Abstract
We theoretically studied coherent excitation energy transfer between self-growth semiconductor quantum dots (QDs) by solving Heisenberg’s equations of motion for density matrix elements in second quantization regime. In a local excitation condition where only one QD electron is optically excited by the pump laser field, coherent excitation energy transfer to the other QD electron can be achieved through Coulomb (Förster) and electron-photon (radiation field) interactions. We calculated three diagonal and one off-diagonal Coulomb coupling constants, which are responsible for the biexcitonic frequency renormalization and the coherent energy transfer between QDs, respectively, and radiation field coupling coefficients by using electron and hole wave functions derived from eight-band kp-theorem, whose validity has already been tested by comparison with experiment. In linear optical regime where the occupation densities of electrons at higher energy level are negligibly small, we could successfully derive fully analytical behaviors of temporal dynamics of the interband polarizations and level occupation densities of both QDs by using Hartree-Fock approximation (HFA), in eventual, the stationary photoluminescence of the coupled QDs in an analytical form. Additionally, the validity of the HFA was examined by comparing the numerical results with those obtained from the exact correlation expansion model for different values of the pump field intensity.
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D. Bimberg, ed., Semiconductor Nanostructures, Nanoscience and technology (Springer, Berlin, 2008).
P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Quyang and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
P. Borri, W. Langbein, U. Woggon, M. Schwab, M. Bayer, S. Fafard, Z. Wasilewski and P. Hawrylak, Phys. Rev. Lett. 91, 267401 (2003).
M. Bayer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusinski, Z. R. Wasilewski, O. Sterna and A. Forchel, Science 291, 451 (2001).
E. Biolatti, I. D’Amico, P. Zanardi and F. Rossi, Phys. Rev. B 65, 075306 (2002).
B. W. Lovett, J. H. Reina, A. Nazir, G. Andrew and D. Briggs, Phys. Rev. B 68, 205319 (2003).
J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke and A. Forchel, nature 432, 197 (2004).
A. Nazir, B. W. Lovett, S. D. Barrett, J. H. Reina, G. Andrew and D. Briggs, Phys. Rev. B 71, 045334 (2005).
K. Becker, J. M. Lupton, J. Müller, A. L. Rogach, D. V. Talapin, H. Weller and J. Feldmann, Nature Materials 5, 777 (2006), URL http://dx.doi.org/10.1038/nmat1738.
T. Frey, P. J. Leek, M. Beck, A. Blais, T. Ihn, K. Ensslin and A. Wallraff, Phys. Rev. Lett. 108, 046807 (2012), URL https:// link.aps.org/doi/10.1103/PhysRevLett.108.046807.
P. Michler, Quantum Dots for Quantum Information Technologies, Nano-Optics and Nanophotonics (Springer, Berlin, 2017).
G. Ortner, M. Bayer, Y. Lyanda-Geller, T. L. Reinecke, A. Kress, J. P. Reithmaier and A. Forchel, Phys. Rev. Lett. 94, 157401 (2005).
T. Förster, Discuss. Faraday. Soc. 27, 7 (1959).
J. Danckwerts, K. J. Ahn, J. Förstner, and A. Knorr, Phys. Rev. B 73, 165318 (2006), URL https://link.aps.org/doi/10.1103/PhysRevB.73.165318.
S. Jang, Y-C. Cheng, D. R. Reichman and J. D. Eaves, The Journal of Chemical Physics 129, 101104 (2008), URL https://doi.org/10.1063/1.2977974.
D. Kim, S. Okahara, M. Nakayama and Y. Shim, Phys. Rev. B 78, 153301 (2008), URL https:// link.aps.org/doi/10.1103/PhysRevB.78.153301.
G. Parascandolo and V. Savona, Phys. Rev. B 71, 045335 (2005).
P. W. Milonni and P. L. Knight, Phys. Rev. A 10, 1096 (1974).
P. W. Milonni and P. L. Knight, Phys. Rev. A 11, 1090 (1975).
M. J. Stephen, J. Chem. Phys. 40, 669 (1964).
P. R. Fontana and D. D. Hearn, Phys. Rev. Lett. 19, 481 (1967).
J. Förstner, K. J. Ahn, J. Danckwerts, M. Schaarschmidt, I. Waldmüller, C. Weber and A. Knorr, Phys. Stat. Sol. (b) 234, 155 (2002).
J. Förstner, C. Weber, J. Danckwerts and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
B. Krummheuer, V. M. Axt and T. Kuhn, Phys. Rev. B 65, 195313 (2002).
J. Förstner, C. Weber, J. Danckwerts and A. Knorr, phys. stat. sol. (b) 238, 419 (2003).
K. J. Ahn, J. Förstner and A. Knorr, Phys. Rev. B 71, 153309 (2005).
E. Rozbicki and P. Machnikowski, Phys. Rev. Lett. 100, 027401 (2008), URL https://link. aps.org/doi/10.1103/PhysRevLett.100.027401.
K. J. Ahn and A. Knorr, Phys. Rev. B 68, 161307(R) (2003).
J-Q. Liao, J-F. Huang, L-M. Kuang and C. P. Sun, Phys. Rev. A 82, 052109 (2010), URL https:// link.aps.org/doi/10.1103/PhysRevA.82.052109.
M. Bayer, T. L. Reinecke, F. Weidner, A. Larionov, A. McDonald and A. Forchel, Phys. Rev. Lett. 86, 3168 (2001).
S. Hughes, Phys. Rev. Lett. 94, 227402 (2005).
F. Reil, U. Hohenester, J. R. Krenn and A. Leitner, Nano Lett. 8, 4128 (2008), URL https:// doi.org/10.1021/nl801480m.
V. K. Komarala, A. L. Bradley, Y. P. Rakovich, S. J. Byrne, Y. K. Gun’ko, and A. L. Rogach, Applied Physics Letters 93, 123102 (2008), https:// doi.org/10.1063/1.2981209, URL https://doi.org//10. 10631.2981209.
O. Stier, M. Grundmann and D. Bimberg, Phys. Rev. B 59, 5688 (1999).
M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
J. M. Gerton, L. A. Wade, G. A. Lessard, Z. Ma and S. R. Quake, Phys. Rev. Lett. 93, 180801 (2004).
G. D. Mahan, Many-Particle Physics (Plenum Press, New York, 1981).
M. Winkelnkemper, A. Schliwa and D. Bimberg, Phys. Rev. B 74, 155322 (2006), URL https://link.aps.org/doi/10.1103/PhysRevB.74.155322.
A. Schliwa, M. Winkelnkemper and D. Bimberg, Phys. Rev. B 76, 205324 (2007), URL https://link.aps.org/doi/10.1103/PhysRevB.76.205324.
S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth and D. Bimberg, Phys. Rev. B 68, 035331 (2003).
O. Stier, Ph. D. thesis, Technical University Berlin, 2000.
L. Allen and J. H. Eberly, Optical Resonance and Two-Level System (Dover Publications, INC., New York, 1987).
G. S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and Their Relation to Other Approach (Springer, Berlin, 1974).
H. Freedhoff, Phys. Rev. A 69, 013814 (2004).
G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Harcourt Academic, London, 2001).
K. J. Ahn, F. Milde and A. Knorr, Phys. Rev. Lett. 98, 027401 (2007), URL https:// link.aps.org/doi/10.1103/PhysRevLett.98.027401.
K. J. Ahn, J. Korean Phys. Soc. 71, 657 (2017), URL https://doi.org/10.3938/jkps.71.722.
J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., New York, 1999), 3rd ed.
K. J. Ahn, Ph. D. thesis, Technische Universität Berlin, 2006.
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Ahn, K.J. Coherent Energy Transfer Dynamics and Photoluminescence of Coupled Quantum Dots: Fully Analytical Approach. J. Korean Phys. Soc. 73, 638–648 (2018). https://doi.org/10.3938/jkps.73.638
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DOI: https://doi.org/10.3938/jkps.73.638