 | Gywat O. Spins in optically active quantum dots: concepts and methods / O.Gywat, H.J.Krenner, J.Berezovsky. - Weinheim: Wiley-VCH, 2010. - x, 209 p. - Incl. bibl. ref. - Ind.: p.191-209. - ISBN 978-3-527-40806-1
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Preface ........................................................ IX
1 Introduction ................................................. 1
1.1 Spin .................................................... 2
1.2 Spin-1/2 Basics ......................................... 3
1.3 Quantum Dots ............................................ 7
1.3.1 Spin-Based Quantum Information Processing with
Artificial Atoms ................................. 8
1.3.2 Optically Active Quantum Dots ................... 11
1.3.3 "Natural" Quantum Dots .......................... 11
2 Optically Active Quantum Dots: Single and Coupled
Structures .................................................. 15
2.1 Epitaxial Quantum Dots ................................. 15
2.2 "Natural" Quantum Dots Revisited ....................... 18
2.2.1 Structure and Fabrication ....................... 18
2.2.2 Energy Levels and Optical Transitions ........... 19
2.3 Self-Assembled Quantum Dots ............................ 21
2.3.1 Strain-Driven Self-Alignment .................... 22
2.3.2 Optical Properties and QD Shell Structure ....... 24
2.4 Alternative Epitaxial Quantum Dot Systems .............. 27
2.4.1 Electrically Gated Quantum Dots ................. 27
2.4.2 Advanced MBE Techniques ......................... 29
2.4.3 Nanowire Quantum Dots ........................... 31
2.5 Chemically-Synthesized Quantum Dots .................... 32
2.5.1 Colloidal Growth ................................ 33
2.5.2 Energy Level Structure and Optical Properties ... 34
3 Theory of Confined States in Quantum Dots ................... 39
3.1 Band Structure of III-V Semiconductors ................. 39
3.1.1 Effective Mass of Crystal Electrons ............. 40
3.1.2 Spin-Orbit Interaction .......................... 41
3.1.3 Band Structure Close to the Band Edges .......... 41
3.1.4 Band-Edge Bloch States .......................... 42
3.1.5 Coupling of Bands and the Luttinger
Hamiltonian ..................................... 43
3.1.6 Splitting of Heavy Hole and Light Hole Bands .... 46
3.1.7 Electrons and Holes ............................. 47
3.2 Quantum Confinement .................................... 47
3.2.1 One-Dimensional Confinement ..................... 48
3.2.2 Quantum Dot Confinement ......................... 48
3.3 Spherical Quantum Dot Confinement ...................... 49
3.3.1 Conduction-В and States ......................... 50
3.3.2 Valence Band States ............................. 53
3.3.3 Deviations from a Spherical Dot Shape ........... 55
3.4 Parabolic Quantum Dot Confinement ...................... 55
3.5 Extensions of the Noninteracting Single-Electron
Picture ................................................ 57
3.5.1 Symmetry of Many-Particle States in Quantum
Dots ............................................ 57
3.5.2 Coulomb Interaction ............................. 58
3.5.3 The Concept of Excitons in Quantum Dots ......... 59
3.5.4 Carrier Configurations in the s Shell and
Energies ........................................ 60
3.6 Few-Carrier Spectra of Self-Assembled Quantum Dots ..... 61
3.6.1 From Ensemble to Single Quantum Dot Spectra ..... 61
3.6.2 Transition Energies of Few-Particle States ...... 63
4 Integration of Quantum Dots in Electro-optical Devices ...... 67
4.1 Tuning Quantum Dots by Electric Fields ................. 67
4.1.1 Semiconductor Diodes ............................ 67
4.1.2 Voltage-Controlled Number of Charges ............ 69
4.1.3 Optically Probing Coulomb Blockade .............. 71
4.1.4 Quantum Confined Stark Effect ................... 73
4.2 Optical Cavities ....................................... 77
5 Quantum Dots Interacting With the Electromagnetic Field ..... 83
5.1 Hamiltonian for Radiative Transitions of Quantum
Dots ................................................... 83
5.1.1 Electromagnetic Field ........................... 83
5.1.2 Nonrelativistic Electron-Photon Interaction ..... 84
5.1.3 Total Hamiltonian for a Quantum Dot and
a Field ......................................... 85
5.2 Electric Dipole Transitions ............................ 86
5.2.1 Electric Dipole Selection Rules ................. 88
5.2.2 Interband Transitions in a III—V
Semiconductor ................................... 89
5.2.3 Equivalent Classical Electric Dipole Picture .... 91
5.2.4 Semiclassical Interaction with a Laser Field .... 92
5.3 Magnetic Dipole Transitions ............................ 93
5.4 Generalized Master Equation of the Driven Two-Level
System
5.4.1 The Driven Two-Level System ..................... 94
5.4.2 System-Reservoir Approach ....................... 94
5.5 Cavity Quantum Electrodynamics ......................... 97
5.5.1 Strong Coupling Regime .......................... 98
5.5.2 Weak Coupling Regime ............................ 99
5.6 Dispersive Interaction ................................ 100
5.6.1 Lamb Shift and AC Stark Shift .................. 100
5.6.2 Two Emitters Interacting with a Cavity ......... 102
6 Spin-spin Interaction in Quantum Dots ...................... 103
6.1 Electron-Electron-Spin Interaction .................... 103
6.2 Electron-Hole Exchange Interaction .................... 104
6.2.1 Exciton Fine Structure ......................... 105
6.2.2 Biexcitons and Polarization-Entangled
Photons ........................................ 107
6.3 Hyperfine Interaction ................................. 109
7 Experimental Methods for Optical Initialization, Readout,
and Manipulation of Spins .................................. 111
7.1 Optical Spin Initialization ........................... 112
7.1.1 Nonresonant Spin Pumping ....................... 114
7.1.2 Resonant Spin Pumping .......................... 117
7.1.3 Nuclear Spin Pumping ........................... 120
7.2 Optical Spin Readout .................................. 123
7.2.1 Time-Resolved Photoluminescence ................ 124
7.2.2 Spin Storage and Retrieval ..................... 125
7.2.3 Magnetic Ions .................................. 130
7.2.4 Spin-Selective Absorption ...................... 132
7.3 Observation of Spin Coherence and Optical
Manipulation .......................................... 134
7.3.1 The Hanle Effect ............................... 134
7.3.2 Ensemble Hanle Effect .......................... 135
7.3.3 Hanle Effect Measurement of a Single Quantum
Dot ............................................ 137
7.3.4 Time-Resolved Faraday Rotation Spectroscopy .... 140
7.3.5 Coherent Spin Echos - Measurement of T2 ........ 145
7.3.6 Single Spin Kerr Rotation Measurement .......... 148
7.3.7 Time-Resolved Observation of Single Spin
Coherence ...................................... 153
7.3.8 Optical Spin Manipulation ...................... 157
7.3.9 Putting It All Together ........................ 163
8 Controlling Charge and Spin Excitations in Coupled
Quantum Dots ............................................... 167
8.1 Tunable Coupling in a Quantum Dot Molecule ............ 167
8.1.1 A Toy Model for Coupled Systems: The Two-Site
Hubbard Model .................................. 167
8.1.2 An Exciton in a QD Molecule: A Coupled
System ......................................... 170
8.2 Molecular Theory of Confined States in Coupled
Quantum Dots .......................................... 173
8.3 Optically Probing Spin and Charge Excitations in
a Tunable Quantum Dot Molecule ........................ 174
8.3.1 Optical Response with Initial and Final State
Couplings ...................................... 174
8.3.2 Electric Field Induced Coupling of Charged
Trions in a QD Molecule ........................ 177
8.4 Future Directions ..................................... 180
Appendix A Valence Band States for Spherical Confinement ...... 183
Appendix В List of Constants .................................. 187
Appendix С Material Parameters ................................ 189
References ................................................. 191
Index ...................................................... 207
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