Abstract

Quantum dots in semiconductor photonic reservoirs are important systems for studying and exploiting quantum optics on a chip, and it is essential to understand fundamental concepts such as spontaneous emission. According to Fermi’s golden rule, the spontaneous emission rate of a quantum emitter weakly coupled to a structured photonic reservoir is proportional to the local density of photon states (LDOS) at the emitter’s position and frequency. Coupling to lattice vibrations or phonons, however, significantly modifies the emission properties of a quantum dot (QD) compared to an isolated emitter (e.g., an atom). In the regime of phonon-dressed reservoir coupling, we demonstrate why and how the broadband frequency dependence of the LDOS determines the spontaneous emission rate of a QD, manifesting in a dramatic breakdown of Fermi’s golden rule. We analyze this problem using a polaron transformed master equation and consider specific examples of a semiconductor microcavity and a coupled-cavity waveguide. For a leaky single cavity resonance, we generalize Purcell’s formula to include the effects of electron–phonon coupling, and for a waveguide, we show a suppression and a 200-fold enhancement of the photon emission rate. These results have important consequences for modeling and understanding emerging QD experiments in a wide range of photonic reservoir systems.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  29. D. P. Fussell and M. M. Dignam, Phys. Rev. A 76, 053801 (2007).
    [Crossref]
  30. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
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2015 (1)

2014 (1)

D. Valente, J. Suffczyński, T. Jakubczyk, A. Dousse, A. Lemaître, I. Sagnes, L. Lanco, P. Voisin, A. Auffèves, and P. Senellart, Phys. Rev. B 89, 041302(R) (2014).

2013 (3)

H. Kim, R. Bose, T. Shen, G. Solomon, and E. Waks, Nat. Photonics 7, 373 (2013).
[Crossref]

L. Monniello, C. Tonin, R. Hostein, A. Lemaitre, A. Martinez, V. Voliotis, and R. Grousson, Phys. Rev. Lett. 111, 026403 (2013).
[Crossref]

D. P. S. McCutcheon and A. Nazir, Phys. Rev. Lett. 110, 217401 (2013); see also the Supplementary Material.
[Crossref]

2012 (3)

P. Kaer, T. R. Nielsen, P. Lodahl, A.-P. Jauho, and J. Mørk, Phys. Rev. B 86, 085302 (2012).

S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetter, P. Michler, C. Roy, and S. Hughes, Phys. Rev. B 86, 241304(R) (2012).

C. A. Foell, E. Schelew, H. Qiao, K. A. Abel, S. Hughes, F. C. J. M. van Veggel, and J. F. Young, Opt. Express 20, 10453 (2012).
[Crossref]

2011 (5)

C. Roy and S. Hughes, Phys. Rev. X 1, 021009 (2011).
[Crossref]

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, Phys. Rev. B 84, 085309 (2011).

C. Roy and S. Hughes, Phys. Rev. Lett. 106, 247403 (2011).
[Crossref]

2010 (3)

U. Hohenester, Phys. Rev. B 81, 155303 (2010).

C. Roy and S. John, Phys. Rev. A 81, 023817 (2010).
[Crossref]

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

2008 (4)

F. Milde, A. Knorr, and S. Hughes, Phys. Rev. B 78, 035330 (2008).

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[Crossref]

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photonics 2, 741 (2008).
[Crossref]

2007 (2)

D. P. Fussell and M. M. Dignam, Phys. Rev. A 76, 053801 (2007).
[Crossref]

V. S. C. Manga Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).

2006 (2)

E. Waks and J. Vučković, Phys. Rev. Lett. 96, 153601 (2006).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

2005 (1)

D. Englund, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, Phys. Rev. Lett. 95, 013904 (2005).
[Crossref]

2003 (1)

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[Crossref]

2002 (2)

B. Krummheuer, V. M. Axt, and T. Kuhn, Phys. Rev. B 65, 195313 (2002).

I. Wilson-Rae and A. Imamoğlu, Phys. Rev. B 65, 235311 (2002).

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[Crossref]

1999 (2)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[Crossref]

S. Scheel, L. Knöll, and D.-G. Welsch, Phys. Rev. A 60, 4094 (1999).
[Crossref]

1946 (1)

E. M. Purcell, Phys. Rev. 69, 37 (1946).
[Crossref]

Abel, K. A.

Arakawa, Y.

D. Englund, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, Phys. Rev. Lett. 95, 013904 (2005).
[Crossref]

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXiv:0908.0788 (2009).

Ates, S.

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

Auffèves, A.

D. Valente, J. Suffczyński, T. Jakubczyk, A. Dousse, A. Lemaître, I. Sagnes, L. Lanco, P. Voisin, A. Auffèves, and P. Senellart, Phys. Rev. B 89, 041302(R) (2014).

Axt, V. M.

B. Krummheuer, V. M. Axt, and T. Kuhn, Phys. Rev. B 65, 195313 (2002).

Bajcsy, M.

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, Phys. Rev. B 84, 085309 (2011).

Bose, R.

H. Kim, R. Bose, T. Shen, G. Solomon, and E. Waks, Nat. Photonics 7, 373 (2013).
[Crossref]

Boyle, S. J.

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Danckwerts, J.

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[Crossref]

Dignam, M. M.

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).

D. P. Fussell and M. M. Dignam, Phys. Rev. A 76, 053801 (2007).
[Crossref]

Dousse, A.

D. Valente, J. Suffczyński, T. Jakubczyk, A. Dousse, A. Lemaître, I. Sagnes, L. Lanco, P. Voisin, A. Auffèves, and P. Senellart, Phys. Rev. B 89, 041302(R) (2014).

Englund, D.

D. Englund, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, Phys. Rev. Lett. 95, 013904 (2005).
[Crossref]

Farrer, I.

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

Foell, C. A.

Forchel, A.

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[Crossref]

Förstner, J.

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[Crossref]

Fox, A. M.

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Fussell, D. P.

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).

D. P. Fussell and M. M. Dignam, Phys. Rev. A 76, 053801 (2007).
[Crossref]

Gauger, E. M.

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Godden, T. M.

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Gong, Y.

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, Phys. Rev. B 84, 085309 (2011).

Griffiths, J. P.

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

Grousson, R.

L. Monniello, C. Tonin, R. Hostein, A. Lemaitre, A. Martinez, V. Voliotis, and R. Grousson, Phys. Rev. Lett. 111, 026403 (2013).
[Crossref]

Hohenester, U.

U. Hohenester, Phys. Rev. B 81, 155303 (2010).

Hostein, R.

L. Monniello, C. Tonin, R. Hostein, A. Lemaitre, A. Martinez, V. Voliotis, and R. Grousson, Phys. Rev. Lett. 111, 026403 (2013).
[Crossref]

Hughes, S.

K. Roy-Choudhury and S. Hughes, Opt. Lett. 40, 1838 (2015).

S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetter, P. Michler, C. Roy, and S. Hughes, Phys. Rev. B 86, 241304(R) (2012).

C. A. Foell, E. Schelew, H. Qiao, K. A. Abel, S. Hughes, F. C. J. M. van Veggel, and J. F. Young, Opt. Express 20, 10453 (2012).
[Crossref]

C. Roy and S. Hughes, Phys. Rev. X 1, 021009 (2011).
[Crossref]

C. Roy and S. Hughes, Phys. Rev. Lett. 106, 247403 (2011).
[Crossref]

F. Milde, A. Knorr, and S. Hughes, Phys. Rev. B 78, 035330 (2008).

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).

V. S. C. Manga Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).

Imamoglu, A.

I. Wilson-Rae and A. Imamoğlu, Phys. Rev. B 65, 235311 (2002).

Iwamoto, S.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXiv:0908.0788 (2009).

Jakubczyk, T.

D. Valente, J. Suffczyński, T. Jakubczyk, A. Dousse, A. Lemaître, I. Sagnes, L. Lanco, P. Voisin, A. Auffèves, and P. Senellart, Phys. Rev. B 89, 041302(R) (2014).

Jauho, A.-P.

P. Kaer, T. R. Nielsen, P. Lodahl, A.-P. Jauho, and J. Mørk, Phys. Rev. B 86, 085302 (2012).

Jetter, M.

S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetter, P. Michler, C. Roy, and S. Hughes, Phys. Rev. B 86, 241304(R) (2012).

John, S.

C. Roy and S. John, Phys. Rev. A 81, 023817 (2010).
[Crossref]

Jones, G. A. C.

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

Julsgaard, B.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[Crossref]

Kaer, P.

P. Kaer, T. R. Nielsen, P. Lodahl, A.-P. Jauho, and J. Mørk, Phys. Rev. B 86, 085302 (2012).

Kalliakos, S.

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

Kamp, M.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[Crossref]

Kim, E. D.

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, Phys. Rev. B 84, 085309 (2011).

Kim, H.

H. Kim, R. Bose, T. Shen, G. Solomon, and E. Waks, Nat. Photonics 7, 373 (2013).
[Crossref]

Knöll, L.

S. Scheel, L. Knöll, and D.-G. Welsch, Phys. Rev. A 60, 4094 (1999).
[Crossref]

Knorr, A.

F. Milde, A. Knorr, and S. Hughes, Phys. Rev. B 78, 035330 (2008).

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[Crossref]

Krummheuer, B.

B. Krummheuer, V. M. Axt, and T. Kuhn, Phys. Rev. B 65, 195313 (2002).

Kuhn, T.

B. Krummheuer, V. M. Axt, and T. Kuhn, Phys. Rev. B 65, 195313 (2002).

Kumagai, N.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXiv:0908.0788 (2009).

Kuramochi, E.

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photonics 2, 741 (2008).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Lanco, L.

D. Valente, J. Suffczyński, T. Jakubczyk, A. Dousse, A. Lemaître, I. Sagnes, L. Lanco, P. Voisin, A. Auffèves, and P. Senellart, Phys. Rev. B 89, 041302(R) (2014).

Lee, R. K.

Lemaitre, A.

L. Monniello, C. Tonin, R. Hostein, A. Lemaitre, A. Martinez, V. Voliotis, and R. Grousson, Phys. Rev. Lett. 111, 026403 (2013).
[Crossref]

Lemaître, A.

D. Valente, J. Suffczyński, T. Jakubczyk, A. Dousse, A. Lemaître, I. Sagnes, L. Lanco, P. Voisin, A. Auffèves, and P. Senellart, Phys. Rev. B 89, 041302(R) (2014).

Lodahl, P.

P. Kaer, T. R. Nielsen, P. Lodahl, A.-P. Jauho, and J. Mørk, Phys. Rev. B 86, 085302 (2012).

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[Crossref]

Löffler, A.

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

Lovett, B. W.

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Lund-Hansen, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[Crossref]

Majumdar, A.

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, Phys. Rev. B 84, 085309 (2011).

Manga Rao, V. S. C.

V. S. C. Manga Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).

Martinez, A.

L. Monniello, C. Tonin, R. Hostein, A. Lemaitre, A. Martinez, V. Voliotis, and R. Grousson, Phys. Rev. Lett. 111, 026403 (2013).
[Crossref]

McCutcheon, D. P. S.

D. P. S. McCutcheon and A. Nazir, Phys. Rev. Lett. 110, 217401 (2013); see also the Supplementary Material.
[Crossref]

Michler, P.

S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetter, P. Michler, C. Roy, and S. Hughes, Phys. Rev. B 86, 241304(R) (2012).

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

Milde, F.

F. Milde, A. Knorr, and S. Hughes, Phys. Rev. B 78, 035330 (2008).

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Monniello, L.

L. Monniello, C. Tonin, R. Hostein, A. Lemaitre, A. Martinez, V. Voliotis, and R. Grousson, Phys. Rev. Lett. 111, 026403 (2013).
[Crossref]

Mørk, J.

P. Kaer, T. R. Nielsen, P. Lodahl, A.-P. Jauho, and J. Mørk, Phys. Rev. B 86, 085302 (2012).

Nakaoka, T.

D. Englund, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, Phys. Rev. Lett. 95, 013904 (2005).
[Crossref]

Nazir, A.

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A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Appl. Phys. Lett. 99, 261108 (2011).
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H. Kim, R. Bose, T. Shen, G. Solomon, and E. Waks, Nat. Photonics 7, 373 (2013).
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S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetter, P. Michler, C. Roy, and S. Hughes, Phys. Rev. B 86, 241304(R) (2012).

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H. Kim, R. Bose, T. Shen, G. Solomon, and E. Waks, Nat. Photonics 7, 373 (2013).
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E. Waks and J. Vučković, Phys. Rev. Lett. 96, 153601 (2006).
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Appl. Phys. Lett. (2)

A. Schwagmann, S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Appl. Phys. Lett. 99, 261108 (2011).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Nat. Photonics (2)

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photonics 2, 741 (2008).
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Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

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P. Kaer, T. R. Nielsen, P. Lodahl, A.-P. Jauho, and J. Mørk, Phys. Rev. B 86, 085302 (2012).

V. S. C. Manga Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).

U. Hohenester, Phys. Rev. B 81, 155303 (2010).

I. Wilson-Rae and A. Imamoğlu, Phys. Rev. B 65, 235311 (2002).

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, Phys. Rev. B 84, 085309 (2011).

F. Milde, A. Knorr, and S. Hughes, Phys. Rev. B 78, 035330 (2008).

S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetter, P. Michler, C. Roy, and S. Hughes, Phys. Rev. B 86, 241304(R) (2012).

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J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[Crossref]

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

L. Monniello, C. Tonin, R. Hostein, A. Lemaitre, A. Martinez, V. Voliotis, and R. Grousson, Phys. Rev. Lett. 111, 026403 (2013).
[Crossref]

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

D. Englund, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, Phys. Rev. Lett. 95, 013904 (2005).
[Crossref]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[Crossref]

D. P. S. McCutcheon and A. Nazir, Phys. Rev. Lett. 110, 217401 (2013); see also the Supplementary Material.
[Crossref]

C. Roy and S. Hughes, Phys. Rev. Lett. 106, 247403 (2011).
[Crossref]

E. Waks and J. Vučković, Phys. Rev. Lett. 96, 153601 (2006).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[Crossref]

Phys. Rev. X (1)

C. Roy and S. Hughes, Phys. Rev. X 1, 021009 (2011).
[Crossref]

Other (1)

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXiv:0908.0788 (2009).

Supplementary Material (1)

» Supplement 1: PDF (572 KB)     

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Figures (3)

Fig. 1.
Fig. 1. Two photonic reservoir systems under consideration and an energy level picture of the various quantum states. Schematic of (a) semiconductor cavity and (b) waveguide using a photonic crystal platform, containing a single QD. (c) Energy level diagram of a neutral QD (electron–hole pair) interacting with a phonon bath and a photon bath. The operator f k creates a photon, and the b q operator creates a phonon.
Fig. 2.
Fig. 2. Phonon-modified spontaneous emission of a QD in a dielectric cavity. Near-resonant PFs (left panels) and phonon-modified SE factor χ (right panels) for cavities with (a),(b)  κ = 0.06 meV , (c),(d) 0.6 meV, and (e),(f) 2.4 meV. We use the continuous form of the phonon spectral function, J pn ( ω ) = α p ω 3 exp [ ω 2 2 ω b 2 ] , for longitudinal acoustic phonon interaction, and adopt experimental numbers for InAs QDs [2]: cavity-QD coupling rate g = 0.08 meV , phonon cutoff frequency ω b = 1 meV , and exciton–phonon coupling strength α p / ( 2 π ) 2 = 0.06 ps 2 [21]. The dark (red) dashed lines on the left panels represent the PF without phonons. The dark and light solid lines correspond to the phonon-modified PF and χ at T = 4 and 40 K, respectively. The dashed lines on the right panels plot χ mean (see text) at T = 4 K (light) and 40 K (dark).
Fig. 3.
Fig. 3. Phonon-modified spontaneous emission of a QD in a coupled-cavity waveguide. (a) Purcell factors and (b) phonon-modified SE factor χ in a log 10 scale, for a PC CROW structure, where ω 0 marks the band center. For the waveguide, PF = γ / γ h , where γ h = d 2 n b ω 3 / ( 6 π ϵ 0 c 3 ) is the SE rate within the homogenous slab material. The solid (dashed) line in (a) represents the PF with (without) phonons; the inset shows J ph ( t ) at the upper mode edge (light line) and band center (dark line) in arbitrary units; the dashed line shows the simple exponential damping function e λ t (see text). The phonon calculations are performed at T = 40 K . Inset in (b) plots χ in a linear scale to show better display χ inside the waveguide band.

Equations (6)

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H = d r 0 d ω f ( r , ω ) f ( r , ω ) + Σ q ω q b q b q [ σ + e i ω x t 0 d ω d · E ( r d , ω ) + H.c ] + σ + σ Σ q λ q ( b q + b q ) ,
γ ˜ ( t ) = 2 0 t Re [ C pn ( τ ) J ph ( τ ) ] d τ ,
J ph ( ω ) = g 2 1 π κ 2 ( ω ω c ) 2 + ( κ 2 ) 2 ,
γ ˜ = 2 g 2 B 2 Re [ 0 e ϕ ( τ ) e i Δ c x τ κ τ / 2 d τ ] ,
PF = [ 3 4 π 2 ( λ 0 n b ) 3 Q V eff ( κ 2 4 Δ c x 2 + κ 2 4 ) ] χ ,
J ph ( ω ) = d 2 ω 2 ϵ 0 n b 2 V eff 1 π Im [ 1 ( ω ω ˜ u ) ( ω ω ˜ l * ) ] ,

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