Controlling electron quantum dot qubits by spin-orbit interactions [Elektronische Ressource] / vorgelegt von Peter Stano
160 Pages
English
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Controlling electron quantum dot qubits by spin-orbit interactions [Elektronische Ressource] / vorgelegt von Peter Stano

Downloading requires you to have access to the YouScribe library
Learn all about the services we offer
160 Pages
English

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Controlling electron quantum dotqubits by spin-orbit interactionsDissertationzur Erlangung des Doktorgradesder Naturwissenschaften (Dr. rer. nat.)der Naturwissenschaftlichen Fakult¨at II-Physikder Universit¨at Regensburgvorgelegt vonPeter Stanoaus Partizanske, SlowakeiJanuar 2007The PhD thesis was submitted on 12.01.2007.The colloquium took place on 23.3.2007.Christoph Strunk ChairmanJaroslav Fabian 1st RefereeBoardofexaminers:Milena Grifoni 2nd RefereeAndreas Schaefer ExaminerAcknowledgmentsI would like here to express my gratitude to Prof. Jaroslav Fabian for his inval-ueable help and support over the whole period of my PhD studies. Without hiscontinual assistance this work would not get much farther than to this page.vContentsAcknowledgments vContents viList of tables ixList of figures xiiList of author’s publications xxi1 Introduction 12 Spectrum of a single electron quantum dot 52.1 Electron in a quantum dot: Single particle approximation . . . . . 52.1.1 Effective mass approximation . . . . . . . . . . . . . . . . 52.1.2 Overview of known results . . . . . . . . . . . . . . . . . . 82.1.3 Parameters of the model . . . . . . . . . . . . . . . . . . . 102.2 Spin-orbit influence on the energy spectrum . . . . . . . . . . . . 102.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Single dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Spin hot spots . . . . . . . . . . . . . . . .

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Published 01 January 2007
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Controlling electron quantum dot
qubits by spin-orbit interactions
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften (Dr. rer. nat.)
der Naturwissenschaftlichen Fakult¨at II-Physik
der Universit¨at Regensburg
vorgelegt von
Peter Stano
aus Partizanske, Slowakei
Januar 2007The PhD thesis was submitted on 12.01.2007.
The colloquium took place on 23.3.2007.
Christoph Strunk Chairman
Jaroslav Fabian 1st Referee
Boardofexaminers:
Milena Grifoni 2nd Referee
Andreas Schaefer ExaminerAcknowledgments
I would like here to express my gratitude to Prof. Jaroslav Fabian for his inval-
ueable help and support over the whole period of my PhD studies. Without his
continual assistance this work would not get much farther than to this page.
vContents
Acknowledgments v
Contents vi
List of tables ix
List of figures xii
List of author’s publications xxi
1 Introduction 1
2 Spectrum of a single electron quantum dot 5
2.1 Electron in a quantum dot: Single particle approximation . . . . . 5
2.1.1 Effective mass approximation . . . . . . . . . . . . . . . . 5
2.1.2 Overview of known results . . . . . . . . . . . . . . . . . . 8
2.1.3 Parameters of the model . . . . . . . . . . . . . . . . . . . 10
2.2 Spin-orbit influence on the energy spectrum . . . . . . . . . . . . 10
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Single dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Spin hot spots . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.2 Effective g-factor . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Double dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5.1 Energy spectrum in zero magnetic field, without spin-orbit
terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.2 Corrections to energy from spin-orbit interaction in zero
magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.3 Finite magnetic field, no spin-orbit terms . . . . . . . . . . 31
2.5.4 Effective spin-orbit Hamiltonian . . . . . . . . . . . . . . . 32
vii2.5.5 Spin-orbitcorrectionstotheeffectiveg-factorandtunneling
frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.6 Tunneling Hamiltonian . . . . . . . . . . . . . . . . . . . . 38
2.6 Summary: effective Hamiltonian, perturbative eigenfunctions . . . 41
2.6.1 Effective spin-orbit Hamiltonian . . . . . . . . . . . . . . . 41
2.6.2 Perturbative expressions for eigenfunctions . . . . . . . . . 43
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 Adding dissipation 47
3.1 Environment induces transitions . . . . . . . . . . . . . . . . . . . 47
3.1.1 Spin relaxation . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.2 Orbital relaxation . . . . . . . . . . . . . . . . . . . . . . . 52
3.2 Experiments on single electron spin relaxation . . . . . . . . . . . 52
3.2.1 Detecting the presence of a spin . . . . . . . . . . . . . . . 53
3.2.2 Measuring spin relaxation and decoherence . . . . . . . . . 58
3.3 Phonon induced spin relaxation due to the admixture mechanism 73
3.4 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4.1 Electron parameters . . . . . . . . . . . . . . . . . . . . . 76
3.4.2 Phonon-induced orbital and spin relaxation rates . . . . . 76
3.5 Single dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.5.1 In-plane magnetic field . . . . . . . . . . . . . . . . . . . . 79
3.5.2 Perpendicular magnetic field . . . . . . . . . . . . . . . . . 81
3.6 Double dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.6.1 In-plane magnetic field . . . . . . . . . . . . . . . . . . . . 87
3.6.2 Perpendicular magnetic field . . . . . . . . . . . . . . . . . 89
3.6.3 Other growth directions . . . . . . . . . . . . . . . . . . . 94
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4 Adding resonant field 101
4.1 Oscillating field in a quantum dot . . . . . . . . . . . . . . . . . . 101
4.2 Spin-orbit influence on induced Rabi oscillations . . . . . . . . . . 102
4.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4 Resonance in a two level model . . . . . . . . . . . . . . . . . . . 105
4.4.1 Current through the dot . . . . . . . . . . . . . . . . . . . 106
4.4.2 Effective spin-orbit Hamiltonian . . . . . . . . . . . . . . . 109
4.5 Matrix elements for the spin resonance . . . . . . . . . . . . . . . 110
4.6 Matrix elements for the orbital resonance . . . . . . . . . . . . . . 115
4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5 Conclusions 1176 Appendices 121
.1 Transient current occupation . . . . . . . . . . . . . . . . . . . . . 121
.1.1 Probe pulse . . . . . . . . . . . . . . . . . . . . . . . . . . 121
.1.2 Fill&wait pulse . . . . . . . . . . . . . . . . . . . . . . . . 122
.2 TRRO – probe pulse . . . . . . . . . . . . . . . . . . . . . . . . . 123
Bibliography 125