Abstract

We study ultrafast excitonic population inversion resulting from the interaction of a semiconductor quantum dot (SQD) with localized surface plasmons. The plasmonic enhanced fields are generated when a metallic nanoparticle (MNP) is subject to a nonlinear chirped few-cycle pulse train. By numerically solving the time-dependent Bloch equations beyond the rotating-wave approximation, we show that the complete population inversion can be achieved for small interparticle distance and the dynamic in population inversion exhibits a steplike transition between absorption and amplifying. This phenomenon can be exploited as an all-optical ultrafast switching device. Moreover, the final state of population inversion is shown to be modified significantly with the interparticle distances, which is not only robust against the variation of probe pulse parameters but also suggests a straightforward method for measuring the interparticle distances via probing the final populations.

© 2015 Optical Society of America

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References

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    [Crossref]
  4. R.D. Artuso and G.W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8, 2106–2111 (2008).
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  21. M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, J. Cox, and M. R. Singh, “Plasmonic effects in excitonic population transfer in a driven semiconductor-metal nanoparticle hybrid system,” Phys. Rev. B 86, 155305 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  26. M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, and M.R. Singh, “Optical pumping of a single hole spin in a p-doped quantum dot coupled to a metallic nanoparticle,” Phys. Rev. B 87, 195303 (2013).
    [Crossref]
  27. P. Vasa, W. Wang, R. Pomraenke, M. Lammers, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates,” Nat. Photonics 7, 128–132 (2013).
    [Crossref]
  28. S.L. Sewall, A. Franceschetti, R.R. Cooney, A. Zunger, and P. Kambhampati, “Direct observation of the structure of band-edge biexcitons in colloidal semiconductor CdSe quantum dots,” Phys. Rev. B 80, 081310 (2009).
    [Crossref]
  29. S.M. Sadeghi and R.G. West, “Coherent control of Forster energy transfer in nanoparticle molecules: energy nanogates and plasmonic heat pulses,” J. Phys.: Condens. Matter 23, 425302 (2011).
  30. D.E. Chang, A.S. Sorensen, P.R. Hemmer, and M.D. Lukin, “Quantum Optics with Surface Plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
    [Crossref] [PubMed]
  31. A. Franceschetti, H. Fu, L.W. Wang, and A. Zunger, “Many-body pseudopotential theory of excitons in InP and CdSe quantum dots,” Phys. Rev. B 60, 1819–1829 (1999).
    [Crossref]
  32. P.B. Johnson and R.W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  33. S.T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
    [Crossref]
  34. M.O. Scully and M.S. Zubariry, “Quantum optics,” (Cambridge University Press, 1997).
    [Crossref]
  35. M.E. Crenshaw and C.M. Bowden, “Quasiadiabatic following approximation for a dense medium of two-level atoms,” Phys. Rev. Lett. 69, 3475–3478 (1992).
    [Crossref] [PubMed]
  36. L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).
  37. A. Tcherniak, J.W. Ha, S. Dominguez-Medina, L.S. Slaughter, and S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
    [Crossref] [PubMed]
  38. L.J.E. Anderson, K.M. Mayer, R.D. Fraleigh, Y. Yang, S. Lee, and J.H. Hafner, “Quantitative measurements of individual gold nanoparticle scattering cross sections,” J. Phys. Chem. C 114, 11127–11132 (2010).
    [Crossref]
  39. L.S. Slaughter, W.-S. Chang, P. Swanglap, A. Tcherniak, B.P. Khanal, E.R. Zubarev, and S. Link, “Single-particle spectroscopy of gold nanorods beyond the quasi-static limit: varying the width at constant aspect ratio,” J. Phys. Chem. C 114, 4934–4938 (2010).
    [Crossref]

2013 (5)

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, and M.R. Singh, “Optical pumping of a single hole spin in a p-doped quantum dot coupled to a metallic nanoparticle,” Phys. Rev. B 87, 195303 (2013).
[Crossref]

P. Vasa, W. Wang, R. Pomraenke, M. Lammers, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates,” Nat. Photonics 7, 128–132 (2013).
[Crossref]

S.G. Kosionis, A.F. Terzis, S.M. Sadeghi, and E. Paspalakis, “Optical response of a quantum dot-metal nanoparticle hybrid interacting with a weak probe field,” J. Phys.: Condens. Matter 25, 045304 (2013).

E. Paspalakis, S. Evangelou, and A.F. Terzis, “Control of excitonic population inversion in a coupled semiconductor quantum dot-metal nanoparticle system,” Phys. Rev. B 87, 235302 (2013).
[Crossref]

A. Hatef, S.M. Sadeghi, S. Fortin-Deschnes, E. Boulais, and M. Meunier, “Coherently-enabled environmental control of optics and energy transfer pathways of hybrid quantum dot-metallic nanoparticle systems,” Opt. Express 21, 5643–5653 (2013).
[Crossref] [PubMed]

2012 (3)

J.B. Li, N.C. Kim, M.T. Cheng, L. Zhou, Z.H. Hao, and Q.Q. Wang, “Optical bistability and nonlinearity of coherently coupled exciton-plasmon systems,” Opt. Express 20, 1856–1861 (2012).
[Crossref] [PubMed]

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, J. Cox, and M. R. Singh, “Plasmonic effects in excitonic population transfer in a driven semiconductor-metal nanoparticle hybrid system,” Phys. Rev. B 86, 155305 (2012).
[Crossref]

S.M. Sadeghi, “Quantum coherence effects in hybrid nanoparticle molecules in the presence of ultra-short dephasing times,” Appl. Phys. Lett. 101, 213102 (2012).
[Crossref]

2011 (7)

R.D. Artuso, G.W. Bryant, A. Garcia-Etxarri, and J. Aizpurua, “Using local fields to tailor hybrid quantumdot/metal nanoparticle systems,” Phys. Rev. B 83, 235406 (2011).
[Crossref]

A.V. Malyshev and V.A. Malyshev, “Optical bistability and hysteresis of a hybrid metal-semiconductor nanodimer,” Phys. Rev. B 84, 035314 (2011).
[Crossref]

A. Hatef, D.G. Schindel, and M.R. Singh, “Dipole-dipole interaction in a quantum dot and metallic nanorod hybrid system,” Appl. Phys. Lett. 99, 181106 (2011).
[Crossref]

M.L. Andersen, S. Stobbe, A.S. Sorensen, and P. Lodahl, “Strongly modified plasmonCmatter interaction with mesoscopic quantum emitters,” Nat. Phys. 7, 215–218 (2011).
[Crossref]

N.T. Fofang, N.K. Grady, Z.Y. Fan, A.O. Govorov, and N.J. Halas, “Plexciton Dynamics: Exciton-Plasmon Coupling in a J-Aggregate?Au Nanoshell Complex Provides a Mechanism for Nonlinearity,” Nano. Lett. 11, 1556–1560 (2011).
[Crossref] [PubMed]

M.T. Cheng, X.S. Ma, Y.Q. Luo, P.Z. Wang, and G.X. Zhao, “Entanglement generation and quantum state transfer between two quantum dot molecules mediated by quantum bus of plasmonic circuits,” Appl. Phys. Lett. 99, 223509 (2011).
[Crossref]

S.M. Sadeghi and R.G. West, “Coherent control of Forster energy transfer in nanoparticle molecules: energy nanogates and plasmonic heat pulses,” J. Phys.: Condens. Matter 23, 425302 (2011).

2010 (9)

S.M. Sadeghi, “Coherent control of metallic nanoparticles near fields: Nanopulse controllers and functional nanoamplifiers,” Phys. Rev. B 82, 035413 (2010).
[Crossref]

A. Ridolfo, O.Di Stefano, N. Fina, R. Saija, and S. Savasta, “Quantum plasmonics with quantum dot-metal nanoparticle molecules: influence of the Fano effect on photon statistics,” Phys. Rev. Lett. 105, 263601 (2010).
[Crossref]

E. Waks and D. Sridharan, “Cavity QED treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A 82, 043845 (2010).
[Crossref]

A.O. Govorov, “Semiconductor-metal nanoparticle molecules in a magnetic field: Spin-plasmon and excitonplasmon interactions,” Phys. Rev. B 82, 155322 (2010).
[Crossref]

R.D. Artuso and G.W. Bryant, “Strongly coupled quantum dot-metal nanoparticle systems: Exciton-induced transparency, discontinuous response, and suppression as driven quantum oscillator effects,” Phys. Rev. B 82, 195419 (2010).
[Crossref]

J.T. Zhang, Y. Tang, K. Lee, and M. Ouyang, “Tailoring light-matter-spin interactions in colloidal heteronanostructures,” Nature (London) 466, 91–95 (2010).
[Crossref]

A. Tcherniak, J.W. Ha, S. Dominguez-Medina, L.S. Slaughter, and S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[Crossref] [PubMed]

L.J.E. Anderson, K.M. Mayer, R.D. Fraleigh, Y. Yang, S. Lee, and J.H. Hafner, “Quantitative measurements of individual gold nanoparticle scattering cross sections,” J. Phys. Chem. C 114, 11127–11132 (2010).
[Crossref]

L.S. Slaughter, W.-S. Chang, P. Swanglap, A. Tcherniak, B.P. Khanal, E.R. Zubarev, and S. Link, “Single-particle spectroscopy of gold nanorods beyond the quasi-static limit: varying the width at constant aspect ratio,” J. Phys. Chem. C 114, 4934–4938 (2010).
[Crossref]

2009 (3)

S.L. Sewall, A. Franceschetti, R.R. Cooney, A. Zunger, and P. Kambhampati, “Direct observation of the structure of band-edge biexcitons in colloidal semiconductor CdSe quantum dots,” Phys. Rev. B 80, 081310 (2009).
[Crossref]

S.M. Sadeghi, “Plasmonic metaresonances: molecular resonances in quantum dot-metallic nanoparticle conjugates,” Phys. Rev. B 79, 233309 (2009).
[Crossref]

Z. Lu and K.D. Zhu, “Slow light in an artificial hybrid nanocrystal complex,” J. Phys. B 42, 015502 (2009).
[Crossref]

2008 (3)

J.Y. Yan, W. Zhang, S.Q. Duan, X.G. Zhao, and A.O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77, 165301 (2008).
[Crossref]

R.D. Artuso and G.W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8, 2106–2111 (2008).
[Crossref] [PubMed]

P. Vasa, R. Pomraenke, S. Schwieger, Yu. I. Mazur, Vas. Kunets, P. Srinivasan, E. Johnson, J.E. Kihm, D.S. Kim, E. Runge, G. Salamo, and C. Lienau, “Coherent exciton-surface-plasmon-polariton interaction in hybrid metal-semiconductor nanostructures, Phys. Rev. Lett. 101, 116801 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (2)

W. Zhang, A.O. Govorov, and G.W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect,” Phys. Rev. Lett. 97, 146804 (2006).
[Crossref] [PubMed]

D.E. Chang, A.S. Sorensen, P.R. Hemmer, and M.D. Lukin, “Quantum Optics with Surface Plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

2003 (1)

S.T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[Crossref]

1999 (1)

A. Franceschetti, H. Fu, L.W. Wang, and A. Zunger, “Many-body pseudopotential theory of excitons in InP and CdSe quantum dots,” Phys. Rev. B 60, 1819–1829 (1999).
[Crossref]

1992 (1)

M.E. Crenshaw and C.M. Bowden, “Quasiadiabatic following approximation for a dense medium of two-level atoms,” Phys. Rev. Lett. 69, 3475–3478 (1992).
[Crossref] [PubMed]

1972 (1)

P.B. Johnson and R.W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Aizpurua, J.

R.D. Artuso, G.W. Bryant, A. Garcia-Etxarri, and J. Aizpurua, “Using local fields to tailor hybrid quantumdot/metal nanoparticle systems,” Phys. Rev. B 83, 235406 (2011).
[Crossref]

Allen, L.

L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Andersen, M.L.

M.L. Andersen, S. Stobbe, A.S. Sorensen, and P. Lodahl, “Strongly modified plasmonCmatter interaction with mesoscopic quantum emitters,” Nat. Phys. 7, 215–218 (2011).
[Crossref]

Anderson, L.J.E.

L.J.E. Anderson, K.M. Mayer, R.D. Fraleigh, Y. Yang, S. Lee, and J.H. Hafner, “Quantitative measurements of individual gold nanoparticle scattering cross sections,” J. Phys. Chem. C 114, 11127–11132 (2010).
[Crossref]

Antón, M.A.

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, and M.R. Singh, “Optical pumping of a single hole spin in a p-doped quantum dot coupled to a metallic nanoparticle,” Phys. Rev. B 87, 195303 (2013).
[Crossref]

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, J. Cox, and M. R. Singh, “Plasmonic effects in excitonic population transfer in a driven semiconductor-metal nanoparticle hybrid system,” Phys. Rev. B 86, 155305 (2012).
[Crossref]

Artuso, R.D.

R.D. Artuso, G.W. Bryant, A. Garcia-Etxarri, and J. Aizpurua, “Using local fields to tailor hybrid quantumdot/metal nanoparticle systems,” Phys. Rev. B 83, 235406 (2011).
[Crossref]

R.D. Artuso and G.W. Bryant, “Strongly coupled quantum dot-metal nanoparticle systems: Exciton-induced transparency, discontinuous response, and suppression as driven quantum oscillator effects,” Phys. Rev. B 82, 195419 (2010).
[Crossref]

R.D. Artuso and G.W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8, 2106–2111 (2008).
[Crossref] [PubMed]

Boulais, E.

Bowden, C.M.

M.E. Crenshaw and C.M. Bowden, “Quasiadiabatic following approximation for a dense medium of two-level atoms,” Phys. Rev. Lett. 69, 3475–3478 (1992).
[Crossref] [PubMed]

Bryant, G.W.

R.D. Artuso, G.W. Bryant, A. Garcia-Etxarri, and J. Aizpurua, “Using local fields to tailor hybrid quantumdot/metal nanoparticle systems,” Phys. Rev. B 83, 235406 (2011).
[Crossref]

R.D. Artuso and G.W. Bryant, “Strongly coupled quantum dot-metal nanoparticle systems: Exciton-induced transparency, discontinuous response, and suppression as driven quantum oscillator effects,” Phys. Rev. B 82, 195419 (2010).
[Crossref]

R.D. Artuso and G.W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. 8, 2106–2111 (2008).
[Crossref] [PubMed]

W. Zhang, A.O. Govorov, and G.W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect,” Phys. Rev. Lett. 97, 146804 (2006).
[Crossref] [PubMed]

Cabrera-Granado, E.

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, and M.R. Singh, “Optical pumping of a single hole spin in a p-doped quantum dot coupled to a metallic nanoparticle,” Phys. Rev. B 87, 195303 (2013).
[Crossref]

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, J. Cox, and M. R. Singh, “Plasmonic effects in excitonic population transfer in a driven semiconductor-metal nanoparticle hybrid system,” Phys. Rev. B 86, 155305 (2012).
[Crossref]

Calderón, O.G.

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, and M.R. Singh, “Optical pumping of a single hole spin in a p-doped quantum dot coupled to a metallic nanoparticle,” Phys. Rev. B 87, 195303 (2013).
[Crossref]

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, J. Cox, and M. R. Singh, “Plasmonic effects in excitonic population transfer in a driven semiconductor-metal nanoparticle hybrid system,” Phys. Rev. B 86, 155305 (2012).
[Crossref]

Carreño, F.

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, and M.R. Singh, “Optical pumping of a single hole spin in a p-doped quantum dot coupled to a metallic nanoparticle,” Phys. Rev. B 87, 195303 (2013).
[Crossref]

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, J. Cox, and M. R. Singh, “Plasmonic effects in excitonic population transfer in a driven semiconductor-metal nanoparticle hybrid system,” Phys. Rev. B 86, 155305 (2012).
[Crossref]

Cerullo, G.

P. Vasa, W. Wang, R. Pomraenke, M. Lammers, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates,” Nat. Photonics 7, 128–132 (2013).
[Crossref]

Chang, D.E.

D.E. Chang, A.S. Sorensen, P.R. Hemmer, and M.D. Lukin, “Quantum Optics with Surface Plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Chang, W.-S.

L.S. Slaughter, W.-S. Chang, P. Swanglap, A. Tcherniak, B.P. Khanal, E.R. Zubarev, and S. Link, “Single-particle spectroscopy of gold nanorods beyond the quasi-static limit: varying the width at constant aspect ratio,” J. Phys. Chem. C 114, 4934–4938 (2010).
[Crossref]

Cheng, M.T.

Christy, R.W.

P.B. Johnson and R.W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Cooney, R.R.

S.L. Sewall, A. Franceschetti, R.R. Cooney, A. Zunger, and P. Kambhampati, “Direct observation of the structure of band-edge biexcitons in colloidal semiconductor CdSe quantum dots,” Phys. Rev. B 80, 081310 (2009).
[Crossref]

Cox, J.

M.A. Antón, F. Carreño, S. Melle, O.G. Calderón, E. Cabrera-Granado, J. Cox, and M. R. Singh, “Plasmonic effects in excitonic population transfer in a driven semiconductor-metal nanoparticle hybrid system,” Phys. Rev. B 86, 155305 (2012).
[Crossref]

Crenshaw, M.E.

M.E. Crenshaw and C.M. Bowden, “Quasiadiabatic following approximation for a dense medium of two-level atoms,” Phys. Rev. Lett. 69, 3475–3478 (1992).
[Crossref] [PubMed]

Cundiff, S.T.

S.T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[Crossref]

Dominguez-Medina, S.

A. Tcherniak, J.W. Ha, S. Dominguez-Medina, L.S. Slaughter, and S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[Crossref] [PubMed]

Duan, S.Q.

J.Y. Yan, W. Zhang, S.Q. Duan, X.G. Zhao, and A.O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77, 165301 (2008).
[Crossref]

Eberly, J.H.

L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Evangelou, S.

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J.Y. Yan, W. Zhang, S.Q. Duan, X.G. Zhao, and A.O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77, 165301 (2008).
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M.T. Cheng, X.S. Ma, Y.Q. Luo, P.Z. Wang, and G.X. Zhao, “Entanglement generation and quantum state transfer between two quantum dot molecules mediated by quantum bus of plasmonic circuits,” Appl. Phys. Lett. 99, 223509 (2011).
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J. Phys.: Condens. Matter (2)

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Nat. Photonics (1)

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Nature (London) (1)

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Opt. Express (2)

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Figures (4)

Fig. 1
Fig. 1 Schematic diagram of our hybrid system composed of a semiconductor quantum dot (SQD) and a metallic nanoparticle (MNP). The centers of the two particles are separated by a distance represented by R.
Fig. 2
Fig. 2 The upper plots are the plasmonic fields inside the SQD for different interparticle distances, i.e., R = 15 nm (red solid curve), R = 30 nm (blue dashed curve), and R = 80 nm (black dotted curve), with (a) the incident Gaussian pulse train (f(t) = exp((tnt0)22)) and (b) the incident hyperbolic secant pulse train (sech((tnt0))). The lower plots are the the corresponding excitonic population inversion S3(t) from the numerical merical solution of Eqs. (5)(7) for R=15 nm (red solid curve), R = 30 nm (blue dashed curve), and R = 80 nm (black dotted curve), with (c) incident Gaussian pulse train and (d) incident hyperbolic secant pulse train. Other parameters of the pulse train are chosen as N = 6, |Ω0| = 12 me V, τ = 25 fs, t0 = 200 fs, and α = 5.
Fig. 3
Fig. 3 The final excitonic population inversion S3 at t = 6t0 obtained from numerical solution of Eqs. (5)(7) as a function of (a) input electric field amplitude |Ω0| with α = 5, with a Gaussian pulse train N = 6, for R = 15 nm (red solid curve), R = 30 nm (blue dashed curve), and R = 80 nm (black dotted curve), and (b) chirp rate α for the input electric field amplitude of the pulse train |Ω0| = 12 meV. Other parameters of the pulse train are chosen as τ = 25 fs and t0 = 200 fs.
Fig. 4
Fig. 4 Contour map of the final population S3(t) obtained from numerical solution of Eqs. (5)(7) as a function of the input electric field amplitudes |Ω0| and chirp rate α of the chirped Gaussian few-cycle pulse train for different interparticle distance R with fixed pulse duration τ = 25 fs: (a) R = 15 nm; (b) R = 80 nm; with fixed pulse duration τ = 10 fs: (c) R = 15 nm; (d) R = 80 nm. Other parameters are the same as Fig. 3.

Equations (7)

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H = h ¯ ω 10 | 1 1 | μ E S Q D ( | 0 1 | + | 1 0 | ) ,
E S Q D ( t ) = h ¯ μ [ ( Ω ( t ) 2 + G ρ 10 ( t ) ) + ( Ω * ( t ) 2 + G * ρ 01 ( t ) ) ] ,
Ω ( t ) = ( Ω 0 + Ω ) n = 0 N 1 f ( t ) e i [ ω ( t n t 0 ) + ϕ ( t ) ]
G = j = 1 l 1 4 π ε e ( j + 1 ) 2 γ j a 2 j + 1 μ 2 h ¯ ε e f f s R 2 j + 4 ,
S ˙ 1 ( t ) = ω 10 S 2 ( t ) S 1 ( t ) T 2 ,
S ˙ 2 ( t ) = ω 10 S 1 ( t ) 2 [ Ω R ( t ) + G R S 1 ( t ) + G I S 2 ( t ) ] S 3 ( t ) S 2 ( t ) T 2 ,
S ˙ 3 ( t ) = 2 [ Ω R ( t ) + G R S 1 ( t ) + G I S 2 ( t ) ] S 2 ( t ) S 3 ( t ) + 1 T 1 ,

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