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

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) ) ) ) 3 4 + ) * - 96 Coupled quantum dots in a phonon cavity =8?@
6.1 Control of dephasing and phonon emission in coupled quantum dots 97 ∝ L/c l,t which leads to a smearing of fine structures in γ(ω) on an energy scale c l,t /L ∼ 1µeV for L = 10b. Finite temperatures yield a similar broadening on a scale k B T . Therefore, low temperatures (20 mK ≈ 2µeV) are required to resolve the step-like features and the van Hove singularities in the inelastic current I in . We mention that vertically polarised shear waves (which are also eigenmodes of the slab) do not couple to electrons via the DP because the induced local change in volume (∝ ∇ · u) is zero. Fortunately, shear waves also do not change the low frequency decoupling discussed above because the only mode that is accessible at low enough energies is the massless mode (linear dispersion) that does not lead to any piezo-electric polarisation field. However, at higher frequencies shear subbands can contribute to the electron scattering. The existence of an energy ω 0 where the electron-phonon interaction vanishes could be used to suppress decoherence in double dot qubit systems with the energy difference ∆ = √ ε 2 + 4Tc 2 tuned to ∆ = ω 0 . For example, using gate voltages to tune T c (t) = ∆/2sin(Ωt), ε(t) = ∆cos(Ωt) as a function of time defines a one-qubit rotation (‘electron from left to right’) free of phonon interaction ∝ γ(∆) = 0. The condition ∆ = ω 0 therefore defines a one dimensional ‘dissipation-free manifold’ (curve) in the T c –ε parameter space. In particular, a suppression of decoherence could then be exploited in adiabatic electron transfers [178] or adiabatic swapping operations [179] in coupled quantum dots. We recall, however, that corrections to γ of 4th and higher order in the coupling constant (virtual processes) can lead to a small but final phonon-induced dephasing rate even at ∆ = ω 0 . Moreover, the dephasing due to spontaneous emission of photons, although negligible with respect to the phonon contribution in second order [147,148], is not altered unless the whole system is embedded into a photon cavity. Similarly, plasmons and electron-hole pair excitations in the leads can lead to dephasing. We suppose that the latter can affect the inter-dot dynamics of the coupled dots only indirectly via coupling to the leads and only weakly contribute to dephasing, as is the case for interactions between dot and lead electrons beyond the Coulomb blockade charging effect. Alternatively to suppressing dissipation from phonons at certain energies, the van Hove singularities of the same system could be used to enormously enhance the spontaneous emission rate of phonons. The electron current I in ≈ −eγ(ε) at ∣ ∣ those energies is due to strong inelastic transitions. The term ∣α ± e iq ‖·d 2 ∣ in (6.4) determines the angular phonon emission characteristic of the double dot. Therefore, as a function of energy and orientation, the double dot can be used as an energy selective phonon emitter with well defined emission characteristics. In conclusion, we have found that phonon confinement is a promising tool for gaining control of dephasing in double quantum dots via phonons. Once this was achieved, it would be possible to study systematically dephasing due to other
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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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Page 51 and 52: 2.4 Summary 45 For weak SO coupling
Page 53 and 54: 2.4 Summary 47 splitting can become
Page 55 and 56: Chapter 3 Rashba spin-orbit couplin
Page 57 and 58: 3.1 Spin-orbit driven coherent osci
Page 59 and 60: 3.1 Spin-orbit driven coherent osci
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Page 63 and 64: 0 0.5 1.5 3.1 Spin-orbit driven coh
Page 65 and 66: 3.2 Introduction to quantum dots an
Page 75 and 76: PSfrag replacements 3.2 Introductio
Page 77 and 78: 3.3 Effects of relaxation 71 page 5
Page 79 and 80: 3.3 Effects of relaxation 73 The re
Page 81 and 82: 3.3 Effects of relaxation 75 with q
Page 83 and 84: 3.3 Effects of relaxation 77 eh 14
Page 85 and 86: Chapter 4 Conclusion In this part o
Page 87 and 88: Tuneable quantum dots connected to
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 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 and 120: Appendix A Jaynes-Cummings model Th
Page 121 and 122: Appendix B Fock-Darwin representati
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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