . . . . . . . . . . 152.

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Publié le 01 janvier 2005
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Decoherence and Measurement
of Charge Qubits
in Double Quantum Dots
Udo Hartmann
Munchen 2005˜Decoherence and Measurement
of Charge Qubits
in Double Quantum Dots
Udo Hartmann
Dissertation
an der Fakultat˜ fur˜ Physik
der Ludwig{Maximilians{Universitat˜
Munchen˜
vorgelegt von
Udo Hartmann
aus Bruhl˜ / Erftkreis
Munc˜ hen, den 11.08.2005Erstgutachter: PD Dr. Frank K. Wilhelm
Zweitgutachter: Prof. Dr. Erwin Frey
Tag der mundlichen Prufung: 13.10.2005˜ ˜v
For my teachers and my parents
Fur˜ meine Lehrer und meine Eltern
Ihr mu…t mal was zu Dots machen. (You should do something about dots.)˜
{ Prof. Dr. J˜org P. Kotthaus
Science is like collecting and recycling garbage.
{ Prof. Dr. Yuli V. Nazarov
The harder you work, the more trouble you have.
{ Dr. Alexander V. KhaetskiiviContents
Abstract xv
Kurzzusammenfassung xvi
Outline 1
I Introduction to qubits and quantum dots 3
1 Introduction to quantum computation and qubits 5
1.1 History and algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Hardware requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Elementary qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Solid-state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Introduction to quantum dots 13
2.1 Deflnition of quantum dots . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Transport through a single quantum dot . . . . . . . . . . . . . . . . . . . 15
2.3 Photon-assisted tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Higher order through a quantum dot . . . . . . . . . . . . . . . . 20
2.5 Kondo efiect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 Double quantum dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7 The double quantum dot charge qubit . . . . . . . . . . . . . . . . . . . . 28
2.8 Experimental realizations of double quantum dot charge qubits . . . . . . . 31
2.8.1 The experiment of Hayashi et al. . . . . . . . . . . . . . . . . . . . 31
2.8.2 The expt of Petta et al. . . . . . . . . . . . . . . . . . . . . . 34
2.8.3 The experiment of Gorman et al. . . . . . . . . . . . . . . . . . . . 36
II Decoherence properties of the double quantum dot charge
qubit 39
3 Nonlinear cotunneling through an artiflcial molecule 41
3.1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Published paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42viii CONTENTS
4 Nonequilibrium stabilization of charge states in double quantum dots 47
4.1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Published paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5 Electron-phonon coupling of charge eigenstates 53
5.1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Weak inter-dot coupling . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.2 Stronger inter-dot . . . . . . . . . . . . . . . . . . . . . . . 57
5.3 Discussion of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6 Intrinsic phonon decoherence and quantum gates in coupled lateral quan-
tum dot charge qubits 63
6.1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 Preprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
III Measurement of charge states and back-action of the detec-
tor 77
7 Strong coupling of a qubit to shot noise 79
7.1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.2 Preprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
8 A quantum dot as a high-frequency shot noise detector 87
8.1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2 Experimental discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.3 Theoretical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.4 Comparison between experiment and theory . . . . . . . . . . . . . . . . . 94
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
IV Perspectives 97
9 Background charge uctuations and 1/f noise 99
9.1 A microscopic model and basic properties . . . . . . . . . . . . . . . . . . . 99
9.2 Dynamical decoupling of the qubit from 1=f noise . . . . . . . . . . . . . . 101
9.3 Advanced analysis of 1=f noise . . . . . . . . . . . . . . . . . . . . . . . . 102
10 Charge qubits in other semiconducting nanostructures 105
10.1 Phonon cavities for lateral quantum dots . . . . . . . . . . . . . . . . . . . 105
10.2 Hybrid vertical-lateral double quantum dots . . . . . . . . . . . . . . . . . 106
10.3 Double quantum dots in carbon nanotubes . . . . . . . . . . . . . . . . . . 107
10.4 Quantum dots in nanowires . . . . . . . . . . . . . . . . . . . . . . . . . . 110Table of Contents ix
Conclusions 113
Deutsche Zusammenfassung 115
A Bloch-Redfleld formalism 119
B Schriefier-Wolfi transformation 123
C Charge eigenstates in a double-well potential 129
C.1 Symmetric potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
C.2 Asymmetric potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
D Ansatz, Polaron transformation and NIBA 135
D.1 Ansatz and Polaron . . . . . . . . . . . . . . . . . . . . . . 135
D.2 Noninteracting blip approximation { NIBA . . . . . . . . . . . . . . . . . . 137
E Photon assisted tunneling in a dot induced by shot noise 141
E.1 Rate equations for photon-assisted tunneling . . . . . . . . . . . . . . . . . 141
E.2 Shot noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
E.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Bibliography 147
List of Publications 163
Acknowledgements 165
Curriculum vitae 169x Table of Contents