半导体量子点结构的光学及输运特性研究
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摘要
本论文重点研究了外加光场作用下半导体量子点结构中的光学特性,包括光吸收特性,量子干涉效应和强场中的非线性光学效应,并利用量子点结构的输运特性表征弱光场与体系相互作用产生的微弱光学信号。
第一部分研究了耦合三量子点和量子环对弱光场的响应。
首先,系统地研究了强驱动下耦合三量子点体系的量子干涉现象。借助光子辅助隧穿输运,将耦合三量子点对光场的响应呈现在体系的隧穿电流上,为实验在固体环境中获取光强较弱的相干光谱提供了一个可行的方案。通过调控耦合三量子点的能级结构,在吸收谱中相继观察到了由量子干涉效应带来的Autler-Townes劈裂、Mollow劈裂、无粒子数反转增益效应、相干俘获等量子相干特性,同时实现了对这些量子相干特性的调控。研究中考虑了声子的自发辐射对各能级电子布居数的影响。探讨了声子的辅助隧穿输运特性,其提供的背景电流可以用来判断驱动场对三能级结构的耦合状况。
其次,研究了磁场调控下的量子环对太赫兹光的吸收特性。借助磁场对量子环能级的调制作用以及光子参与隧穿输运特性,提出了一种频率可调的太赫兹光探测理论模型。在此模型中,连续变化的外磁场实现了对太赫兹光探测的连续可调性；通过调控量子环的半径和宽度可以改变太赫兹光探测的频率范围。
第二部分研究了量子点和耦合三量子点体系在强光场驱动下的高次谐波辐射特性。
本论文研究了强微波场驱动下量子点体系的高次谐波辐射特性,提出了利用此非线性光学效应产生太赫兹辐射的设想。从量子输运动力学角度,揭示了输运体系准能带宽对高次谐波辐射效率起到的决定性作用。
本论文进一步研究了强微波场驱动下的耦合三量子点三能级结构的高次谐波辐射机制和谐波辐射的偏振特性。发现在反演对称性缺失的多能级体系中,可以产生奇次、偶次谐波共存的高次谐波辐射,并阐明这种辐射特性的动力学机制。在耦合三量子点谐波辐射偏振特性的初步研究中,发现谐波辐射场中既有线偏振光又有椭圆偏振光,高次谐波辐射的偏振特性依赖于谐波阶次,并指出这些现象与耦合三量子点中各个偶极子的空间分布有着密切的联系。
In this dissertation, we mainly focus on a theoretical study of the optical prop-erties of semiconductor quantum dot structures, including optical absorption prop-erties, quantum interference effects and nonlinear optical effects induced by intense fields. In particular, we use the transport properties of the quantum dot structures to obtain the optical signals induced by weak fields.
In the first part of the dissertation, the response of coupled quantum dots and quantum rings to weak optical fields are investigated.
Firstly, we systematically study the interference phenomena of serially coupled triple quantum dots driven by a strong driving and a weak probe field. The probe absorption spectra are shown in the photon-assisted tunneling current, which pro-vides a feasible way to obtain weak coherent optical signals in a solid environment. By changing the configuration of the three-level coupled triple quantum dot, we can obtain and control various quantum coherent properties such as Autler-Townes splitting, Mollow triplet, gain effect without population inversion, and coherent pop-ulation trapping. We also find that the effect of spontaneous emission of phonons may lead to an obvious background current, which can be used to distinguish which transition is driven by the driving field in experiments.
And then we investigate the magnetic-field-modulated terahertz absorption spectra of a real GaAs quantum ring. As the energy levels of the quantum ring are modulated by an external magnetic field, the photon-participated tunneling current is used to show the features of the terahertz spectra of the quantum ring. Our study provides a possible way to realize tunable detection of terahertz fields. In such a scheme, tuning is performed via the external magnetic field, and the resonant frequency bands are handled by controlling the radius and width of the quantum ring.
In the second part of the dissertation, the features of high-order harmonic generation in quantum dots and coupled quantum dots are explored.
We first study the high-order harmonic spectra of a quantum dots driven by an intense microwave field. We propose a way to obtain terahertz radiation by using these nonlinear optical effects. By mapping the optical processes to quantum transport processes, we find that the efficiency of high-order harmonic generation is determined by the bandwidth of the quasienergy spectrum.
Finally, we explore the features of high-order harmonic generation in coupled triple quantum dots in intense microwave fields. We find that multi-level systems in coupled triple quantum dots can generate odd-even order harmonics. The dynamic mechanism of high-order harmonic generation in optical coupled multi-level system is investigated. In addition, we make an elementary study on the polarization of the radiation. Due to the spatial configuration of the coupled triple quantum dots, the harmonic emission can be either linearly or elliptically polarized when driven by linearly polarized fields, and the polarization properties are found to be strongly dependent on the harmonic order.
第一部分研究了耦合三量子点和量子环对弱光场的响应。
首先,系统地研究了强驱动下耦合三量子点体系的量子干涉现象。借助光子辅助隧穿输运,将耦合三量子点对光场的响应呈现在体系的隧穿电流上,为实验在固体环境中获取光强较弱的相干光谱提供了一个可行的方案。通过调控耦合三量子点的能级结构,在吸收谱中相继观察到了由量子干涉效应带来的Autler-Townes劈裂、Mollow劈裂、无粒子数反转增益效应、相干俘获等量子相干特性,同时实现了对这些量子相干特性的调控。研究中考虑了声子的自发辐射对各能级电子布居数的影响。探讨了声子的辅助隧穿输运特性,其提供的背景电流可以用来判断驱动场对三能级结构的耦合状况。
其次,研究了磁场调控下的量子环对太赫兹光的吸收特性。借助磁场对量子环能级的调制作用以及光子参与隧穿输运特性,提出了一种频率可调的太赫兹光探测理论模型。在此模型中,连续变化的外磁场实现了对太赫兹光探测的连续可调性；通过调控量子环的半径和宽度可以改变太赫兹光探测的频率范围。
第二部分研究了量子点和耦合三量子点体系在强光场驱动下的高次谐波辐射特性。
本论文研究了强微波场驱动下量子点体系的高次谐波辐射特性,提出了利用此非线性光学效应产生太赫兹辐射的设想。从量子输运动力学角度,揭示了输运体系准能带宽对高次谐波辐射效率起到的决定性作用。
本论文进一步研究了强微波场驱动下的耦合三量子点三能级结构的高次谐波辐射机制和谐波辐射的偏振特性。发现在反演对称性缺失的多能级体系中,可以产生奇次、偶次谐波共存的高次谐波辐射,并阐明这种辐射特性的动力学机制。在耦合三量子点谐波辐射偏振特性的初步研究中,发现谐波辐射场中既有线偏振光又有椭圆偏振光,高次谐波辐射的偏振特性依赖于谐波阶次,并指出这些现象与耦合三量子点中各个偶极子的空间分布有着密切的联系。
In this dissertation, we mainly focus on a theoretical study of the optical prop-erties of semiconductor quantum dot structures, including optical absorption prop-erties, quantum interference effects and nonlinear optical effects induced by intense fields. In particular, we use the transport properties of the quantum dot structures to obtain the optical signals induced by weak fields.
In the first part of the dissertation, the response of coupled quantum dots and quantum rings to weak optical fields are investigated.
Firstly, we systematically study the interference phenomena of serially coupled triple quantum dots driven by a strong driving and a weak probe field. The probe absorption spectra are shown in the photon-assisted tunneling current, which pro-vides a feasible way to obtain weak coherent optical signals in a solid environment. By changing the configuration of the three-level coupled triple quantum dot, we can obtain and control various quantum coherent properties such as Autler-Townes splitting, Mollow triplet, gain effect without population inversion, and coherent pop-ulation trapping. We also find that the effect of spontaneous emission of phonons may lead to an obvious background current, which can be used to distinguish which transition is driven by the driving field in experiments.
And then we investigate the magnetic-field-modulated terahertz absorption spectra of a real GaAs quantum ring. As the energy levels of the quantum ring are modulated by an external magnetic field, the photon-participated tunneling current is used to show the features of the terahertz spectra of the quantum ring. Our study provides a possible way to realize tunable detection of terahertz fields. In such a scheme, tuning is performed via the external magnetic field, and the resonant frequency bands are handled by controlling the radius and width of the quantum ring.
In the second part of the dissertation, the features of high-order harmonic generation in quantum dots and coupled quantum dots are explored.
We first study the high-order harmonic spectra of a quantum dots driven by an intense microwave field. We propose a way to obtain terahertz radiation by using these nonlinear optical effects. By mapping the optical processes to quantum transport processes, we find that the efficiency of high-order harmonic generation is determined by the bandwidth of the quasienergy spectrum.
Finally, we explore the features of high-order harmonic generation in coupled triple quantum dots in intense microwave fields. We find that multi-level systems in coupled triple quantum dots can generate odd-even order harmonics. The dynamic mechanism of high-order harmonic generation in optical coupled multi-level system is investigated. In addition, we make an elementary study on the polarization of the radiation. Due to the spatial configuration of the coupled triple quantum dots, the harmonic emission can be either linearly or elliptically polarized when driven by linearly polarized fields, and the polarization properties are found to be strongly dependent on the harmonic order.
引文
[1]J. S. Koehler. Attempt to design a strong solid[J]. Phys. Rev. B,1970,2:547-551.
[2]L. Esaki and R. Tsu. Superlattice and negative differential conductivity in semicon-ductors[J]. IBM J. Res. Dev.,1970,14:61-65.
[3]D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff. Direct formation of quantum-sized dots from uniform coherent islands of InGaAs on GaAs surfaces[J]. Appl. Phys. Lett.,1993,63:3203-3205.
[4]R. H. Blick, R. J. Haug, J. Weis, D. Pfannkuche, K. v. Klitzing, and K. Eberl. Single-electron tunneling through a double quantum dot:The artificial molecule[J]. Phys. Rev. B,1996,53:7899-7902.
[5]A. Lorke and R. J. Luyken. Many-particle ground states and excitations in nanometer-size quantum structures[J]. Physica B,1998,256:424-430.
[6]A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M. Garcia, and P. M. Petroff. Spectroscopy of nanoscopic semiconductor rings[J]. Phys. Rev. Lett.,2000, 84:2223-2226.
[7]R. J. Warburton, C. Schaflein, D. Haft, F. Bickel, A. Lorke, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff. Optical emission from a charge-tunable quantum ring[J]. Natrue (London),2000,405:926-929.
[8]L. P. Kouwenhoven, N. C. van der Vaart, A. T. Johnson, W. Kool, C. J. P. M. Harmans, J. G. Williamson, A. A. M. Staring, and C. T. Foxon. Single electron charging effects in semiconductor quantum dots[J]. Z. Phys. B,1991,85:367-373.
[9]E. B. Foxman, P. L. McEuen, U. Meirav, N. S. Wingreen, Y. Meir, P. A. Belk, N. R. Belk, and M. A. Kastner. Effects of quantum levels on transport through a Coulomb island[J]. Phys. Rev. B,1993,47:10020-10023.
[10]Y. Nagamune, H. Sakaki, L. P. Kouwenhoven, L. C. Mur, C. J. P. M. Harmans, J. Motohisa, and H. Noge. Single electron transport and current quantization in a novel quantumdot structure[J]. Appl. Phys. Lett.,1994,64:3279-3281.
[11]W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha, and L. P. Kouwenhoven. Electron transport through double quantum dots[J]. Rev. Mod. Phys.,2003,75:1-22.
[12]L. Gaudreau, S. A. Studenikin, A. S. Sachrajda, P. Zawadzki, A. Kam, J. Lapointe, M. Korkusinski, and P. Hawrylak. Stability diagram of a few-electron triple dot[J]. Phys. Rev. Lett.,2006,97:036807.
[13]D. Schroer, A. D. Greentree, L. Gaudreau, K. Eberl, L. C. L. Hollenberg, J. P. Kotthaus, and S. Ludwig. Electrostatically defined serial triple quantum dot charged with few electrons[J]. Phys. Rev. B,2007,76:075306.
[14]M. C. Rogge and R. J. Haug. Two-path transport measurements on a triple quantum dot[J]. Phys. Rev. B,2008,77:193306.
[15]A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider and M. Bichler. Energy spectra of quantum rings[J]. Nature (London),2001,413:822-825.
[16]R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi. Terahertz semiconductor-heterostructure laser[J]. Nature (London),2002,417:156-159.
[17]K. J. Ahn, F. Milde, and A. Knorr. Phonon-wave-induced resonance fluorescence in semiconductor nanostructures:acoustoluminescence in the terahertz range[J]. Phys. Rev. Lett.,2007,98:027401.
[18]X. H. Su, J. Yang, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera. Terahertz detection with tunneling quantum dot intersublevel photodetector[J]. Appl. Phys. Lett.,2006,89:031117.
[19]G. Huang, J. Yang, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera. A multicolor quantum dot intersublevel detector with photoresponse in the terahertz range[J]. Appl. Phys. Lett.,2008,92:011117.
[20]K. Ikushima, Y. Yoshimura, T. Hasegawa, S. Komiyama, T. Ueda, and K. Hirakawa. Photon-counting microscopy of terahertz radiation[J]. Appl. Phys. Lett.,2006,88: 152110.
[21]H. Hashiba, V. Antonov, L. Kulik, A. Tzalenchuk, P. Kleinschmid, S. Giblin, and S. Komiyama. Isolated quantum dot in application to terahertz photon counting[J]. Phys. Rev. B,2006,73:081310(R).
[22]S. G. Carter, V. Birkedal, C. S. Wang, L. A. Coldren, A. V. Maslov, D. S. Citrin, and M. S. Sherwin. Quantum Coherence in an Optical Modulator[J]. Science,2005, 310:651-653.
[23]E. Rasanen, A. Castro, J. Werschnik, A. Rubio, and E. K. U. Gross. Optimal Control of Quantum Rings by Terahertz Laser Pulses[J]. Phys. Rev. Lett.,2007,98:157404.
[24]E. Rasanen, A. Castro, J. Werschnik, A. Rubio, and E. K. U. Gross. Optimal laser control of double quantum dots[J]. Phys. Rev. B,2008,77:085324.
[25]S. E. Harris, J. E. Field, and A. Imamoglu. Nonlinear optical processes using elec-tromagnetically induced transparency[J]. Phys. Rev. Lett.,1990,64:1107-1110.
[26]K.-J. Boller, A. Imamolu, and S. E. Harris. Observation of electromagnetically in-duced transparency[J]. Phys. Rev. Lett.,1991,66:2593-2596.
[27]G. Alzetta, A. Gozzini, L. Moi, and G. Orriols. An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour[J]. Nuovo Cimento B,1976,36:5-20.
[28]S. H. Autler and C. H. Townes. Stark effects in rapidly varying fields[J]. Phys. R.ev., 1955,100:703-722.
[29]B. R. Mollow. Stimulated emission and absorption near resonance for driven sys-tems[J]. Phys. Rev. A,1972,5:2217-2222.
[30]S. E. Harris. Lasers without inversion:Interference of lifetime-broadened reso-nances[J]. Phys. Rev. Lett.,1988,62:1033-1036.
[31]M. Fleischhauer, A. Imamoglu, and J. P. Marangos. Electromagnetically induced transparency:Optics in coherent media[J]. Rev. Mod. Phys.,2005,77:633-673.
[32]X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham. Coherent optical spectroscopy of a strongly driven quantum dot[J]. Science, 2007,317:929-932.
[33]G. Jundt, L. Robledo, A. Hogele, S. Falt, and A. Imamoglu. Observation of dressed excitonic states in a single quantum dot[J]. Phys. Rev. Lett.,2008,100:177401.
[34]A. Muller, W. Fang, J. Lawall, and G. S. Solomon. Emission spectrum of a dressed exciton-biexciton complex in a semiconductor quantum dot[J]. Phys. Rev. Lett., 2008,101:027401.
[35]M. Kroner, C. Lux, S. Seidl, A. W. Holleitner, K. Karrai, A. Badolato, P. M. Petroff, and R. J. Warburton. Rabi splitting and ac-Stark shift of a charged exciton[J]. Appl. Phys. Lett.,2008,92:031108.
[36]T. Brandes and F. Renzoni. Current switch by coherent trapping of electrons in quantum dots[J]. Phys. Rev. Lett.,2000,85:4148-4151.
[37]J. Danckwerts, K. J. Ahn, J. Forstner, and A. Knorr. Theory of ultrafast nonlin-ear optics of Coulomb-coupled semiconductor quantum dots:Rabi oscillations and pump-probe spectra[J]. Phys. Rev. B,2006,73:165318.
[38]J. Gea-Banacloche, Mambwe Mumba, and Min Xiao. Optical switching in arrays of quantum dots with dipole-dipole interactions[J]. Phys. Rev. B,2006,74:165330.
[39]T. H. Stoof and Yu. V. Nazarov. Time-dependent resonant tunneling via two discrete states[J]. Phys. Rev. B,1996,53:1050-1053.
[40]B. L. Hazelzet, M. R. Wegewijs, T. H. Stoof, and Yu. V. Nazarov. Coherent and incoherent pumping of electrons in double quantum dots[J]. Phys. Rev. B,2001,63: 165313.
[41]R. H. Blick, D. W. van der Weide, R. J. Haug, and K. Eberl. Complex broadband millimeter wave response of a double quantum dot:Rabi oscillations in an artificial molecule[J]. Phys. Rev. Lett.,1998,81:689-692.
[42]T. H. Oosterkamp, T. Fujisawa, W. G. van der Wiel, K. Ishibashi, R. V. Hijman, S. Tarucha, and L. P. Kouwenhoven. Microwave spectroscopy of a quantum-dot molecule[J]. Nature (London),1998,395:873-876.
[43]J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H. Willems van Beveren, S. De Franceschi, L. M. K. Vandersypen, S. Tarucha, and L. P. Kouwenhoven. Few-electron quantum dot circuit with integrated charge read out[J]. Phys. Rev. B,2003,67: 161308(R).
[44]Y.-S. Shin, T. Obata, Y. Tokura, M. Pioro-Ladriere, R. Brunner, T. Kubo, K. Yoshidal, and S. Tarucha. Single-spin readout in a double quantum dot including a micromagnet[J]. Phys. Rev. Lett.,2010,104:046802.
[45]P. B. Corkum. Plasma perspective on strong field multiphoton ionization[J]. Phys. Rev. Lett.,1993,71:1994-1997.
[46]M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L'Huillier, and P. B. Corkum. Theory of high-harmonic generation by low-frequency laser fields[J]. Phys. Rev. A, 1994,49:2117-2132.
[47]B. Sundaram and P. W. Milonni. High-order harmonic generation:Simplified model and relevance of single-atom theories to experiment[J]. Phys. Rev. A,1990,41: 6571-6573.
[48]A. E. Kaplan and P. L. Shkolnikov. Superdressed two-level atom:Very high har-monic generation and multiresonances[J]. Phys. Rev. A,1994,49:1275-1280.
[49]F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet. Phase of harmonics from strongly driven two-level atoms[J]. Phys. Rev. A,1997,55:615-621.
[50]F. I. Gauthey, B. M. Garraway, and P. L. Knight. High harmonic generation and periodic level crossings[J]. Phys. Rev. A,1997,56:3093-3096.
[51]P. P. Corso, L. Lo Cascio, and F. Persico. Simple vectorial model for the spectrum of a two-level atom in an intense low-frequency field[J]. Phys. Rev. A,1998,58: 1549-1558.
[52]R. Bavli and H. Metiu. Properties of an electron in a quantum double well driven by a strong laser:Localization, low-frequency, and even-harmonic generation[J]. Phys. Rev. A,1993,47:3299-3310.
[53]A. F. Terzis and E. Paspalakis. High-order harmonic generation in a two-electron quantum dot molecule[J]. J. Appl. Phys.,2005,97:023523.
[54]F. R. Waugh, M. J. Berry, D. J. Mar, and R. M. Westervelt. Single-electron charging in double and triple quantum dots with tunable coupling[J]. Phys. Rev. Lett.,1995, 75:705-708.
[55]M. L. Ladron de Guevara and P. A. Orellana. Electronic transport through a parallel-coupled triple quantum dot molecule:Fano resonances and bound states in the continuum[J]. Phys. Rev. B,2006,73:205303.
[56]W. Xie, W. Chu, W. Zhang and S. Duan. Photon-assistant Fano resonance in serially coupled triple quantum dots[J]. J. Phys.:Condens. Matter,2008,20:325223.
[57]S. Duan, W. Zhang, W. Xie, Y. Ma and W. Chu. Time-dependent transport of symmetric A-type coupled triple quantum dots:competition between coherent de-struction of tunneling and Fano resonance[J]. N. J. Phys.,2009,11,013037.
[58]R. Zitko and J. Bonca. Fermi-liquid versus non-Fermi-liquid behavior in triple quan-tum dots[J]. Phys. Rev. Lett.,2007,98:047203.
[59]T. Kuzmenko, K. Kikoin, and Y. Avishai. Kondo effect in systems with dynamical symmetries[J]. Phys. Rev. B,2004,69:195109.
[60]D. S. Saraga and D. Loss. Spin-entangled currents created by a triple quantum dot[J]. Phys. Rev. Lett.,2003,90:166803.
[61]J. Kim, D. V. Melnikov, J. P. Leburton, D. G. Austing, and S. Tarucha. Spin charging sequences in three colinear laterally coupled vertical quantum dots[J]. Phys. Rev. B,2006,74:035307.
[62]F. Delgado, Y.-P. Shim, M. Korkusinski, and P. Hawrylak. Theory of spin, electronic, and transport properties of the lateral triple quantum dot molecule in a magnetic field[J]. Phys. Rev. B,2007,76:115332.
[63]N. S. Wingreen, K. W. Jacobsen, and J. W. Wilkins. Inelastic scattering in resonant tunneling[J]. Phys. Rev. B,1989,40:11834-11850.
[64]T. Kwapiriski, R.. Taranko, and E. Taranko. Photon-assisted electron transport through a three-terminal quantum dot system with nonresonant tunneling chan-nels[J]. Phys. Rev. B,2005,72:125312.
[65]T. Fujisawa, T. H. Oosterkamp, W. G. van der Wiel, B.W. Broer, R. Aguado, S. Tarucha, and L. P. Kouwenhoven. Spontaneous emission spectrum in double quantum dot devices[J]. Science,1998,282:932-935.
[66]T. Brandes and B. Kramer. Spontaneous emission of phonons by coupled quantum dots[J]. Phys. Rev. Lett.,1999,83:3021-3024.
[67]L. M. Narducci, M. O. Scully, G.-L. Oppo, P. Ru and J. R. Tredicce. Spontaneous emission and absorption properties of a driven three-level system[J]. Phys. Rev. A, 1990,42:1630-1649.
[68]C. Cohen-Tannoudji and S. Reynaud. Dressed-atom description of resonance fluo-rescence and absorption spectra of a multi-level atom in an intense laser beam[J]. J. Phys. B:Atom. Molec. Phys.,1977,3:345-363.
[69]C. Cohen-Tannoudji and S. Reynaud. Modification of resonance Raman scattering in very intense laser fields[J]. J. Phys. B:Atom. Molec. Phys.,1977,3:365-383.
[70]T. Ihn, A. Fuhrer, L. Meier, M. Sigrist, and K. Ensslin. Quantum physics in quantum rings[J]. Europhys. News,2005,36:78-81.
[71]J.-L. Zhu, W. Chu, Z. Dai, and D. Xu. Exciton states and their entanglement in coupled quantum dots[J]. Phys. Rev. B,2005,72:165346.
[72]M. Tonouchi. Cutting-edge terahertz technology[J]. Nat. Photonics,2007,1:97-105.
[73]X.-G. Zhao. A formal solution for the evolution operator and its application in two-level systems[J]. Phys. Lett. A,1994,193:5-10.
[74]J. H. Shirley. Solution of the Schrodinger equation with a Hamiltonian periodic in time[J]. Phys. Rev.,1965,138:B979-B987.
[75]F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Magquet. Role of intital coher-ence in the generatoin of harmonics and sidebands from a strongly driven two-level atom[J]. Phys. Rev. A,1995,52:525-540.
[76]X.-G. Zhao, R. Jahnke, and Q. Niu. Dynamic fractional stark ladders in dc-ac fields[J]. Phys. Lett. A,1995,202:297-304.
[77]D. R. Hofstadter. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields[J]. Phys. Rev. B,1976,14:2239-2249.
[78]M. Holthaus. Collapse of minibands in far-infrared irradiated superlattices[J]. Phys. Rev. Lett.,1992,69:351-354.
[79]F. Grossmann, T. Dittrich, P. Jung, and P. Hanggi. Coherent destruction of tunnel-ing[J]. Phys. Rev. Lett.,1991,67:516-519.
[80]T. Zuo, S. Chelkowski, and A. D. Bandrauk. Harmonic generation by the H2+ molec-ular ion in intense laser fields[J]. Phys. Rev. A.1993,48:3837-3844.
[81]Y. Chen, J. Chen, and J. Liu. Charge-resonance effect on harmonic generation by symmetric diatomic molecular ions in intense laser fields[J]. Phys. Rev. A,2006,74: 063405.
[82]J.-P. Connerade and C. H. Keitel. High harmonic generation in a static magnetic field[J]. Phys. Rev. A,1996,53:2748-2751.
[83]V. Averbukh, O. E. Alon, and N. Moiseyev. Stability and instability of dipole selec-tion rules for atomic high-order-harmonic-generation spectra in two-beam setups[J]. Phys. Rev. A,2002,65:063402.
[84]A. D. Bandrauk and H. Z. Lu. Controlling harmonic generation in molecules with intense laser and static magnetic fields:Orientation effects[J]. Phys. Rev. A,2003, 68:043408.
[85]G. L. Kamta and A. D. Bandrauk. Three-dimensional time-profile analysis of high-order harmonic generation in molecules:Nuclear interferences in H2+[J]. Phys. Rev. A,2005,71:053407.
[86]A. D. Bandrauk and H. Z. Lu. Molecules in intense laser fields:Beyond the dipole approximation[J]. Phys. Rev. A,2006,73:013412.
[87]T. Kreibich, M. Lein, V. Engel, and E. K. U. Gross. Even-Harmonic generation due to beyond-Born-Oppenheimer dynamics[J]. Phys. Rev. Lett.,2001,87:103901.
[88]T. Iwasa and K. Nobusada. Nonuniform light-matter interaction theory for near-field-induced electron dynamics[J]. Phys. Rev. A,2009,80:043409.
[89]X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, and M. M. Murnane. Ellip-tically polarized high-order harmonic emission from molecules in linearly polarized laser fields[J]. Phys. Rev. Lett.,2009,102:073902.
[2]L. Esaki and R. Tsu. Superlattice and negative differential conductivity in semicon-ductors[J]. IBM J. Res. Dev.,1970,14:61-65.
[3]D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff. Direct formation of quantum-sized dots from uniform coherent islands of InGaAs on GaAs surfaces[J]. Appl. Phys. Lett.,1993,63:3203-3205.
[4]R. H. Blick, R. J. Haug, J. Weis, D. Pfannkuche, K. v. Klitzing, and K. Eberl. Single-electron tunneling through a double quantum dot:The artificial molecule[J]. Phys. Rev. B,1996,53:7899-7902.
[5]A. Lorke and R. J. Luyken. Many-particle ground states and excitations in nanometer-size quantum structures[J]. Physica B,1998,256:424-430.
[6]A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M. Garcia, and P. M. Petroff. Spectroscopy of nanoscopic semiconductor rings[J]. Phys. Rev. Lett.,2000, 84:2223-2226.
[7]R. J. Warburton, C. Schaflein, D. Haft, F. Bickel, A. Lorke, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff. Optical emission from a charge-tunable quantum ring[J]. Natrue (London),2000,405:926-929.
[8]L. P. Kouwenhoven, N. C. van der Vaart, A. T. Johnson, W. Kool, C. J. P. M. Harmans, J. G. Williamson, A. A. M. Staring, and C. T. Foxon. Single electron charging effects in semiconductor quantum dots[J]. Z. Phys. B,1991,85:367-373.
[9]E. B. Foxman, P. L. McEuen, U. Meirav, N. S. Wingreen, Y. Meir, P. A. Belk, N. R. Belk, and M. A. Kastner. Effects of quantum levels on transport through a Coulomb island[J]. Phys. Rev. B,1993,47:10020-10023.
[10]Y. Nagamune, H. Sakaki, L. P. Kouwenhoven, L. C. Mur, C. J. P. M. Harmans, J. Motohisa, and H. Noge. Single electron transport and current quantization in a novel quantumdot structure[J]. Appl. Phys. Lett.,1994,64:3279-3281.
[11]W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha, and L. P. Kouwenhoven. Electron transport through double quantum dots[J]. Rev. Mod. Phys.,2003,75:1-22.
[12]L. Gaudreau, S. A. Studenikin, A. S. Sachrajda, P. Zawadzki, A. Kam, J. Lapointe, M. Korkusinski, and P. Hawrylak. Stability diagram of a few-electron triple dot[J]. Phys. Rev. Lett.,2006,97:036807.
[13]D. Schroer, A. D. Greentree, L. Gaudreau, K. Eberl, L. C. L. Hollenberg, J. P. Kotthaus, and S. Ludwig. Electrostatically defined serial triple quantum dot charged with few electrons[J]. Phys. Rev. B,2007,76:075306.
[14]M. C. Rogge and R. J. Haug. Two-path transport measurements on a triple quantum dot[J]. Phys. Rev. B,2008,77:193306.
[15]A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider and M. Bichler. Energy spectra of quantum rings[J]. Nature (London),2001,413:822-825.
[16]R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi. Terahertz semiconductor-heterostructure laser[J]. Nature (London),2002,417:156-159.
[17]K. J. Ahn, F. Milde, and A. Knorr. Phonon-wave-induced resonance fluorescence in semiconductor nanostructures:acoustoluminescence in the terahertz range[J]. Phys. Rev. Lett.,2007,98:027401.
[18]X. H. Su, J. Yang, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera. Terahertz detection with tunneling quantum dot intersublevel photodetector[J]. Appl. Phys. Lett.,2006,89:031117.
[19]G. Huang, J. Yang, P. Bhattacharya, G. Ariyawansa, and A. G. U. Perera. A multicolor quantum dot intersublevel detector with photoresponse in the terahertz range[J]. Appl. Phys. Lett.,2008,92:011117.
[20]K. Ikushima, Y. Yoshimura, T. Hasegawa, S. Komiyama, T. Ueda, and K. Hirakawa. Photon-counting microscopy of terahertz radiation[J]. Appl. Phys. Lett.,2006,88: 152110.
[21]H. Hashiba, V. Antonov, L. Kulik, A. Tzalenchuk, P. Kleinschmid, S. Giblin, and S. Komiyama. Isolated quantum dot in application to terahertz photon counting[J]. Phys. Rev. B,2006,73:081310(R).
[22]S. G. Carter, V. Birkedal, C. S. Wang, L. A. Coldren, A. V. Maslov, D. S. Citrin, and M. S. Sherwin. Quantum Coherence in an Optical Modulator[J]. Science,2005, 310:651-653.
[23]E. Rasanen, A. Castro, J. Werschnik, A. Rubio, and E. K. U. Gross. Optimal Control of Quantum Rings by Terahertz Laser Pulses[J]. Phys. Rev. Lett.,2007,98:157404.
[24]E. Rasanen, A. Castro, J. Werschnik, A. Rubio, and E. K. U. Gross. Optimal laser control of double quantum dots[J]. Phys. Rev. B,2008,77:085324.
[25]S. E. Harris, J. E. Field, and A. Imamoglu. Nonlinear optical processes using elec-tromagnetically induced transparency[J]. Phys. Rev. Lett.,1990,64:1107-1110.
[26]K.-J. Boller, A. Imamolu, and S. E. Harris. Observation of electromagnetically in-duced transparency[J]. Phys. Rev. Lett.,1991,66:2593-2596.
[27]G. Alzetta, A. Gozzini, L. Moi, and G. Orriols. An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour[J]. Nuovo Cimento B,1976,36:5-20.
[28]S. H. Autler and C. H. Townes. Stark effects in rapidly varying fields[J]. Phys. R.ev., 1955,100:703-722.
[29]B. R. Mollow. Stimulated emission and absorption near resonance for driven sys-tems[J]. Phys. Rev. A,1972,5:2217-2222.
[30]S. E. Harris. Lasers without inversion:Interference of lifetime-broadened reso-nances[J]. Phys. Rev. Lett.,1988,62:1033-1036.
[31]M. Fleischhauer, A. Imamoglu, and J. P. Marangos. Electromagnetically induced transparency:Optics in coherent media[J]. Rev. Mod. Phys.,2005,77:633-673.
[32]X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham. Coherent optical spectroscopy of a strongly driven quantum dot[J]. Science, 2007,317:929-932.
[33]G. Jundt, L. Robledo, A. Hogele, S. Falt, and A. Imamoglu. Observation of dressed excitonic states in a single quantum dot[J]. Phys. Rev. Lett.,2008,100:177401.
[34]A. Muller, W. Fang, J. Lawall, and G. S. Solomon. Emission spectrum of a dressed exciton-biexciton complex in a semiconductor quantum dot[J]. Phys. Rev. Lett., 2008,101:027401.
[35]M. Kroner, C. Lux, S. Seidl, A. W. Holleitner, K. Karrai, A. Badolato, P. M. Petroff, and R. J. Warburton. Rabi splitting and ac-Stark shift of a charged exciton[J]. Appl. Phys. Lett.,2008,92:031108.
[36]T. Brandes and F. Renzoni. Current switch by coherent trapping of electrons in quantum dots[J]. Phys. Rev. Lett.,2000,85:4148-4151.
[37]J. Danckwerts, K. J. Ahn, J. Forstner, and A. Knorr. Theory of ultrafast nonlin-ear optics of Coulomb-coupled semiconductor quantum dots:Rabi oscillations and pump-probe spectra[J]. Phys. Rev. B,2006,73:165318.
[38]J. Gea-Banacloche, Mambwe Mumba, and Min Xiao. Optical switching in arrays of quantum dots with dipole-dipole interactions[J]. Phys. Rev. B,2006,74:165330.
[39]T. H. Stoof and Yu. V. Nazarov. Time-dependent resonant tunneling via two discrete states[J]. Phys. Rev. B,1996,53:1050-1053.
[40]B. L. Hazelzet, M. R. Wegewijs, T. H. Stoof, and Yu. V. Nazarov. Coherent and incoherent pumping of electrons in double quantum dots[J]. Phys. Rev. B,2001,63: 165313.
[41]R. H. Blick, D. W. van der Weide, R. J. Haug, and K. Eberl. Complex broadband millimeter wave response of a double quantum dot:Rabi oscillations in an artificial molecule[J]. Phys. Rev. Lett.,1998,81:689-692.
[42]T. H. Oosterkamp, T. Fujisawa, W. G. van der Wiel, K. Ishibashi, R. V. Hijman, S. Tarucha, and L. P. Kouwenhoven. Microwave spectroscopy of a quantum-dot molecule[J]. Nature (London),1998,395:873-876.
[43]J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H. Willems van Beveren, S. De Franceschi, L. M. K. Vandersypen, S. Tarucha, and L. P. Kouwenhoven. Few-electron quantum dot circuit with integrated charge read out[J]. Phys. Rev. B,2003,67: 161308(R).
[44]Y.-S. Shin, T. Obata, Y. Tokura, M. Pioro-Ladriere, R. Brunner, T. Kubo, K. Yoshidal, and S. Tarucha. Single-spin readout in a double quantum dot including a micromagnet[J]. Phys. Rev. Lett.,2010,104:046802.
[45]P. B. Corkum. Plasma perspective on strong field multiphoton ionization[J]. Phys. Rev. Lett.,1993,71:1994-1997.
[46]M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L'Huillier, and P. B. Corkum. Theory of high-harmonic generation by low-frequency laser fields[J]. Phys. Rev. A, 1994,49:2117-2132.
[47]B. Sundaram and P. W. Milonni. High-order harmonic generation:Simplified model and relevance of single-atom theories to experiment[J]. Phys. Rev. A,1990,41: 6571-6573.
[48]A. E. Kaplan and P. L. Shkolnikov. Superdressed two-level atom:Very high har-monic generation and multiresonances[J]. Phys. Rev. A,1994,49:1275-1280.
[49]F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet. Phase of harmonics from strongly driven two-level atoms[J]. Phys. Rev. A,1997,55:615-621.
[50]F. I. Gauthey, B. M. Garraway, and P. L. Knight. High harmonic generation and periodic level crossings[J]. Phys. Rev. A,1997,56:3093-3096.
[51]P. P. Corso, L. Lo Cascio, and F. Persico. Simple vectorial model for the spectrum of a two-level atom in an intense low-frequency field[J]. Phys. Rev. A,1998,58: 1549-1558.
[52]R. Bavli and H. Metiu. Properties of an electron in a quantum double well driven by a strong laser:Localization, low-frequency, and even-harmonic generation[J]. Phys. Rev. A,1993,47:3299-3310.
[53]A. F. Terzis and E. Paspalakis. High-order harmonic generation in a two-electron quantum dot molecule[J]. J. Appl. Phys.,2005,97:023523.
[54]F. R. Waugh, M. J. Berry, D. J. Mar, and R. M. Westervelt. Single-electron charging in double and triple quantum dots with tunable coupling[J]. Phys. Rev. Lett.,1995, 75:705-708.
[55]M. L. Ladron de Guevara and P. A. Orellana. Electronic transport through a parallel-coupled triple quantum dot molecule:Fano resonances and bound states in the continuum[J]. Phys. Rev. B,2006,73:205303.
[56]W. Xie, W. Chu, W. Zhang and S. Duan. Photon-assistant Fano resonance in serially coupled triple quantum dots[J]. J. Phys.:Condens. Matter,2008,20:325223.
[57]S. Duan, W. Zhang, W. Xie, Y. Ma and W. Chu. Time-dependent transport of symmetric A-type coupled triple quantum dots:competition between coherent de-struction of tunneling and Fano resonance[J]. N. J. Phys.,2009,11,013037.
[58]R. Zitko and J. Bonca. Fermi-liquid versus non-Fermi-liquid behavior in triple quan-tum dots[J]. Phys. Rev. Lett.,2007,98:047203.
[59]T. Kuzmenko, K. Kikoin, and Y. Avishai. Kondo effect in systems with dynamical symmetries[J]. Phys. Rev. B,2004,69:195109.
[60]D. S. Saraga and D. Loss. Spin-entangled currents created by a triple quantum dot[J]. Phys. Rev. Lett.,2003,90:166803.
[61]J. Kim, D. V. Melnikov, J. P. Leburton, D. G. Austing, and S. Tarucha. Spin charging sequences in three colinear laterally coupled vertical quantum dots[J]. Phys. Rev. B,2006,74:035307.
[62]F. Delgado, Y.-P. Shim, M. Korkusinski, and P. Hawrylak. Theory of spin, electronic, and transport properties of the lateral triple quantum dot molecule in a magnetic field[J]. Phys. Rev. B,2007,76:115332.
[63]N. S. Wingreen, K. W. Jacobsen, and J. W. Wilkins. Inelastic scattering in resonant tunneling[J]. Phys. Rev. B,1989,40:11834-11850.
[64]T. Kwapiriski, R.. Taranko, and E. Taranko. Photon-assisted electron transport through a three-terminal quantum dot system with nonresonant tunneling chan-nels[J]. Phys. Rev. B,2005,72:125312.
[65]T. Fujisawa, T. H. Oosterkamp, W. G. van der Wiel, B.W. Broer, R. Aguado, S. Tarucha, and L. P. Kouwenhoven. Spontaneous emission spectrum in double quantum dot devices[J]. Science,1998,282:932-935.
[66]T. Brandes and B. Kramer. Spontaneous emission of phonons by coupled quantum dots[J]. Phys. Rev. Lett.,1999,83:3021-3024.
[67]L. M. Narducci, M. O. Scully, G.-L. Oppo, P. Ru and J. R. Tredicce. Spontaneous emission and absorption properties of a driven three-level system[J]. Phys. Rev. A, 1990,42:1630-1649.
[68]C. Cohen-Tannoudji and S. Reynaud. Dressed-atom description of resonance fluo-rescence and absorption spectra of a multi-level atom in an intense laser beam[J]. J. Phys. B:Atom. Molec. Phys.,1977,3:345-363.
[69]C. Cohen-Tannoudji and S. Reynaud. Modification of resonance Raman scattering in very intense laser fields[J]. J. Phys. B:Atom. Molec. Phys.,1977,3:365-383.
[70]T. Ihn, A. Fuhrer, L. Meier, M. Sigrist, and K. Ensslin. Quantum physics in quantum rings[J]. Europhys. News,2005,36:78-81.
[71]J.-L. Zhu, W. Chu, Z. Dai, and D. Xu. Exciton states and their entanglement in coupled quantum dots[J]. Phys. Rev. B,2005,72:165346.
[72]M. Tonouchi. Cutting-edge terahertz technology[J]. Nat. Photonics,2007,1:97-105.
[73]X.-G. Zhao. A formal solution for the evolution operator and its application in two-level systems[J]. Phys. Lett. A,1994,193:5-10.
[74]J. H. Shirley. Solution of the Schrodinger equation with a Hamiltonian periodic in time[J]. Phys. Rev.,1965,138:B979-B987.
[75]F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Magquet. Role of intital coher-ence in the generatoin of harmonics and sidebands from a strongly driven two-level atom[J]. Phys. Rev. A,1995,52:525-540.
[76]X.-G. Zhao, R. Jahnke, and Q. Niu. Dynamic fractional stark ladders in dc-ac fields[J]. Phys. Lett. A,1995,202:297-304.
[77]D. R. Hofstadter. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields[J]. Phys. Rev. B,1976,14:2239-2249.
[78]M. Holthaus. Collapse of minibands in far-infrared irradiated superlattices[J]. Phys. Rev. Lett.,1992,69:351-354.
[79]F. Grossmann, T. Dittrich, P. Jung, and P. Hanggi. Coherent destruction of tunnel-ing[J]. Phys. Rev. Lett.,1991,67:516-519.
[80]T. Zuo, S. Chelkowski, and A. D. Bandrauk. Harmonic generation by the H2+ molec-ular ion in intense laser fields[J]. Phys. Rev. A.1993,48:3837-3844.
[81]Y. Chen, J. Chen, and J. Liu. Charge-resonance effect on harmonic generation by symmetric diatomic molecular ions in intense laser fields[J]. Phys. Rev. A,2006,74: 063405.
[82]J.-P. Connerade and C. H. Keitel. High harmonic generation in a static magnetic field[J]. Phys. Rev. A,1996,53:2748-2751.
[83]V. Averbukh, O. E. Alon, and N. Moiseyev. Stability and instability of dipole selec-tion rules for atomic high-order-harmonic-generation spectra in two-beam setups[J]. Phys. Rev. A,2002,65:063402.
[84]A. D. Bandrauk and H. Z. Lu. Controlling harmonic generation in molecules with intense laser and static magnetic fields:Orientation effects[J]. Phys. Rev. A,2003, 68:043408.
[85]G. L. Kamta and A. D. Bandrauk. Three-dimensional time-profile analysis of high-order harmonic generation in molecules:Nuclear interferences in H2+[J]. Phys. Rev. A,2005,71:053407.
[86]A. D. Bandrauk and H. Z. Lu. Molecules in intense laser fields:Beyond the dipole approximation[J]. Phys. Rev. A,2006,73:013412.
[87]T. Kreibich, M. Lein, V. Engel, and E. K. U. Gross. Even-Harmonic generation due to beyond-Born-Oppenheimer dynamics[J]. Phys. Rev. Lett.,2001,87:103901.
[88]T. Iwasa and K. Nobusada. Nonuniform light-matter interaction theory for near-field-induced electron dynamics[J]. Phys. Rev. A,2009,80:043409.
[89]X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, and M. M. Murnane. Ellip-tically polarized high-order harmonic emission from molecules in linearly polarized laser fields[J]. Phys. Rev. Lett.,2009,102:073902.