Abstract

In this paper, we analyze the performance of an electro-optic modulator based on a single quantum dot strongly coupled to a nano-resonator, where electrical control of the quantum dot frequency is achieved via quantum confined Stark effect. Using realistic system parameters, we show that modulation speeds of a few tens of GHz are achievable with this system, while the energy per switching operation can be as small as 0.5 fJ. In addition, we study the non-linear distortion, and the effect of pure quantum dot dephasing on the performance of the modulator.

©2010 Optical Society of America

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  1. Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 gbit/s carrierinjection-based silicon micro-ring silicon modulators,” Opt. Express 15, 430–436 (2007).
    [Crossref] [PubMed]
  2. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
    [Crossref] [PubMed]
  3. Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic deflection switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
    [Crossref]
  4. J. L. O’Brien, “Optical quantum computing,” Science 318, 1567–1570 (2007).
    [Crossref] [PubMed]
  5. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
    [Crossref] [PubMed]
  6. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15, 5550–5558 (2007).
    [Crossref] [PubMed]
  7. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
    [Crossref] [PubMed]
  8. D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
    [Crossref]
  9. C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
    [Crossref]
  10. N. Hitoshi, Y. Sugimoto, K. Kanamoto, N. Ikeda, Y. Tanaka, Y. Nakamura, S. Ohkouchi, Y. Watanabe, K. Inoue, H. Ishikawa, and K. Asakawa, “Ultra-fast photonic crystal/quantum dot alloptical switch for future photonic networks,” Opt. Express 12, 6606–6614 (2004).
    [Crossref] [PubMed]
  11. A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
    [Crossref] [PubMed]
  12. D. Englund, A. Faraon, A. Majumdar, N. Stoltz, P. Petroff, and J. Vuckovic, “An optical modulator based on a single strongly coupled quantum dot - cavity system in a p-i-n junction,” Opt. Express 17, 18651–18658 (2009).
    [Crossref]
  13. D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
    [Crossref]
  14. D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
    [Crossref] [PubMed]
  15. C. W. Gardiner and P. Zoller, Quantum Noise, (Springer-Verlag, 2005).
  16. E. Waks and J. Vuckovic, “Dipole induced transparency in drop filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
    [Crossref] [PubMed]
  17. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
    [Crossref] [PubMed]
  18. J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
    [Crossref]
  19. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-um radius,” Opt. Express 16, 4309–4315 (2008).
    [Crossref] [PubMed]

2010 (1)

A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
[Crossref] [PubMed]

2009 (4)

D. Englund, A. Faraon, A. Majumdar, N. Stoltz, P. Petroff, and J. Vuckovic, “An optical modulator based on a single strongly coupled quantum dot - cavity system in a p-i-n junction,” Opt. Express 17, 18651–18658 (2009).
[Crossref]

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

2008 (6)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic deflection switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-um radius,” Opt. Express 16, 4309–4315 (2008).
[Crossref] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
[Crossref] [PubMed]

2007 (4)

2006 (1)

E. Waks and J. Vuckovic, “Dipole induced transparency in drop filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

2004 (2)

N. Hitoshi, Y. Sugimoto, K. Kanamoto, N. Ikeda, Y. Tanaka, Y. Nakamura, S. Ohkouchi, Y. Watanabe, K. Inoue, H. Ishikawa, and K. Asakawa, “Ultra-fast photonic crystal/quantum dot alloptical switch for future photonic networks,” Opt. Express 12, 6606–6614 (2004).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Asakawa, K.

Beals, M.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Beausoleil, R. G.

Bernardis, S.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Cheng, J.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Combrie, S.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

Englund, D.

Faraon, A.

A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
[Crossref] [PubMed]

D. Englund, A. Faraon, A. Majumdar, N. Stoltz, P. Petroff, and J. Vuckovic, “An optical modulator based on a single strongly coupled quantum dot - cavity system in a p-i-n junction,” Opt. Express 17, 18651–18658 (2009).
[Crossref]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
[Crossref] [PubMed]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref] [PubMed]

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15, 5550–5558 (2007).
[Crossref] [PubMed]

Fattal, D.

Fox, A. M.

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

Fushman, I.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
[Crossref] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref] [PubMed]

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise, (Springer-Verlag, 2005).

Green, W. M. J.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic deflection switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

Hitoshi, N.

Husko, C.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

Ikeda, N.

Inoue, K.

Ishikawa, H.

Jones, B. D.

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Kanamoto, K.

Kim, H.

A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
[Crossref] [PubMed]

Kimerling, L. C.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Krauss, T. F.

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

Liao, L.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Lipson, M.

Liu, A.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Liu, J.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Majumdar, A.

A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
[Crossref] [PubMed]

D. Englund, A. Faraon, A. Majumdar, N. Stoltz, P. Petroff, and J. Vuckovic, “An optical modulator based on a single strongly coupled quantum dot - cavity system in a p-i-n junction,” Opt. Express 17, 18651–18658 (2009).
[Crossref]

Manipatruni, S.

Michel, J.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Miller, D. A. B.

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

Nakamura, Y.

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

O’Brien, D.

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

J. L. O’Brien, “Optical quantum computing,” Science 318, 1567–1570 (2007).
[Crossref] [PubMed]

Ohkouchi, S.

Paniccia, M.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Petroff, P.

A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
[Crossref] [PubMed]

D. Englund, A. Faraon, A. Majumdar, N. Stoltz, P. Petroff, and J. Vuckovic, “An optical modulator based on a single strongly coupled quantum dot - cavity system in a p-i-n junction,” Opt. Express 17, 18651–18658 (2009).
[Crossref]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
[Crossref] [PubMed]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref] [PubMed]

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

Pomerene, A.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Raineri, F.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

Roberts, J. S.

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

Rossi, A. D.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

Rubin, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Samara-Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Schmidt, B.

Shakya, J.

Skolnick, M. S.

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

Stoltz, N.

D. Englund, A. Faraon, A. Majumdar, N. Stoltz, P. Petroff, and J. Vuckovic, “An optical modulator based on a single strongly coupled quantum dot - cavity system in a p-i-n junction,” Opt. Express 17, 18651–18658 (2009).
[Crossref]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
[Crossref] [PubMed]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref] [PubMed]

Sugimoto, Y.

Sun, R.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Szymanski, D. M.

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

Tanaka, Y.

Tran, Q. V.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

Vlasov, Y.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic deflection switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

Vuckovic, J.

A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
[Crossref] [PubMed]

D. Englund, A. Faraon, A. Majumdar, N. Stoltz, P. Petroff, and J. Vuckovic, “An optical modulator based on a single strongly coupled quantum dot - cavity system in a p-i-n junction,” Opt. Express 17, 18651–18658 (2009).
[Crossref]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
[Crossref] [PubMed]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref] [PubMed]

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vuckovic, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15, 5550–5558 (2007).
[Crossref] [PubMed]

E. Waks and J. Vuckovic, “Dipole induced transparency in drop filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

Waks, E.

E. Waks and J. Vuckovic, “Dipole induced transparency in drop filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

Watanabe, Y.

Wong, C. W.

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

Xia, F.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic deflection switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

Xu, Q.

Yamamoto, Y.

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

Zhang, B.

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise, (Springer-Verlag, 2005).

Appl. Phys. Lett. (2)

D. M. Szymanski, B. D. Jones, M. S. Skolnick, A. M. Fox, D. O’Brien, T. F. Krauss, and J. S. Roberts, “Ultrafast all-optical switching in algaas photonic crystal waveguide interferometers,” Appl. Phys. Lett. 95(14), 141108–141110 (2009).
[Crossref]

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94(2), 021111 (2009).
[Crossref]

Nat. Photonics (2)

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic deflection switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy gesi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Nature (2)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref] [PubMed]

Opt. Express (6)

Phys. Rev. Lett. (2)

E. Waks and J. Vuckovic, “Dipole induced transparency in drop filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

A. Faraon, A. Majumdar, H. Kim, P. Petroff, and J. Vuckovic, “Fast electrical control of a quantum dot strongly coupled to a nano-resonator,” Phys. Rev. Lett. 104, 047402 (2010).
[Crossref] [PubMed]

Proc. IEEE (1)

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

Science (3)

J. L. O’Brien, “Optical quantum computing,” Science 318, 1567–1570 (2007).
[Crossref] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

Other (1)

C. W. Gardiner and P. Zoller, Quantum Noise, (Springer-Verlag, 2005).

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Figures (8)

Fig. 1.
Fig. 1. (a) Transmission spectra of coupled cavity-QD system for two different detunings. The blue arrow shows the wavelength of the laser whose transmission is being modified. (b) Normalized steady state transmission with different QD detunings. The laser is resonant with the cavity. We used the following parameters:g/2π = κ/2π = 20 GHz; γ = κ/80; the pure dephasing rate is assumed to be zero for this analysis (γd /2π = 0).

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Fig. 2.
Fig. 2. The frequency response of the switch for different (a) κ. (g/2π) is kept constant at 20 GHz and (b) g. (κ/2π) is kept constant at 20 GHz. For both simulations Ω = 1 GHz; Δω 0/2π = 10 GHz; γd /2π = γ/2π = 0.1 GHz.

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Fig. 3.
Fig. 3. (a) Cut-off frequency of the modulator as a function of g and κ. In the color scheme, the maximum cutoff frequency of ~ 90 GHz is red and the minimum cut-off frequency of ~ 10 GHz is blue; (b) On-off ratio of the modulator at a modulating frequency of ωe /2π = 5 GHz as a function of g and κ. For both plots Δω 0/2π = 5 GHz; γd /2π = 0.1 GHz; Ω = 1 GHz.

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Fig. 4.
Fig. 4. Normalized output signal for two different maximal QD detunings Δω 0. (a) Δω 0/2π = 2 GHz. (b) Δω 0/2π = 40 GHz. For both simulations the frequency of the electrical signal is Δωe /2π = 20 GHz, κ/2π = g/2π = 20 GHz and Ω = 1 GHz.

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Fig. 5.
Fig. 5. Ratio of the second and third harmonic to the first harmonic of the modulated signal, as a function of the maximum frequency shift of the QD, scaled by a factor of g 2/κ. The first harmonic is proportional to the actual signal. For the simulation we assumed that the modulation is working in the passband (ωe /2π = 20 GHz); κ∣/2π = g/2π = 20 GHz and the dephasing rate γd /2π = 0.

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Fig. 6.
Fig. 6. Step response of the single QD electro-optic modulator. The parameters used for the simulation are: κ/2π = 5 GHz; g/2π = 20 GHz; Δω 0/2π = 20 GHz; Ω = 1 GHz.

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Fig. 7.
Fig. 7. Ratio between the third and first harmonic of the modulated signal for different QD-cavity coupling g and maximum QD detuning Δω 0. The cavity decay rate κ/2π = 20 GHz and the modulation frequency ωe /2π = 5 GHz.

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Fig. 8.
Fig. 8. (a) Normalized steady state transmission of the laser resonant with the dot (i.e., Δωa = 0) with pure dephasing rate γd /2π. Parameters used are: g/2π = κ/2π = 20 GHz; γ = κ/80; (b) On-off ratio of the modulated signal as a function of the dephasing rate, for κ/2π = g/2π = 20 GHz. The modulation frequency ωe /2π = 5 GHz and the amplitude of the change in resonance frequency Δω0/2π =10 GHz.

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Equations (19)

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dρ dt = − i [ H , ρ ] + κℒ [ a ] + γℒ [ σ ] + γd 2 ( σ z ρ σ z − ρ )
ℒ [ D ] = 2 Dρ D † − D † Dρ − ρ D † D
H = Δ ω c a † a + Δ ω a σ † σ + ig ( a † σ − a σ † ) + Ω ( a + a † )
d 〈 X 〉 dt = A 〈 X 〉 + i Ω B
d 〈 Y 〉 dt = C 〈 Y 〉 + i Ω D 〈 X 〉
X = [ a σ a † σ † ] T
Y = [ a † a σ † σ a † σ a σ † ] T
A = [ − κ g 0 0 − g Γ 0 0 0 0 − κ g 0 0 − g Γ * ]
B = [ − 1 0 1 0 ] T
C = [ − 2 κ 0 g g 0 − 2 γ − g − g − g g Γ − κ 0 − g g 0 Γ * − κ ]
D = [ 1 0 − 1 0 0 0 0 0 0 1 0 0 0 0 0 − 1 ]
〈 a ( t ) 〉 Δ ω 0 → 0 = r ( 0 ) e − α ( 0 ) t cos ( β ( 0 ) t + ϕ ( 0 ) ) + SS ( 0 )
〈 a ( t ) 〉 0 →Δ ω 0 = r ( Δ ω 0 ) e − α ( Δ ω 0 ) t cos ( β ( Δ ω 0 ) t + ϕ ( Δ ω 0 ) ) + SS ( Δ ω 0 )
α ( ω ) = κ + γ + iω 2
β ( ω ) = 4 g 2 − ( κ − γ − iω ) 2 2
SS ( ω ) = i Ω ( γ + iω ) g 2 + κ ( γ + iω )
ϕ ( ω ) = tan ⁡ − 1 ( α ( ω ) β ( ω ) )
r ( 0 ) = SS ( Δ ω 0 ) − SS ( 0 ) cos ⁡ ( ϕ ( 0 ) )
r ( Δ ω 0 ) = SS ( 0 ) − SS ( Δ ω 0 ) cos ⁡ ( ϕ ( Δ ω 0 ) )

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