Spin-orbit coupling and electron-phonon scattering - Fachbereich ...

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114 Jaynes–Cummings model PSfrag replacements 1.5 1 |0,↑〉 |ψ + 0 〉 E ± 0 0.5 2λ 0 |1,↓〉 |ψ − 0 〉 −0.5 −1 −0.5 0 0.5 1 δ Figure A.1: Eigenenergies of lowest JCM-subspace (n=0) as function of detuning δ. Energies in units of ω (dashed lines: eigenenergies for the uncoupled system). (see Fig. A.1). For the resonant JCM (δ=0) eigenstates are given by the symmetric and (anti-)symmetric superposition |ψ ± n 〉 δ=0 = 1 √ 2 ( |n,↑〉 ± |n + 1,↓〉 ) . (A.6)
Appendix B Fock–Darwin representation of electron-phonon interaction For representing the electron-phonon interaction Eq. (3.51), V ep (q) = λ q e iq·r( ) b q + b † −q , in the Fock–Darwin basis of the quantum dot, we rewrite the coordinate operators in terms of creation and annihilation operators of the ω ± fields [see Eq. (3.14)], x = ˜l ( ) a − + a † − + a + + a † + , y = ˜l ( ) a − − a † − − a + + a † + . (B.1) 2 2i It is convenient to introduce complex phonon wave vectors and define displacement operators α + q = ˜l 2 (q y + iq x ), α − q = − ˜l 2 (q y − iq x ), (B.2) D ± (α) = e αa† ± −α∗ a ± , (B.3) leading to ( ) V ep (q) = λ q e iqzz D + (α + q )D − (α − q ) b q + b † −q . (B.4) Thus, the matrix elements for spontaneous emission of a phonon in the Fock– Darwin basis {|n + ,n − ,σ〉} factorise to 〈n ′ +,n ′ −,σ ′ |V ep (q)|n + ,n − ,σ〉 = δ σσ ′λ q 〈n ′ +|D + (α + q )|n + 〉〈n ′ −|D − (α − q )|n − 〉. (B.5) 115
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Interaction and confinement in nano
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Abstract iii Abstract It is the pur
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Publications v Publications Some of
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2 Table of Contents 3 Rashba spin-o
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4 Introduction (phonons). Therefore
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6 Introduction Figure 1: Scanning e
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Chapter 1 The Rashba effect Effects
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1.2 The model 11 the position-depen
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1.3 Rashba effect in a perpendicula
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Chapter 2 Rashba spin-orbit couplin
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2.1 Rashba effect and magnetic fiel
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PSfrag replacements 2.1 Rashba effe
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2.2 Spectral properties, various li
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2.3 Electron transport in one-dimen
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PSfrag replacements 2.3 Electron tr
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PSfrag replacements 2.3 Electron tr
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2.4 Summary 45 For weak SO coupling
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2.4 Summary 47 splitting can become
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Chapter 3 Rashba spin-orbit couplin
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3.1 Spin-orbit driven coherent osci
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3.1 Spin-orbit driven coherent osci
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0 0.5 1.5 3.1 Spin-orbit driven coh
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3.2 Introduction to quantum dots an
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3.2 Introduction to quantum dots an
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Page 77 and 78: 3.3 Effects of relaxation 71 page 5
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Page 85 and 86: Chapter 4 Conclusion In this part o
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Page 89: Part II Phonon confinement in nanos
Page 92 and 93: 86 Introduction to electron-phonon
Page 94 and 95: 88 Introduction to electron-phonon
Page 96 and 97: 90 Coupled quantum dots in a phonon
Page 102 and 103: ) ) ) ) 3 4 + ) * - 96 Coupled quan
Page 106 and 107: 100 Coupled quantum dots in a phono
Page 110 and 111: PSfrag replacements 1042 Coupled qu
Page 116 and 117: 110 Conclusion due to phonon van-Ho
Page 119: Appendix A Jaynes-Cummings model Th
Page 123 and 124: Appendix C Evaluation of the phonon
Page 125 and 126: Appendix D Matrix elements of dot e
Page 127 and 128: 121 with λ ± l (q ‖) = F n B pz
Page 129 and 130: Bibliography [1] G. Bergmann, Phys.
Page 131 and 132: Bibliography 125 [31] M. Pletyukhov
Page 133 and 134: Bibliography 127 [72] T. Schäpers,
Page 135 and 136: Bibliography 129 [109] U. Merkt, J.
Page 137 and 138: Bibliography 131 [144] B. Auld, Aco
Page 139 and 140: Bibliography 133 [182] A. A. Kisele
Page 141: Acknowledgements Finally, I would l
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