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

Sujets

• Physik

Informations

• Publié par: universitat_regensburg
• Publié le: 01 janvier 2007
• Nombre de lectures: 6
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

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