Abstract

We have theoretically studied the effect of deterministic temporal control of spontaneous emission in a dynamic optical microcavity. We propose a new paradigm in light emission: we envision an ensemble of two-level emitters in an environment where the local density of optical states is modified on a time scale shorter than the decay time. A rate equation model is developed for the excited state population of two-level emitters in a time-dependent environment in the weak coupling regime in quantum electrodynamics. As a realistic experimental system, we consider emitters in a semiconductor microcavity that is switched by free-carrier excitation. We demonstrate that a short temporal increase of the radiative decay rate depletes the excited state and drastically increases the emission intensity during the switch time. The resulting time-dependent spontaneous emission shows a distribution of photon arrival times that strongly deviates from the usual exponential decay: A deterministic burst of photons is spontaneously emitted during the switch event.

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  26. N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65, 043808 (2002).
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  36. The resonant index change contribution from the excited emitters themselves can be neglected due to the low emitter density. Likewise the emission frequency shift caused by the refractive index change of the of the surrendering material is small compared to the cavity resonance shift and has been neglected.
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    [CrossRef]
  39. M. O. Scully, V. V. Kocharovsky, A. Belyanin, E. Fry, and F. Capasso, “Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics,” Phys. Rev. Lett.91, 243004 (2003).
    [CrossRef] [PubMed]
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  42. J. Dilley, P. Nisbet-Jones, B. W. Shore, and A. Kuhn, “Single-photon absorption in coupled atom-cavity systems,” Phys. Rev. A85, 023834 (2012).
    [CrossRef]
  43. M. Fernée, H. Rubinsztein-Dunlop, and G. Milburn, “Improving single-photon sources with Stark tuning,” Phys. Rev. A75, 043815 (2007).
    [CrossRef]
  44. C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: Single photons and qudits,” Phys. Rev. A80, 033811 (2009).
    [CrossRef]
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    [CrossRef]
  46. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Phys.6, 283–292 (2012).
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2012 (7)

S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
[CrossRef] [PubMed]

A. Majumdar, D. Englund, M. Bajcsy, and J. Vučković, “Nonlinear temporal dynamics of a strongly coupled quantum-dot cavity system,” Phys. Rev. A85, 033802 (2012).
[CrossRef]

A. A. Svidzinsky, “Nonlocal effects in single-photon superradiance,” Phys. Rev. A85, 013821 (2012).
[CrossRef]

J. Dilley, P. Nisbet-Jones, B. W. Shore, and A. Kuhn, “Single-photon absorption in coupled atom-cavity systems,” Phys. Rev. A85, 023834 (2012).
[CrossRef]

K. E. Dorfman and S. Mukamel, “Nonlinear spectroscopy with time- and frequency-gated photon counting: A superoperator diagrammatic approach,” Phys. Rev. A86, 013810 (2012).
[CrossRef]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Phys.6, 283–292 (2012).

P. J. Harding, H. J. Bakker, A. Hartsuiker, J. Claudon, A. P. Mosk, J.-M. Gérard, and W. L. Vos, “Observation of a stronger-than-adiabatic change of light trapped in an ultrafast switched GaAs-AlAs microcavity,” J. Opt. Soc. Am. B29, A1–A5 (2012).
[CrossRef]

2011 (4)

R. Johne and A. Fiore, “Single-photon absorption and dynamic control of the exciton energy in a coupled quantum-dot-cavity system,” Phys. Rev. A84, 053850 (2011).
[CrossRef]

L. Novotny and N. van Hulst, “Antennas for light,” Nature Photon.5, 83–90 (2011).
[CrossRef]

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3d photonic band gap,” Phys. Rev. Lett.107, 193903 (2011).
[CrossRef] [PubMed]

Q. Wang, S. Stobbe, and P. Lodahl, “Mapping the local density of optical states of a photonic crystal with single quantum dots,” Phys. Rev. Lett.107, 167404 (2011).
[CrossRef] [PubMed]

2010 (3)

H. Thyrrestrup, L. Sapienza, and P. Lodahl, “Extraction of the beta-factor for single quantum dots coupled to a photonic crystal waveguide,” Appl. Phys. Lett.96, 231106 (2010).
[CrossRef]

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. García, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes.” Science327, 1352–1355 (2010).
[CrossRef] [PubMed]

D. Chruściński and A. Kossakowski, “Non-Markovian Quantum Dynamics: Local versus Nonlocal”, Phys. Rev. Lett.104, 070406 (2010).
[CrossRef]

2009 (2)

W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A80, 053802 (2009).
[CrossRef]

C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: Single photons and qudits,” Phys. Rev. A80, 033811 (2009).
[CrossRef]

2008 (4)

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B77, 115214 (2008).
[CrossRef]

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonicbandgap microcavity,” Nat. Phot.2, 185–189 (2008).
[CrossRef]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett.101, 113903 (2008).
[CrossRef] [PubMed]

J. P. Reithmaier, “Strong exciton-photon coupling in semiconductor quantum dot systems,” Semicond. Sci. Technol.23, 123001 (2008).
[CrossRef]

2007 (6)

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett.90, 091118 (2007).
[CrossRef]

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett.91, 111103 (2007).
[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445, 896–899 (2007).
[CrossRef] [PubMed]

A. F. van Driel, I. S. Nikolaev, P. Vergeer, P. Lodahl, D. Vanmaekelbergh, and W. L. Vos, “Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models,” Phys. Rev. B75, 035329 (2007).
[CrossRef]

M. W. McCutcheon, A. G. Pattantyus-Abraham, G. W. Rieger, and J. F. Young, “Emission spectrum of electromagnetic energy stored in a dynamically perturbed optical microcavity,” Opt. Express15, 11472–11480 (2007).
[CrossRef] [PubMed]

M. Fernée, H. Rubinsztein-Dunlop, and G. Milburn, “Improving single-photon sources with Stark tuning,” Phys. Rev. A75, 043815 (2007).
[CrossRef]

2005 (1)

P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72, 052332 (2005).
[CrossRef]

2003 (3)

M. O. Scully, V. V. Kocharovsky, A. Belyanin, E. Fry, and F. Capasso, “Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics,” Phys. Rev. Lett.91, 243004 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
[CrossRef] [PubMed]

J. M. Gérard, “Solid-state cavity-quantum electrodynamics with self-assembled quantum dots,” Topics Appl. Phys.90, 283–327 (2003).

2002 (3)

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65, 043808 (2002).
[CrossRef]

P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B66, 081102 (2002).
[CrossRef]

M. Bayer and A. Forchel, “Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots,” Phys. Rev. B65, 041308 (2002).
[CrossRef]

2001 (2)

H. Nemec, A. Pashkin, P. Kuzel, M. Khazan, S. Schnüll, and I. Wilke, “Carrier dynamics in low-temperature grown GaAs studied by terahertz emission spectroscopy,” J. Appl. Phys.90, 1303–1306 (2001).
[CrossRef]

M. Bayer, T. L. Reinecke, F. Weidner, A. Larionov, A. McDonald, and A. Forchel, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett.86, 3168–3171 (2001).
[CrossRef] [PubMed]

1998 (1)

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett.81, 1110–1113 (1998).
[CrossRef]

1996 (1)

R. Sprik, B. A. van Tiggelen, and A. Lagendijk, “Optical emission in periodic dielectrics,” Europhys. Lett.35, 265–270 (1996).
[CrossRef]

1994 (1)

T. Rivera, F. R. Ladan, A. Izrael, R. Azoulay, R. Kuszelewicz, and J. L. Oudar, “Reduced threshold all-optical bistability in etched quantum well microresonators,” Appl. Phys. Lett.64, 869–871 (1994).
[CrossRef]

1993 (2)

A. Lagendijk, “Vibrational relaxation studied with light,” in Ultrashort Processes in Condensed Matter, vol. 314 (1993), pp. 197–236.
[CrossRef]

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, “Controlled atomic spontaneous emission from Er3+in a transparent Si/SiO2microcavity,” Phys. Rev. Lett.71, 517–520 (1993).
[CrossRef] [PubMed]

1989 (2)

J. L. Jewell, S. L. McCall, A. Scherer, H. H. Houh, N. A. Whitaker, A. C. Gossard, and J. H. English, “Transverse modes, waveguide dispersion, and 30 ps recovery in submicron GaAs/AlAs microresonators,” Appl. Phys. Lett.55, 22–24 (1989).
[CrossRef]

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today42, 24–30 (1989).
[CrossRef]

1981 (1)

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett.47, 233–236 (1981).
[CrossRef]

1932 (1)

E. Fermi, “Quantum theory of radiation,” Rev. Mod. Phys.4, 87–132 (1932).
[CrossRef]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445, 896–899 (2007).
[CrossRef] [PubMed]

Azoulay, R.

T. Rivera, F. R. Ladan, A. Izrael, R. Azoulay, R. Kuszelewicz, and J. L. Oudar, “Reduced threshold all-optical bistability in etched quantum well microresonators,” Appl. Phys. Lett.64, 869–871 (1994).
[CrossRef]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445, 896–899 (2007).
[CrossRef] [PubMed]

Bajcsy, M.

A. Majumdar, D. Englund, M. Bajcsy, and J. Vučković, “Nonlinear temporal dynamics of a strongly coupled quantum-dot cavity system,” Phys. Rev. A85, 033802 (2012).
[CrossRef]

Bakker, H. J.

Bayer, M.

M. Bayer and A. Forchel, “Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots,” Phys. Rev. B65, 041308 (2002).
[CrossRef]

M. Bayer, T. L. Reinecke, F. Weidner, A. Larionov, A. McDonald, and A. Forchel, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett.86, 3168–3171 (2001).
[CrossRef] [PubMed]

Belyanin, A.

M. O. Scully, V. V. Kocharovsky, A. Belyanin, E. Fry, and F. Capasso, “Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics,” Phys. Rev. Lett.91, 243004 (2003).
[CrossRef] [PubMed]

Buckley, S.

S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
[CrossRef] [PubMed]

Busch, K.

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65, 043808 (2002).
[CrossRef]

Capasso, F.

M. O. Scully, V. V. Kocharovsky, A. Belyanin, E. Fry, and F. Capasso, “Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics,” Phys. Rev. Lett.91, 243004 (2003).
[CrossRef] [PubMed]

Chruscin´ski, D.

D. Chruściński and A. Kossakowski, “Non-Markovian Quantum Dynamics: Local versus Nonlocal”, Phys. Rev. Lett.104, 070406 (2010).
[CrossRef]

Claudon, J.

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett.81, 1110–1113 (1998).
[CrossRef]

Dilley, J.

J. Dilley, P. Nisbet-Jones, B. W. Shore, and A. Kuhn, “Single-photon absorption in coupled atom-cavity systems,” Phys. Rev. A85, 023834 (2012).
[CrossRef]

Ding, C.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonicbandgap microcavity,” Nat. Phot.2, 185–189 (2008).
[CrossRef]

Dorfman, K. E.

K. E. Dorfman and S. Mukamel, “Nonlinear spectroscopy with time- and frequency-gated photon counting: A superoperator diagrammatic approach,” Phys. Rev. A86, 013810 (2012).
[CrossRef]

English, J. H.

J. L. Jewell, S. L. McCall, A. Scherer, H. H. Houh, N. A. Whitaker, A. C. Gossard, and J. H. English, “Transverse modes, waveguide dispersion, and 30 ps recovery in submicron GaAs/AlAs microresonators,” Appl. Phys. Lett.55, 22–24 (1989).
[CrossRef]

Englund, D.

A. Majumdar, D. Englund, M. Bajcsy, and J. Vučković, “Nonlinear temporal dynamics of a strongly coupled quantum-dot cavity system,” Phys. Rev. A85, 033802 (2012).
[CrossRef]

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett.90, 091118 (2007).
[CrossRef]

Euser, T. G.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B77, 115214 (2008).
[CrossRef]

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett.91, 111103 (2007).
[CrossRef]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445, 896–899 (2007).
[CrossRef] [PubMed]

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J. P. Reithmaier, “Strong exciton-photon coupling in semiconductor quantum dot systems,” Semicond. Sci. Technol.23, 123001 (2008).
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T. Rivera, F. R. Ladan, A. Izrael, R. Azoulay, R. Kuszelewicz, and J. L. Oudar, “Reduced threshold all-optical bistability in etched quantum well microresonators,” Appl. Phys. Lett.64, 869–871 (1994).
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S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
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P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72, 052332 (2005).
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L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. García, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes.” Science327, 1352–1355 (2010).
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H. Nemec, A. Pashkin, P. Kuzel, M. Khazan, S. Schnüll, and I. Wilke, “Carrier dynamics in low-temperature grown GaAs studied by terahertz emission spectroscopy,” J. Appl. Phys.90, 1303–1306 (2001).
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A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, “Controlled atomic spontaneous emission from Er3+in a transparent Si/SiO2microcavity,” Phys. Rev. Lett.71, 517–520 (1993).
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M. O. Scully, V. V. Kocharovsky, A. Belyanin, E. Fry, and F. Capasso, “Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics,” Phys. Rev. Lett.91, 243004 (2003).
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J. Dilley, P. Nisbet-Jones, B. W. Shore, and A. Kuhn, “Single-photon absorption in coupled atom-cavity systems,” Phys. Rev. A85, 023834 (2012).
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L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. García, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes.” Science327, 1352–1355 (2010).
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Q. Wang, S. Stobbe, and P. Lodahl, “Mapping the local density of optical states of a photonic crystal with single quantum dots,” Phys. Rev. Lett.107, 167404 (2011).
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J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett.81, 1110–1113 (1998).
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L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. García, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes.” Science327, 1352–1355 (2010).
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T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett.101, 113903 (2008).
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L. Novotny and N. van Hulst, “Antennas for light,” Nature Photon.5, 83–90 (2011).
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R. Sprik, B. A. van Tiggelen, and A. Lagendijk, “Optical emission in periodic dielectrics,” Europhys. Lett.35, 265–270 (1996).
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A. F. van Driel, I. S. Nikolaev, P. Vergeer, P. Lodahl, D. Vanmaekelbergh, and W. L. Vos, “Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models,” Phys. Rev. B75, 035329 (2007).
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W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A80, 053802 (2009).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B77, 115214 (2008).
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A. F. van Driel, I. S. Nikolaev, P. Vergeer, P. Lodahl, D. Vanmaekelbergh, and W. L. Vos, “Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models,” Phys. Rev. B75, 035329 (2007).
[CrossRef]

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett.91, 111103 (2007).
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P. J. Harding, A. P. Mosk, A. Hartsuiker, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Time-resolved resonance and linewidth of an ultrafast switched GaAs/AlAs microcavity,” arXiv:0901.3855 [physics.optics] (2009).

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[CrossRef] [PubMed]

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A. Majumdar, D. Englund, M. Bajcsy, and J. Vučković, “Nonlinear temporal dynamics of a strongly coupled quantum-dot cavity system,” Phys. Rev. A85, 033802 (2012).
[CrossRef]

S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
[CrossRef] [PubMed]

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[CrossRef]

Waks, E.

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett.90, 091118 (2007).
[CrossRef]

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[CrossRef] [PubMed]

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M. Bayer, T. L. Reinecke, F. Weidner, A. Larionov, A. McDonald, and A. Forchel, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett.86, 3168–3171 (2001).
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J. L. Jewell, S. L. McCall, A. Scherer, H. H. Houh, N. A. Whitaker, A. C. Gossard, and J. H. English, “Transverse modes, waveguide dispersion, and 30 ps recovery in submicron GaAs/AlAs microresonators,” Appl. Phys. Lett.55, 22–24 (1989).
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H. Nemec, A. Pashkin, P. Kuzel, M. Khazan, S. Schnüll, and I. Wilke, “Carrier dynamics in low-temperature grown GaAs studied by terahertz emission spectroscopy,” J. Appl. Phys.90, 1303–1306 (2001).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Appl. Phys. Lett. (5)

H. Thyrrestrup, L. Sapienza, and P. Lodahl, “Extraction of the beta-factor for single quantum dots coupled to a photonic crystal waveguide,” Appl. Phys. Lett.96, 231106 (2010).
[CrossRef]

J. L. Jewell, S. L. McCall, A. Scherer, H. H. Houh, N. A. Whitaker, A. C. Gossard, and J. H. English, “Transverse modes, waveguide dispersion, and 30 ps recovery in submicron GaAs/AlAs microresonators,” Appl. Phys. Lett.55, 22–24 (1989).
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I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett.90, 091118 (2007).
[CrossRef]

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett.91, 111103 (2007).
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H. Nemec, A. Pashkin, P. Kuzel, M. Khazan, S. Schnüll, and I. Wilke, “Carrier dynamics in low-temperature grown GaAs studied by terahertz emission spectroscopy,” J. Appl. Phys.90, 1303–1306 (2001).
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J. Opt. Soc. Am. B (1)

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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445, 896–899 (2007).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
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[CrossRef]

M. Fernée, H. Rubinsztein-Dunlop, and G. Milburn, “Improving single-photon sources with Stark tuning,” Phys. Rev. A75, 043815 (2007).
[CrossRef]

C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: Single photons and qudits,” Phys. Rev. A80, 033811 (2009).
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A. Majumdar, D. Englund, M. Bajcsy, and J. Vučković, “Nonlinear temporal dynamics of a strongly coupled quantum-dot cavity system,” Phys. Rev. A85, 033802 (2012).
[CrossRef]

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65, 043808 (2002).
[CrossRef]

W. L. Vos, A. F. Koenderink, and I. S. Nikolaev, “Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment,” Phys. Rev. A80, 053802 (2009).
[CrossRef]

A. A. Svidzinsky, “Nonlocal effects in single-photon superradiance,” Phys. Rev. A85, 013821 (2012).
[CrossRef]

Phys. Rev. B (4)

M. Bayer and A. Forchel, “Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots,” Phys. Rev. B65, 041308 (2002).
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A. F. van Driel, I. S. Nikolaev, P. Vergeer, P. Lodahl, D. Vanmaekelbergh, and W. L. Vos, “Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models,” Phys. Rev. B75, 035329 (2007).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B77, 115214 (2008).
[CrossRef]

P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B66, 081102 (2002).
[CrossRef]

Phys. Rev. Lett. (9)

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, “Controlled atomic spontaneous emission from Er3+in a transparent Si/SiO2microcavity,” Phys. Rev. Lett.71, 517–520 (1993).
[CrossRef] [PubMed]

M. O. Scully, V. V. Kocharovsky, A. Belyanin, E. Fry, and F. Capasso, “Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics,” Phys. Rev. Lett.91, 243004 (2003).
[CrossRef] [PubMed]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett.81, 1110–1113 (1998).
[CrossRef]

M. Bayer, T. L. Reinecke, F. Weidner, A. Larionov, A. McDonald, and A. Forchel, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett.86, 3168–3171 (2001).
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[CrossRef] [PubMed]

Q. Wang, S. Stobbe, and P. Lodahl, “Mapping the local density of optical states of a photonic crystal with single quantum dots,” Phys. Rev. Lett.107, 167404 (2011).
[CrossRef] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett.101, 113903 (2008).
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S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys.75, 126503 (2012).
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Other (5)

The resonant index change contribution from the excited emitters themselves can be neglected due to the low emitter density. Likewise the emission frequency shift caused by the refractive index change of the of the surrendering material is small compared to the cavity resonance shift and has been neglected.

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I. S. Nikolaev, Spontaneous-Emission Rates of Quantum Dots and Dyes Controlled with Photonic Crystals, available online: http://www.photonicbandgaps.com , Ph.D. thesis, Universiteit of Twente (2006).

P. J. Harding, Photonic crystals modified by optically resonant systems, available online: http://www.photonicbandgaps.com , Ph.D. thesis, Universiteit of Twente (2008).

P. J. Harding, A. P. Mosk, A. Hartsuiker, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Time-resolved resonance and linewidth of an ultrafast switched GaAs/AlAs microcavity,” arXiv:0901.3855 [physics.optics] (2009).

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Figures (4)

Fig. 1
Fig. 1

Schematic graph of the switching process as experienced by a quantum emitter (green) emitting at a frequency ωd in the spectral vicinity of a cavity resonance whose frequency is switched in time. The cavity has a Lorentzian local density of states (solid line). Initially the emitter is detuned from the cavity resonance ωcav,0 by nearly one cavity linewidth, leading to an effective radiative rate Γ0. The switching process moves the cavity resonance up in frequency ωcav(t) (gray dashed). The cavity is then tuned into resonance with the emitter that thus experiences a decay rate strongly enhanced by ΔΓrad. Within one cavity linewidth from the resonance, switching of the cavity resonance can be approximated by a linear shift of the decay rate versus frequency (red dashed line).

Fig. 2
Fig. 2

Radiative decay rate normalized to the unswitched rate Γ0 (solid line) as a function of time after exciting the emitter. The two thick curves show the result of a switching event at t0pu = 10 ps that either enhances (long dashed) or inhibits (short dashed) the decay rate by a factor of 5. The modified decay rate relaxes back to the unswitched rate within the effective switching time of τsw = 35 ps after the switching event.

Fig. 3
Fig. 3

(a) Time resolved population density for an emitter excited at t = texc = 0 ps showing the effect of two different switch events at t = tpu = 150 ps. The chosen parameters model the effect of a switch event that either tunes a cavity resonance into (green long dashed) or out of (red short dashed) resonance with the emitter frequency. Without switch the populations decay exponentially with a rate of Γ0 = 1 ns−1and Γ0 = 5 ns−1, respectively, in the two examples (solid lines). The switch event leads to an enhanced or inhibited radiative rate by a factor of 5 relative to the unswitched rate. These time-dependent rates result in a short decrease or increase in the populations relative to the unswitched cases. At long times after the effective switching time τsw = 35 ps, the slopes tend to their initial values for both examples. (b) The corresponding spontaneous emission intensities from the emitter relative to the initial values after excitation for the same two examples presented in (a). The small changes in the population density corresponds to large changes in the emitted intensity. Switching the cavity into resonance with the quantum dot (green long dashed) results in a sharp burst of intensity with a temporal duration of τsw. Tuning out of resonance leads to a fast drop in the intensity.

Fig. 4
Fig. 4

The effect of free carrier absorption on the time resolved emitted intensity for emitters embedded in a switched cavity. After the emitter is excited at t = tex = 0 ps the cavity resonance is switched one linewidth S = Δω/γi = 1 at t = tpu = 150 ps. At this time the radiative decay rate is increased by ΔΓrad = 4Γ0from Γ0 = 1 ns−1. Afterwards the resonance frequency relaxes exponentially back to its original value with a switching time ofτsw = 35 ps. The black dashed line shows the emitted intensity neglecting the effect of free carrier absorption whereas the red line include absorption with a = 0.083 extracted from [47]. The free carrier absorption only inflict a reduction of 15% on the height of the peak intensity.

Equations (26)

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d c a ( t ) d t = d 2 2 h ¯ ε 0 0 t 0 c a ( t ) ω ρ ( ω , e d , r , t ) e i ( ω ω d ) ( t t ) d ω d t .
d c a ( t ) d t = d 2 2 h ¯ ε 0 0 t c a ( t ) π δ ( t t ) ω d ρ ( ω d , e d , r , t ) d t .
d c a ( t ) d t = d 2 2 h ¯ ε 0 c a ( t ) π ω d ρ ( ω d , e d , r , t ) ,
d c a ( t ) d t = Γ rad 2 c a ( t ) ,
Γ rad ( t ) = d 2 ω d π h ¯ ε 0 ρ ( ω d , e d , r , t ) .
| c a ( t ) | 2 = | c a ( 0 ) | 2 e Γ rad t .
d N 2 ( t ) d t = η abs P exc ( t ) h ¯ ω exc ( Γ rad ( t ) + Γ nrad ) N 2 ( t ) .
N 2 ( t ) = N 2 ( t ) = N 2 ( 0 ) + 0 t ( η abs P exc ( t ) h ¯ ω exc ( Γ rad ( t ) + Γ nrad ) N 2 ( t ) ) d t .
I ( t ) = Γ rad ( t ) N 2 ( t ) ,
Γ rad ( t ) = Γ 0 + Δ Γ rad ( t ) .
Δ Γ rad ( t ) = 2 π d 2 ω d h ¯ ε 0 Δ ρ ( t ) .
τ sw = Δ t | ω cav ( Δ t ) ω cav , 0 | γ cav .
Γ rad ( t ) = Γ 0 + Δ Γ rad e ( t t 0 pu ) τ sw Θ ( t t 0 pu , τ pu )
d N 2 ( t t 0 exc ) d t = ( Γ rad ( t t 0 exc ) + Γ nrad ) N 2 ( t t 0 exc ) ,
N 2 ( t t 0 exc ) = N 02 exp ( 0 t t 0 exc ( Γ rad ( t ) + Γ nrad ) d t ) .
N 2 ( t t 0 exc ) = N 02 e ( Γ 0 + Γ 0 nrad ) ( t t 0 exc ) Δ α rad ( t )
Δ α rad ( t ) 0 t Δ Γ rad e ( t t 0 pu ) τ sw Θ ( t t 0 pu , τ pu ) d t .
Δ α rad ( t ) = Δ Γ rad τ sw ( 1 e ( t t 0 pu ) τ sw ) Θ ( t t 0 pu , τ pu ) .
Δ α = lim t Δ α rad ( t ) = Δ Γ rad τ sw .
lim t N 2 ( t ) N 2 us ( t ) = e Δ Γ rad τ sw = e Δ α .
I ( t ) = ( Γ 0 + Δ Γ rad ( t ) ) N 02 e Γ 0 tot ( t t 0 exc ) Δ α rad ( t ) Θ ( t t 0 exc , τ exc ) ,
γ ( t ) = γ i + γ a ( t ) .
S ( t ) Δ ω ( t ) γ i
γ ( t ) γ i = 1 + a S ( t )
I ( t ) = Γ rad ( t ) ( γ i γ ( t ) ) 2 N 02 exp ( 0 t t 0 exc γ i γ ( t ) Γ rad ( t ) d t ) .
S ( t ) = S 0 e ( t t 0 pu ) τ sw Θ ( t t 0 pu , τ pu )

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