Abstract
Due to their quasi-zero-dimensional structure, quantum dots show optical properties which are different from those of nanostructures with spatial confinement in less than three dimensions. In this chapter, the theory of both the linear optical properties and nonlinear dynamics of semiconductor quan- tum dots is discussed. The main focus is on the experimentally accessible quantities such as absorption/luminescence and pump-probe spectra. The results are calculated for single and coupled quantum dots (Förster coupling) as well as quantum dot ensembles. The focus is on obtaining a microscopic understanding of the interactions of optically excited quantum dot electrons with the surrounding crystal vibrations (electron–phonon coupling). The discussed interactions are important for applications in, e.g., quantum information processing and laser devices.
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References
D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum Dot Heterostructures (Wiley, Chichester, 1999)
P.Y. Yu, M. Cardona, Fundamentals of Semiconductors (Springer, Berlin, 1999)
N. Baer, S. Schulz, S. Schumacher, P. Gartner, G. Czycholl, F. Jahnke, Optical properties of self-organized wurtzite InN/GaN quantum dots: A combined atomistic tight-binding and full configuration interaction calculation. Appl. Phys. Lett. 87(23), 231114 (2005)
A.J. Williamson, A. Zunger, InAs quantum dots: Predicted electronic structure of free-standing versus GaAs-embedded structures. Phys. Rev. B 59(24), 15819 (1999)
O. Stier, M. Grundmann, D. Bimberg, Electronic and optical properties of strained quantum dots modeled by 8-band k⋅p theory. Phys. Rev. B 59(8), 5688 (1999)
R. Heitz, O. Stier, I. Mukhametzhanov, A. Madhukar, D. Bimberg, Quantum size effect in self-organized InAs/GaAs quantum dots. Phys. Rev. B 62(16), 11017 (2000)
B. Krummheuer, V.M. Axt, T. Kuhn, Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots. Phys. Rev. B 65(19), 195313 (2002)
T. Unold, K. Mueller, C. Lienau, T. Elsaesser, A.D. Wieck, Optical control of excitons in a pair of quantum dots coupled by the dipole–dipole interaction. Phys. Rev. Lett. 94(13), 137404 (2005)
H. Haug, S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2004)
A. Thränhardt, S. Kuckenburg, A. Knorr, T. Meier, S.W. Koch, Quantum theory of phonon-assisted exciton formation and luminescence in semiconductor quantum wells. Phys. Rev. B 62(4), 2706 (2000)
G.D. Mahan, Many-Particle Physics (Kluwer Academic/Plenum, New York, 2000)
J. Förstner, C. Weber, J. Danckwerts, A. Knorr, Phonon-assisted damping of Rabi oscillations in semiconductor quantum dots. Phys. Rev. Lett. 91(12), 127401 (2003)
M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997)
K.J. Ahn, J. Förstner, A. Knorr, Resonance fluorescence of semiconductor quantum dots: Signatures of the electron-phonon interaction. Phys. Rev. B 71(15), 153309 (2005)
F. Rossi, T. Kuhn, Theory of ultrafast phenomena in photoexcited semiconductors. Rev. Mod. Phys. 74(3), 895 (2002)
J. Förstner, C. Weber, J. Danckwerts, A. Knorr, Phonon-induced damping of Rabi oscillations in semiconductor quantum dots. Phys. Status Solidi B 238(3), 419 (2003)
J. Danckwerts, K.J. Ahn, J. Förstner, A. Knorr, Theory of ultrafast nonlinear optics of Coulomb-coupled semiconductor quantum dots: Rabi oscillations and pump-probe spectra. Phys. Rev. B 73(16), 165318 (2006)
T. Förster, Zwischenmolekulare Energiewanderung und Fluoreszenz. Ann. Phys. 6, 55 (1948)
T. Förster, Delocalized excitation and excitation transfer, in Modern Quantum Chemistry, ed. by O. Sinanoglu (Academic, New York, 1965), p. 93
T. Stauber, R. Zimmermann, Optical absorption in quantum dots: Coupling to longitudinal optical phonons treated exactly. Phys. Rev. B 73(11), 115303 (2006)
M. Kira, S.W. Koch, Quantum-optical spectroscopy of semiconductors. Phys. Rev. A 73(1), 013813 (2006)
I. Waldmüller, J. Förstner, A. Knorr, Self-consistent projection operator theory of intersubband absorbance in semiconductor quantum wells, in Nonequilibrium Physics at Short Time Scales, ed. by K. Morawetz (Springer, Berlin, 2004), p. 251
M. Richter, M. Schaarschmidt, A. Knorr, W. Hoyer, J.V. Moloney, E.M. Wright, M. Kira, S.W. Koch, Quantum theory of incoherent THz emission of an interacting electron-ion plasma. Phys. Rev. A 71(5), 053819 (2005)
M. Richter, S. Butscher, M. Schaarschmidt, A. Knorr, Model of thermal terahertz light emission of a two-dimensional electron gas. Phys. Rev. B 75(11), 115331 (2007)
H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)
V.M. Axt, A. Stahl, A dynamics-controlled truncation scheme for the hierarchy of density matrices in semiconductor optics. Z. Phys. B 93, 195 (1994)
S. Butscher, A. Knorr, Theory of strong electron-phonon coupling for ultrafast intersubband excitations. Phys. Status Solidi B 243(10), 2423 (2006)
S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995)
N.G. van Kampen, A cumulant expansion for stochastic linear differential equations. II. Physica 74, 239 (1974)
J. Förstner, K.J. Ahn, J. Danckwerts, M. Schaarschmidt, I. Waldmüller, C. Weber, A. Knorr, Light propagation- and many-particle-induced non-Lorentzian lineshapes in semiconductor nanooptics. Phys. Status Solidi B 234(1), 155 (2002)
R. Zimmermann, E. Runge, Dephasing in quantum dots via electron-phonon interaction, in Proc. 26th ICPS Edinburgh, ed. by A.R. Long, J.H. Davies. IOP Conf. Series, vol. 171 (IOP Publishing, Bristol, 2002). Paper M 3.1
T. Feldtmann, L. Schneebeli, M. Kira, S.W. Koch, Quantum theory of light emission from a semiconductor quantum dot. Phys. Rev. B 73(15), 155319 (2006)
N. Baer, C. Gies, J. Wiersig, F. Jahnke, Luminescence of a semiconductor quantum dot system. Eur. Phys. J. B 50(3), 411 (2006)
E.A. Muljarov, T. Takagahara, R. Zimmermann, Phonon-induced exciton dephasing in quantum dot molecules. Phys. Rev. Lett. 95(17), 177405 (2005)
E.A. Muljarov, R. Zimmermann, Dephasing in quantum dots: Quadratic coupling to acoustic phonons. Phys. Rev. Lett. 93(23), 237401 (2004)
P. Machnikowski, Change of decoherence scenario and appearance of localization due to reservoir anharmonicity. Phys. Rev. Lett. 96(14), 140405 (2006)
P. Borri, W. Langbein, S. Schneider, U. Woggon, R.L. Sellin, D. Ouyang, D. Bimberg, Ultralong dephasing time in InGaAs quantum dots. Phys. Rev. Lett. 87(15), 157401 (2001)
L. Besombes, K. Kheng, L. Marsal, H. Mariette, Acoustic phonon broadening mechanism in single quantum dot emission. Phys. Rev. B 63(15), 155307 (2001)
I. Favero, G. Cassabois, R. Ferreira, D. Darson, C. Voisin, J. Tignon, C. Delalande, G. Bastard, P. Roussignol, Acoustic phonon sidebands in the emission line of single InAs/GaAs quantum dots. Phys. Rev. B 68(23), 233301 (2003)
A.V. Uskov, A.-P. Jauho, B. Tromborg, J. Mørk, R. Lang, Dephasing times in quantum dots due to elastic LO phonon-carrier collisions. Phys. Rev. Lett. 85(7), 1516 (2000)
P. Machnikowski, L. Jacak, Exciton-LO phonon dynamics in InAs/GaAs quantum dots: Effects of zone-edge phonon damping. Phys. Rev. B 71(11), 115309 (2005)
E.A. Muljarov, R. Zimmermann, Exciton dephasing in quantum dots due to LO-phonon coupling: An exactly solvable model. Phys. Rev. Lett. 98(18), 187401 (2007)
B.R. Mollow, Pure-state analysis of resonant light scattering: Radiative damping, saturation, and multiphoton effects. Phys. Rev. A 12(5), 1919 (1975)
I.I. Rabi, Space quantization in a gyrating magnetic field. Phys. Rev. 51(8), 652 (1937)
I.I. Rabi, J.R. Zacharias, S. Millman, P. Kusch, A new method of measuring nuclear magnetic moment. Phys. Rev. 53(4), 318 (1938)
A. Krügel, V.M. Axt, T. Kuhn, P. Machnikowski, A. Vagov, The role of acoustic phonons for Rabi oscillations in semiconductor quantum dots. Appl. Phys. B 81, 897 (2005)
A. Vagov, M.D. Croitoru, V.M. Axt, T. Kuhn, F.M. Peeters, High pulse area undamping of Rabi oscillations in quantum dots coupled to phonons. Phys. Status Solidi B 243(10), 2233 (2006)
A. Krügel, V.M. Axt, T. Kuhn, Back action of nonequilibrium phonons on the optically induced dynamics in semiconductor quantum dots. Phys. Rev. B 73(3), 035302 (2006)
S. Stufler, P. Ester, A. Zrenner, M. Bichler, Quantum optical properties of a single In x Ga1−x As-GaAs quantum dot two-level system. Phys. Rev. B 72(12), 121301 (2005)
A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, G. Abstreiter, Coherent properties of a two-level system based on a quantum-dot photodiode. Nature 418, 612 (2002)
P. Borri, W. Langbein, S. Schneider, U. Woggon, R.L. Sellin, D. Ouyang, D. Bimberg, Rabi oscillations in the excitonic ground-state transition of InGaAs quantum dots. Phys. Rev. B 66(8), 081306 (2002)
S.W. Koch, N. Peyghambarian, M. Lindberg, Transient and steady-state optical non-linearities in semiconductors. J. Phys. C 21, 5229 (1988)
T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V.M. Axt, T. Kuhn, S. Eshlaghi, A.D. Wieck, Coherent nonlinear optical response of single quantum dots studied by ultrafast near-field spectroscopy. Phys. Rev. Lett. 89(5), 057401 (2002)
T. Unold, K. Mueller, C. Lienau, T. Elsaesser, A.D. Wieck, Optical Stark effect in a quantum dot: Ultrafast control of single exciton polarizations. Phys. Rev. Lett. 92(15), 157401 (2004)
I.V. Ostrovskii, A.K. Rozhko, V.N. Lysenko, Ultrasonic luminescence of CdS single crystals. Sov. Tech. Phys. Lett. 5, 377 (1979)
P.P. Corso, L. Lo Cascio, F. Persico, Simple vectorial model for the spectrum of a two-level atom in an intense low-frequency field. Phys. Rev. A 58(2), 1549 (1998)
F. Milde, K.J. Ahn, A. Knorr, Theory of quantum dot luminescence from acoustically excited intersubband transitions. Phys. Status Solidi B 243(10), 2257 (2006)
K.J. Ahn, F. Milde, A. Knorr, Phonon-wave-induced resonance fluorescence in semiconductor nanostructures: Acoustoluminescence in the terahertz range. Phys. Rev. Lett. 98(2), 027401 (2007)
T. Renger, R.A. Marcus, On the relation of protein dynamics and exciton relaxation in pigment-protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra. J. Chem. Phys. 116(22), 9997 (2002)
M. Richter, K.J. Ahn, A. Knorr, A. Schliwa, D. Bimberg, M. El-Amine Madjet, T. Renger, Theory of excitation transfer in coupled nanostructures—from quantum dots to light harvesting complexes. Phys. Status Solidi B 243(10), 2302 (2006)
Y. Mitsumori, A. Hasegawa, M. Sasaki, H. Maruki, F. Minami, Local field effect on Rabi oscillations of excitons localized to quantum islands in a single quantum well. Phys. Rev. B 71(23), 233305 (2005)
A. Knorr, K.-E. Süsse, D.-G. Welsch, Coherent interatomic interaction and cooperative effects in resonance fluorescence. J. Opt. Soc. Am. B 9(7), 1174 (1992)
K.J. Ahn, A. Knorr, Radiative lifetime of quantum confined excitons near interfaces. Phys. Rev. B 68(16), 161307 (2003)
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Weber, C., Richter, M., Ritter, S., Knorr, A. (2008). Theory of the Optical Response of Singleand Coupled Semiconductor Quantum Dots. In: Bimberg, D. (eds) Semiconductor Nanostructures. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77899-8_9
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DOI: https://doi.org/10.1007/978-3-540-77899-8_9
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