## Measurement and modification of biexciton-exciton time correlations |

Optics Express, Vol. 21, Issue 8, pp. 9890-9898 (2013)

http://dx.doi.org/10.1364/OE.21.009890

Acrobat PDF (1172 KB)

### Abstract

Photons which are generated in a two-photon cascade process have an underlying time correlation since the spontaneous emission of the upper level populates the intermediate state. This correlation leads to a reduction of the purity of the photon emitted from the intermediate state. Here we characterize this time correlation for the biexciton-exciton cascade of an InAs/GaAs quantum dot. We show that the correlation can be reduced by tuning the biexciton transition in resonance to a planar distributed Bragg reflector cavity. The enhanced and inhibited emission into the cavity accelerates the biexciton emission and slows down the exciton emission thus reduces the correlation and increases the purity of the exciton photon. This is essential for schemes like creating time-bin entangled photon pairs from quantum dot systems.

© 2013 OSA

## 1. Introduction

1. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger “Quantum cryptography with entangled photons,” Phys. Rev. Lett. **84**, 4729–4732 (2000) [CrossRef] [PubMed] .

3. H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. **81**, 5932–5935 (1998) [CrossRef] .

4. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. Sergienko, and Y. Shih “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. **75**, 4337–4341 (1995) [CrossRef] [PubMed] .

6. O. Benson, C. Santori, M. Pelton, and Y. Yamamoto “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. **84**, 2513–2516 (2000) [CrossRef] [PubMed] .

9. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science **290**, 2282–2285 (2000) [CrossRef] [PubMed] .

10. N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. **96**, 130501 (2006) [CrossRef] [PubMed] .

12. A. Muller, W. Fang, J. Lawall, and G. S. Solomon “Creating polarization-entangled photon pairs from a semiconductor quantum dot using the optical Stark effect,” Phys. Rev. Lett. **103**, 217402 (2009) [CrossRef] .

13. R. J. Young, R. M. Stevenson, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields “Improved fidelity of triggered entangled photons from single quantum dots,” New. J. Phys. **8**, 29 (2006) [CrossRef] .

14. J. E. Avron, G. Bisker, D. Gershoni, N. H. Lindner, and E. A. Meirom “Entanglement on demand through time
reordering,” Phys. Rev. Lett. **100**, 120501 (2008) [CrossRef] .

15. N. Gisin, R. Passy, J. Bishoff, and B. Perny “Experimental investigations of the statistical properties of polarization mode dispersion in single mode fibers,” IEEE Photon. Technol. Lett. **5**, 819–821 (1993) [CrossRef] .

16. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin “Violation of Bell inequalities by photons more than 10 Km apart,” Phys. Rev. Lett. **81**, 3563–3566 (1998) [CrossRef] .

17. D. Stucki, H. Zbinden, and N. Gisin “A Fabry-Perot-like two-photon interferometer for high-dimensional time-bin entanglement,” J. Mod. Opt. **52**, 2637–2648 (2005) [CrossRef] .

18. C. Simon and J.-P. Poizat “Creating single time-bin-entangled photon pairs,” Phys. Rev. Lett. **94**, 030502 (2005) [CrossRef] [PubMed] .

19. P. K. Pathak and S. Hughes “Coherent generation of time-bin entangled photon pairs using the biexciton cascade and cavity-assisted piecewise adiabatic passage,” Phys. Rev. B **83**, 245301 (2011) [CrossRef] .

## 2. Influence of temporal correlations on time-bin entanglement

*|early〉*

_{b}*is not a product state, but a state of the form: where*

_{x}*t*

_{b(x)}is the emission time of the biexciton (exciton) photon and

*τ*

_{b(x)}is the lifetime of the biexciton (exciton) state [18

18. C. Simon and J.-P. Poizat “Creating single time-bin-entangled photon pairs,” Phys. Rev. Lett. **94**, 030502 (2005) [CrossRef] [PubMed] .

*θ*(

*t*−

_{x}*t*) describes the temporal ordering of the two emitted photons and leads to an entanglement of the single cascade, which necessarily reduces the purity of the exciton state and therefore impedes multi-pair experiments [18

_{b}18. C. Simon and J.-P. Poizat “Creating single time-bin-entangled photon pairs,” Phys. Rev. Lett. **94**, 030502 (2005) [CrossRef] [PubMed] .

**94**, 030502 (2005) [CrossRef] [PubMed] .

*ρ*is the reduced density matrix of the exciton for a single cascade and

_{x}*τ*

_{x(b)}is the lifetime of the exciton (biexciton) state, respectively. The matrix

*ρ*is derived by performing a partial trace of the biexciton emission time

_{x}*t*over the density matrix corresponding to the single cascade wave-function Φ(

_{b}*t*,

_{b}*t*). For multi-pair experiments to work perfectly, the purity of the exciton emission should be one [18

_{x}**94**, 030502 (2005) [CrossRef] [PubMed] .

## 3. Experimental setup

*dot1*,

*dot2*,

*dot3*) consisting of alternating layers of AlAs and GaAs. Here,

*dot1*is a randomly picked quantum dot which emits far away from the cavity resonance. For

*dot2*the biexciton is red-shifted with respect to the cavity resonance at 6 K and can be red-tuned by increasing the temperature.

*Dot3*is blue-shifted with respect to the cavity at 6 K and is in resonance with the cavity at 30 K (see Table 1). From the measured correlation we extracted the true lifetimes, whereby we mean the lifetime of a decay process regardless of the level loading dynamics, be it an excitation laser or a higher level feeding the one under consideration. As a reference we performed the same measurement with an InAs/GaAs quantum dot without a cavity (

*dot0*).

21. B. Ohnesorge, M. Bayer, A. Forchel, J. P. Reithmaier, N. A. Gippius, and S. G. Tikhodeev “Enhancement of spontaneous emission rates by three-dimensional photon confinement in Bragg microcavities,” Phys. Rev. B **56**, R4367–R4370 (1997) [CrossRef] .

22. J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature **432**, 197–200 (2004) [CrossRef] [PubMed] .

23. G. Ramon, U. Mizrahi, N. Akopian, S. Braitbart, D. Gershoni, T. L. Reinecke, B. D. Gerardot, and P. M. Petroff “Emission characteristics of quantum dots in planar microcavities,” Phys. Rev. B **73**, 205330 (2006) [CrossRef] .

## 4. Results

*dot3*at 6 K where both the transitions - the exciton and the biexciton - are out of resonance, and Fig. 3(b) shows the decay extracted from (a). The measurements resulted in a biexciton lifetime of

*τ*= 0.56(1) ns and an exciton lifetime of

_{b}*τ*= 0.66(1) ns. The resulting value for the purity is

_{x}*τ*= 0.37(2) ns and an exciton lifetime of

_{b}*τ*= 0.98(1) ns. The resulting value for the purity is

_{x}24. C. de Mello Donega, M. Bode, and A. Meijerink “Size- and temperature-dependence of exciton lifetimes in CdSe quantum dots,” Phys. Rev. B **74**, 085320 (2006) [CrossRef] .

25. J. Arlett, F. Yang, K. Hinzer, S. Fafard, Y. Feng, S. Charbonneau, and R. Leon “Temperature independent lifetime in InAlAs quantum dots,” J. Vac. Sci. Technol. B **16**, 578–581 (1998) [CrossRef] .

24. C. de Mello Donega, M. Bode, and A. Meijerink “Size- and temperature-dependence of exciton lifetimes in CdSe quantum dots,” Phys. Rev. B **74**, 085320 (2006) [CrossRef] .

*dot0*. The red square is a reference measurement from a randomly picked quantum dot (

*dot1*) on the sample with the DBR cavity. The blue filled circles represent a series of measurements on the quantum

*dot2*. Here, at the temperature 6K, the biexciton emission is red-shifted but proximate to cavity resonance. With the temperature increase the biexciton emission was tuned away from the resonance. Therefore, the value of the trace presented in Fig. 4 decreases. The open black circles are measurements for

*dot3*, where two single measurements for 6 K and 30 K were shown before. The emission from this dot is at 6 K blue shifted with respect to the cavity. With the temperature increase we can tune the biexciton emission in resonance to the cavity.

*dot3*, which could be tuned in and out of resonance with the cavity. For this we took the ratio between the unaltered lifetime of the biexciton and its enhanced lifetime. The resulting enhancement factor is

## 5. Comparison to a theoretical estimate

28. J. M. Gerard, 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 (1998) [CrossRef] .

*ω*is the transition frequency and

_{a}*μ*the transition dipole. For a quantum dot between planar cavity mirrors, such that it is in resonance with the lowest cavity mode at zero in-plane wave vector, and is taken to be localized at the maximum of the mode function, the damping rate within a cavity is Γ

*=*

_{c}*F*Γ

_{P}*. The Purcell factor is given by*

_{f}*V*

_{eff}is the effective cavity mode volume,

*λ*the cavity mode wavelength at resonance, and

_{c}*n*the refractive index of the medium. Here,

*Q*is the cavity quality factor that is defined by

*Q*=

*ω*/Δ

_{c}*ω*. From the reflection spectrum of the cavity we extracted a Q factor of 900(30). Our sample contained self-assembled InAs quantum dots of low density (≈ 10

*μ*m

^{−2}) grown by molecular beam epitaxy. The quantum dots were embedded in a distributed Bragg reflector (DBR) micro-cavity consisting of 15.5 lower and 10 upper

*λ*/4 thick DBR layer pairs of AlAs and GaAs, with a cavity mode at

*λ*= 920 nm. The physical thickness of the central cavity layer is

*L*= 542.7 nm. For an estimated Purcell factor of

*F*= 1.5 the effective mode volume is a cylinder with the height equal to the cavity length L and a diameter of 1.4

_{P}*μ*m.

## 6. Conclusion

29. 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 (2000) [CrossRef] .

30. D. Englund, I. Fushman, A. Faraon, and J. Vuckovic, “Quantum dots in photonic crystals: From quantum information processing to single photon nonlinear optics,” Photonic. Nanostruct. **7**, 56–62 (2009) [CrossRef] .

31. H. Jayakumar, A. Predojevic, T. Huber, T. Kauten, G. S. Solomon, and G. Weihs, “Deterministic photon pairs and coherent optical control of a single quantum dot,” Phys. Rev. Lett. **110**, 135505 (2013) [CrossRef] .

32. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. **82**, 2594–2597 (1999) [CrossRef] .

33. D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. **77**, 2818–2821 (1996) [CrossRef] [PubMed] .

34. W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A **59**, 169–181 (1999) [CrossRef] .

## Acknowledgments

## References and links

1. | T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger “Quantum cryptography with entangled photons,” Phys. Rev. Lett. |

2. | E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature |

3. | H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. |

4. | P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. Sergienko, and Y. Shih “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. |

5. | D. F. Walls and G. J. Milburn |

6. | O. Benson, C. Santori, M. Pelton, and Y. Yamamoto “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. |

7. | C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto “Triggered single photons from a quantum dot,” Phys. Rev. Lett. |

8. | J. Sabarinathan, P. Bhattacharya, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel “An electrically injected InAs/GaAs quantum-dot photonic crystal microcavity light-emitting diode,” Appl. Phys. Lett. |

9. | P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science |

10. | N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. |

11. | A. Dousse, J. Suffczynski, A. Beveratos, O. Krebs, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart “Ultrabright source of entangled photon pairs,” Nature |

12. | A. Muller, W. Fang, J. Lawall, and G. S. Solomon “Creating polarization-entangled photon pairs from a semiconductor quantum dot using the optical Stark effect,” Phys. Rev. Lett. |

13. | R. J. Young, R. M. Stevenson, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields “Improved fidelity of triggered entangled photons from single quantum dots,” New. J. Phys. |

14. | J. E. Avron, G. Bisker, D. Gershoni, N. H. Lindner, and E. A. Meirom “Entanglement on demand through time
reordering,” Phys. Rev. Lett. |

15. | N. Gisin, R. Passy, J. Bishoff, and B. Perny “Experimental investigations of the statistical properties of polarization mode dispersion in single mode fibers,” IEEE Photon. Technol. Lett. |

16. | W. Tittel, J. Brendel, H. Zbinden, and N. Gisin “Violation of Bell inequalities by photons more than 10 Km apart,” Phys. Rev. Lett. |

17. | D. Stucki, H. Zbinden, and N. Gisin “A Fabry-Perot-like two-photon interferometer for high-dimensional time-bin entanglement,” J. Mod. Opt. |

18. | C. Simon and J.-P. Poizat “Creating single time-bin-entangled photon pairs,” Phys. Rev. Lett. |

19. | P. K. Pathak and S. Hughes “Coherent generation of time-bin entangled photon pairs using the biexciton cascade and cavity-assisted piecewise adiabatic passage,” Phys. Rev. B |

20. | G. Jaeger |

21. | B. Ohnesorge, M. Bayer, A. Forchel, J. P. Reithmaier, N. A. Gippius, and S. G. Tikhodeev “Enhancement of spontaneous emission rates by three-dimensional photon confinement in Bragg microcavities,” Phys. Rev. B |

22. | J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature |

23. | G. Ramon, U. Mizrahi, N. Akopian, S. Braitbart, D. Gershoni, T. L. Reinecke, B. D. Gerardot, and P. M. Petroff “Emission characteristics of quantum dots in planar microcavities,” Phys. Rev. B |

24. | C. de Mello Donega, M. Bode, and A. Meijerink “Size- and temperature-dependence of exciton lifetimes in CdSe quantum dots,” Phys. Rev. B |

25. | J. Arlett, F. Yang, K. Hinzer, S. Fafard, Y. Feng, S. Charbonneau, and R. Leon “Temperature independent lifetime in InAlAs quantum dots,” J. Vac. Sci. Technol. B |

26. | E. M. Purcell “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. |

27. | S. Haroche, “Cavity quantum electrodynamics,” |

28. | J. M. Gerard, 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. |

29. | 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. |

30. | D. Englund, I. Fushman, A. Faraon, and J. Vuckovic, “Quantum dots in photonic crystals: From quantum information processing to single photon nonlinear optics,” Photonic. Nanostruct. |

31. | H. Jayakumar, A. Predojevic, T. Huber, T. Kauten, G. S. Solomon, and G. Weihs, “Deterministic photon pairs and coherent optical control of a single quantum dot,” Phys. Rev. Lett. |

32. | J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. |

33. | D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. |

34. | W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A |

**OCIS Codes**

(000.1600) General : Classical and quantum physics

(130.5990) Integrated optics : Semiconductors

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 19, 2013

Revised Manuscript: April 4, 2013

Manuscript Accepted: April 4, 2013

Published: April 12, 2013

**Citation**

Tobias Huber, Ana Predojević, Hashem Zoubi, Harishankar Jayakumar, Glenn S. Solomon, and Gregor Weihs, "Measurement and modification of biexciton-exciton time correlations," Opt. Express **21**, 9890-9898 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9890

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### References

- T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000). [CrossRef] [PubMed]
- E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature409, 46–52 (2001). [CrossRef] [PubMed]
- H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932–5935 (1998). [CrossRef]
- P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. Sergienko, and Y. Shih “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75, 4337–4341 (1995). [CrossRef] [PubMed]
- D. F. Walls and G. J. MilburnQuantum Optics (Springer, 1994).
- O. Benson, C. Santori, M. Pelton, and Y. Yamamoto “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett.84, 2513–2516 (2000). [CrossRef] [PubMed]
- C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto “Triggered single photons from a quantum dot,” Phys. Rev. Lett.86, 1502–1505 (2001). [CrossRef] [PubMed]
- J. Sabarinathan, P. Bhattacharya, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel “An electrically injected InAs/GaAs quantum-dot photonic crystal microcavity light-emitting diode,” Appl. Phys. Lett.81, 3876–3878 (2002). [CrossRef]
- P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science290, 2282–2285 (2000). [CrossRef] [PubMed]
- N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett.96, 130501 (2006). [CrossRef] [PubMed]
- A. Dousse, J. Suffczynski, A. Beveratos, O. Krebs, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart “Ultrabright source of entangled photon pairs,” Nature466, 217–220 (2010). [CrossRef] [PubMed]
- A. Muller, W. Fang, J. Lawall, and G. S. Solomon “Creating polarization-entangled photon pairs from a semiconductor quantum dot using the optical Stark effect,” Phys. Rev. Lett.103, 217402 (2009). [CrossRef]
- R. J. Young, R. M. Stevenson, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields “Improved fidelity of triggered entangled photons from single quantum dots,” New. J. Phys.8, 29 (2006). [CrossRef]
- J. E. Avron, G. Bisker, D. Gershoni, N. H. Lindner, and E. A. Meirom “Entanglement on demand through time reordering,” Phys. Rev. Lett.100, 120501 (2008). [CrossRef]
- N. Gisin, R. Passy, J. Bishoff, and B. Perny “Experimental investigations of the statistical properties of polarization mode dispersion in single mode fibers,” IEEE Photon. Technol. Lett.5, 819–821 (1993). [CrossRef]
- W. Tittel, J. Brendel, H. Zbinden, and N. Gisin “Violation of Bell inequalities by photons more than 10 Km apart,” Phys. Rev. Lett.81, 3563–3566 (1998). [CrossRef]
- D. Stucki, H. Zbinden, and N. Gisin “A Fabry-Perot-like two-photon interferometer for high-dimensional time-bin entanglement,” J. Mod. Opt.52, 2637–2648 (2005). [CrossRef]
- C. Simon and J.-P. Poizat “Creating single time-bin-entangled photon pairs,” Phys. Rev. Lett.94, 030502 (2005). [CrossRef] [PubMed]
- P. K. Pathak and S. Hughes “Coherent generation of time-bin entangled photon pairs using the biexciton cascade and cavity-assisted piecewise adiabatic passage,” Phys. Rev. B83, 245301 (2011). [CrossRef]
- G. JaegerQuantum Information (Springer, 2007).
- B. Ohnesorge, M. Bayer, A. Forchel, J. P. Reithmaier, N. A. Gippius, and S. G. Tikhodeev “Enhancement of spontaneous emission rates by three-dimensional photon confinement in Bragg microcavities,” Phys. Rev. B56, R4367–R4370 (1997). [CrossRef]
- J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432, 197–200 (2004). [CrossRef] [PubMed]
- G. Ramon, U. Mizrahi, N. Akopian, S. Braitbart, D. Gershoni, T. L. Reinecke, B. D. Gerardot, and P. M. Petroff “Emission characteristics of quantum dots in planar microcavities,” Phys. Rev. B73, 205330 (2006). [CrossRef]
- C. de Mello Donega, M. Bode, and A. Meijerink “Size- and temperature-dependence of exciton lifetimes in CdSe quantum dots,” Phys. Rev. B74, 085320 (2006). [CrossRef]
- J. Arlett, F. Yang, K. Hinzer, S. Fafard, Y. Feng, S. Charbonneau, and R. Leon “Temperature independent lifetime in InAlAs quantum dots,” J. Vac. Sci. Technol. B16, 578–581 (1998). [CrossRef]
- E. M. Purcell “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).
- S. Haroche, “Cavity quantum electrodynamics,” Fundamental systems in quantum optics, J. Dalibard, J. M. Raimond, and J. Zinn-Justin (eds.), Les Houches summer school, Session LIII, p.767 (North-Holland, Amsterdam, 1992).
- J. M. Gerard, 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 (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 (2000). [CrossRef]
- D. Englund, I. Fushman, A. Faraon, and J. Vuckovic, “Quantum dots in photonic crystals: From quantum information processing to single photon nonlinear optics,” Photonic. Nanostruct.7, 56–62 (2009). [CrossRef]
- H. Jayakumar, A. Predojevic, T. Huber, T. Kauten, G. S. Solomon, and G. Weihs, “Deterministic photon pairs and coherent optical control of a single quantum dot,” Phys. Rev. Lett.110, 135505 (2013). [CrossRef]
- J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett.82, 2594–2597 (1999). [CrossRef]
- D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett.77, 2818–2821 (1996). [CrossRef] [PubMed]
- W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,” Phys. Rev. A59, 169–181 (1999). [CrossRef]

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