## Cavity-assisted emission of polarization-entangled photons from biexcitons in quantum dots with fine-structure splitting |

Optics Express, Vol. 20, Issue 5, pp. 5335-5342 (2012)

http://dx.doi.org/10.1364/OE.20.005335

Acrobat PDF (734 KB)

### Abstract

We study the quantum properties and statistics of photons emitted by a quantum-dot biexciton inside a cavity. In the biexciton-exciton cascade, fine-structure splitting between exciton levels degrades polarization-entanglement for the emitted pair of photons. However, here we show that the polarization-entanglement can be preserved in such a system through simultaneous emission of two degenerate photons into cavity modes tuned to half the biexciton energy. Based on detailed theoretical calculations for realistic quantum-dot and cavity parameters, we quantify the degree of achievable entanglement.

© 2012 OSA

## 1. Introduction

1. K. Edamatsu, “Entangled photons: generation,
observation, and characterization,” Jpn. J.
Appl. Phys. **46**, 7175–7187
(2007). [CrossRef]

2. K.-I. Yoshino, T. Aoki, and A. Furusawa, “Generation of continuous-wave broadband
entangled beams using periodically poled lithium niobate
waveguides,” Appl. Phys. Lett. **90**, 041111 (2007). [CrossRef]

3. A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from
semiconductors,” Nat. Photonics **2**, 238–241
(2008). [CrossRef]

4. S. Strauf, N. G. Stoltz, M. T. Rakher, L. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single photon source
with polarization control,” Nat.
Photonics **1**, 704–708
(2007). [CrossRef]

5. M. Mehta, D. Reuter, A. D. Wieck, S. Michaelis de Vasconcellos, A. Zrenner, and C. Meier, “An intentionally positioned (In,Ga)As
quantum dot in a micron sized light emitting diode,”
Appl. Phys. Lett. **97**, 143101 (2010). [CrossRef]

6. J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations
between individual photon emission events of a microcavity
laser,” Nature **460**, 245–249
(2009). [CrossRef] [PubMed]

8. 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. 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 **466**, 217–220
(2010). [CrossRef] [PubMed]

10. R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon
pairs from a single quantum dot up to 30 k,”
New J. Phys. **9**, 315 (2007). [CrossRef]

13. A. Carmele and A. Knorr, “Analytical solution of the
quantum-state tomography of the biexciton cascade in semiconductor quantum
dots: pure dephasing does not affect entanglement,”
Phys. Rev. B **84**, 075328 (2011). [CrossRef]

14. A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced
with high-symmetry site-controlled quantum dots,”
Nat. Photonics **4**, 302–306
(2010). [CrossRef]

15. E. Stock, T. Warming, I. Ostapenko, S. Rodt, A. Schliwa, J. A. Töfflinger, A. Lochmann, A. I. Toropov, S. A. Moshchenko, D. V. Dmitriev, V. A. Haisler, and D. Bimberg, “Single-photon emission from InGaAs
quantum dots grown on (111) GaAs,” Appl.
Phys. Lett. **96**, 093112 (2010). [CrossRef]

16. L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting
in InAs/InP quantum dots offering an efficient on-demand entangled 1.55
– μm photon emitter,” Phys.
Rev. Lett. **101**, 157405 (2008). [CrossRef] [PubMed]

17. B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, D. Granados, J. M. Garcia, K. Kowalik, O. Krebs, K. Karrai, A. Badolato, and P. M. Petroff, “Manipulating exciton fine structure in
quantum dots with a lateral electric field,”
Appl. Phys. Lett. **90**, 041101 (2007). [CrossRef]

18. R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered
entangled photon pairs,” Nature **439**, 179–182
(2006). [CrossRef] [PubMed]

19. S. Seidl, M. Kroner, A. Högele, K. Karrai, R. J. Warburton, A. Badolato, and P. M. Petroff, “Effect of uniaxial stress on excitons
in a self-assembled quantum dot,” Appl.
Phys. Lett. **88**, 203113 (2006). [CrossRef]

## 2. Theory & methods

10. R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon
pairs from a single quantum dot up to 30 k,”
New J. Phys. **9**, 315 (2007). [CrossRef]

11. F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled
photon pairs by a quantum-dot cascade decay,”
Phys. Rev. B **74**, 235310 (2006). [CrossRef]

20. E. del Valle, A. Gonzalez-Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a
quantum dot in a microcavity,” New J.
Phys. **13**, 113014 (2011). [CrossRef]

22. Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a
single quantum dot,” Phys. Rev.
Lett. **107**, 233602 (2011). [CrossRef] [PubMed]

*E*

*, of the excitons,*

_{G}*E*

*,*

_{H}*E*

*, respectively, and of the biexciton,*

_{V}*E*

*, in the respective electronic configurations |*

_{B}*G*〉, |

*X*

*〉, |*

_{H}*X*

*〉 and |*

_{V}*B*〉. The second line represents the free part of the photon field in the two orthogonal cavity modes at frequencies

*ω*

*with photon creation and annihilation operators,*

_{i}*b*

*, respectively. The excitation and de-excitation of the electronic system through photon absorption or emission takes place with coupling strength*

_{i}*g*. The coupled biexciton-exciton-photon dynamics obey the following equation of motion for the system density operator

*ρ*

*in Lindblad [23*

_{s}23. G. Lindblad, “On the generators of quantum dynamical
semigroups,” Commun. Math. Phys. **48**, 119–130
(1976). [CrossRef]

*h̄/*

*κ*of the photons inside the cavity through

*χ*,

*χ*′ ∈ {

*G,X*

_{H}*, X*

_{V}*, B*} [11

11. F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled
photon pairs by a quantum-dot cascade decay,”
Phys. Rev. B **74**, 235310 (2006). [CrossRef]

24. A. Laucht, N. Hauke, J. M. Villas-Boas, F. Hofbauer, M. Kaniber, G. Böhm, and J. J. Finley, “Dephasing of exciton polaritons in
photoexcited InGaAs quantum dots in GaAs
nanocavities,” Phys. Rev. Lett. **103**, 087405 (2009). [CrossRef] [PubMed]

*i*≠

*j*[11

11. F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled
photon pairs by a quantum-dot cascade decay,”
Phys. Rev. B **74**, 235310 (2006). [CrossRef]

6. J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations
between individual photon emission events of a microcavity
laser,” Nature **460**, 245–249
(2009). [CrossRef] [PubMed]

27. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum
entanglement,” Rev. Mod. Phys. **81**, 865–942
(2009). [CrossRef]

*ρ*

*, with*

_{i,j}*i, j*=

*H,V*, which is needed for the quantum-state tomography of the emitted photon pair (

*ρ*is normalized such that tr{

*ρ*} = 1). All calculations in this work are performed for typical parameters of present high-quality QD-cavity systems. For the biexciton binding energy we use

*g*=

*h̄*/10 ps

^{−1}≈ 66

*μ*eV. The cavity modes are tuned to half the biexciton energy

*h̄*

*ω*

*≈ (*

_{i}*E*

*–*

_{B}*E*

*)/2 and a finite fine-structure splitting*

_{G}*δ*(varied from −40 to +40

*μ*eV) between exciton levels is included. We note that even for the highest cavity quality studied, no pronounced Rabi-flopping occurs at the ground-state to exciton and exciton to biexciton transitions, as those are far off-resonant from the cavity modes.

## 3. Results & discussion

*C*= 2|

*ρ*

*| (defined as in Ref. [11*

_{H,V}**74**, 235310 (2006). [CrossRef]

*g/*

*κ*(

*κ*is the loss rate of photons from the cavity). Cavity quality-factors Q are given in each panel for wavelength

*λ*= 880 nm, corresponding to InGaAs systems. Note that the cavity is tuned to the two-photon resonance of the biexciton transition unless otherwise noted and, hence, it is detuned from the single-photon biexciton and exciton transitions.

*C*= 1 is not reached for zero fine-structure splitting as our model takes into account a finite lifetime (cross-dephasing [11

**74**, 235310 (2006). [CrossRef]

*X*

*〉 and |*

_{H}*X*

*〉.*

_{V}28. T. Flissikowski, A. Betke, I. A. Akimov, and F. Henneberger, “Two-photon coherent control of a single
quantum dot,” Phys. Rev. Lett. **92**, 227401 (2004). [CrossRef] [PubMed]

17. B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, D. Granados, J. M. Garcia, K. Kowalik, O. Krebs, K. Karrai, A. Badolato, and P. M. Petroff, “Manipulating exciton fine structure in
quantum dots with a lateral electric field,”
Appl. Phys. Lett. **90**, 041101 (2007). [CrossRef]

19. S. Seidl, M. Kroner, A. Högele, K. Karrai, R. J. Warburton, A. Badolato, and P. M. Petroff, “Effect of uniaxial stress on excitons
in a self-assembled quantum dot,” Appl.
Phys. Lett. **88**, 203113 (2006). [CrossRef]

**74**, 235310 (2006). [CrossRef]

*g/*

*κ*= 0.4, for different detuning of the cavity resonance from half the biexciton energy. For

*h̄*

*ω*

*= (*

_{i}*E*

*–*

_{B}*E*

*)/2 a strongly increased probability for simultaneous emission of both photons at*

_{G}*τ*≈ 0 is clearly visible (“bunching”), whereas for

*h̄*

*ω*

*= (*

_{i}*E*

*–*

_{B}*E*

*)/2 – 0.25 meV and*

_{G}*h̄*

*ω*

*= (*

_{i}*E*

*–*

_{B}*E*

*)/2 – 0.5 meV it is more likely to have the two photons emitted with a certain time-delay. This is evidence for step-wise decay through the biexciton-exciton cascade. Spectral features of the emitted photons under similar conditions are discussed in detail in Ref. [20*

_{G}20. E. del Valle, A. Gonzalez-Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a
quantum dot in a microcavity,” New J.
Phys. **13**, 113014 (2011). [CrossRef]

## 4. Conclusions

## Acknowledgments

^{2}Paderborn Center for Parallel Computing.

## References and links

1. | K. Edamatsu, “Entangled photons: generation,
observation, and characterization,” Jpn. J.
Appl. Phys. |

2. | K.-I. Yoshino, T. Aoki, and A. Furusawa, “Generation of continuous-wave broadband
entangled beams using periodically poled lithium niobate
waveguides,” Appl. Phys. Lett. |

3. | A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from
semiconductors,” Nat. Photonics |

4. | S. Strauf, N. G. Stoltz, M. T. Rakher, L. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single photon source
with polarization control,” Nat.
Photonics |

5. | M. Mehta, D. Reuter, A. D. Wieck, S. Michaelis de Vasconcellos, A. Zrenner, and C. Meier, “An intentionally positioned (In,Ga)As
quantum dot in a micron sized light emitting diode,”
Appl. Phys. Lett. |

6. | J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations
between individual photon emission events of a microcavity
laser,” Nature |

7. | S. Strauf and F. Jahnke, “Single quantum dot
nanolaser,” Laser Photon. Rev. |

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

9. | 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 |

10. | R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon
pairs from a single quantum dot up to 30 k,”
New J. Phys. |

11. | F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled
photon pairs by a quantum-dot cascade decay,”
Phys. Rev. B |

12. | A. Carmele, F. Milde, M.-R. Dachner, M. B. Harouni, R. Roknizadeh, M. Richter, and A. Knorr, “Formation dynamics of an entangled
photon pair: a temperature-dependent analysis,”
Phys. Rev. B |

13. | A. Carmele and A. Knorr, “Analytical solution of the
quantum-state tomography of the biexciton cascade in semiconductor quantum
dots: pure dephasing does not affect entanglement,”
Phys. Rev. B |

14. | A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced
with high-symmetry site-controlled quantum dots,”
Nat. Photonics |

15. | E. Stock, T. Warming, I. Ostapenko, S. Rodt, A. Schliwa, J. A. Töfflinger, A. Lochmann, A. I. Toropov, S. A. Moshchenko, D. V. Dmitriev, V. A. Haisler, and D. Bimberg, “Single-photon emission from InGaAs
quantum dots grown on (111) GaAs,” Appl.
Phys. Lett. |

16. | L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting
in InAs/InP quantum dots offering an efficient on-demand entangled 1.55
– μm photon emitter,” Phys.
Rev. Lett. |

17. | B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, D. Granados, J. M. Garcia, K. Kowalik, O. Krebs, K. Karrai, A. Badolato, and P. M. Petroff, “Manipulating exciton fine structure in
quantum dots with a lateral electric field,”
Appl. Phys. Lett. |

18. | R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered
entangled photon pairs,” Nature |

19. | S. Seidl, M. Kroner, A. Högele, K. Karrai, R. J. Warburton, A. Badolato, and P. M. Petroff, “Effect of uniaxial stress on excitons
in a self-assembled quantum dot,” Appl.
Phys. Lett. |

20. | E. del Valle, A. Gonzalez-Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a
quantum dot in a microcavity,” New J.
Phys. |

21. | U. Hohenester, T. Volz, M. Winger, and A. Imamoglu, “Cavity-assisted two-photon decay of biexcitons,” OECS12 Conference Proceedings, page 110 (2011). |

22. | Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a
single quantum dot,” Phys. Rev.
Lett. |

23. | G. Lindblad, “On the generators of quantum dynamical
semigroups,” Commun. Math. Phys. |

24. | A. Laucht, N. Hauke, J. M. Villas-Boas, F. Hofbauer, M. Kaniber, G. Böhm, and J. J. Finley, “Dephasing of exciton polaritons in
photoexcited InGaAs quantum dots in GaAs
nanocavities,” Phys. Rev. Lett. |

25. | G. Pfanner, M. Seliger, and U. Hohenester, “Entangled photon sources based on
semiconductor quantum dots: the role of pure
dephasing,” Phys. Rev. B |

26. | H. J. Carmichael, |

27. | R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum
entanglement,” Rev. Mod. Phys. |

28. | T. Flissikowski, A. Betke, I. A. Akimov, and F. Henneberger, “Two-photon coherent control of a single
quantum dot,” Phys. Rev. Lett. |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5565) Quantum optics : Quantum communications

(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: January 13, 2012

Revised Manuscript: February 13, 2012

Manuscript Accepted: February 13, 2012

Published: February 17, 2012

**Citation**

Stefan Schumacher, Jens Förstner, Artur Zrenner, Matthias Florian, Christopher Gies, Paul Gartner, and Frank Jahnke, "Cavity-assisted emission of polarization-entangled photons from biexcitons in quantum dots with fine-structure splitting," Opt. Express **20**, 5335-5342 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5335

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### References

- K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys.46, 7175–7187 (2007). [CrossRef]
- K.-I. Yoshino, T. Aoki, and A. Furusawa, “Generation of continuous-wave broadband entangled beams using periodically poled lithium niobate waveguides,” Appl. Phys. Lett.90, 041111 (2007). [CrossRef]
- A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of two-photon emission from semiconductors,” Nat. Photonics2, 238–241 (2008). [CrossRef]
- S. Strauf, N. G. Stoltz, M. T. Rakher, L. Coldren, P. M. Petroff, and D. Bouwmeester, “High-frequency single photon source with polarization control,” Nat. Photonics1, 704–708 (2007). [CrossRef]
- M. Mehta, D. Reuter, A. D. Wieck, S. Michaelis de Vasconcellos, A. Zrenner, and C. Meier, “An intentionally positioned (In,Ga)As quantum dot in a micron sized light emitting diode,” Appl. Phys. Lett.97, 143101 (2010). [CrossRef]
- J. Wiersig, C. Gies, F. Jahnke, M. Assmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature460, 245–249 (2009). [CrossRef] [PubMed]
- S. Strauf and F. Jahnke, “Single quantum dot nanolaser,” Laser Photon. Rev.5, 607–633 (2011).
- 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]
- 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]
- R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon pairs from a single quantum dot up to 30 k,” New J. Phys.9, 315 (2007). [CrossRef]
- F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled photon pairs by a quantum-dot cascade decay,” Phys. Rev. B74, 235310 (2006). [CrossRef]
- A. Carmele, F. Milde, M.-R. Dachner, M. B. Harouni, R. Roknizadeh, M. Richter, and A. Knorr, “Formation dynamics of an entangled photon pair: a temperature-dependent analysis,” Phys. Rev. B81, 195319 (2010).
- A. Carmele and A. Knorr, “Analytical solution of the quantum-state tomography of the biexciton cascade in semiconductor quantum dots: pure dephasing does not affect entanglement,” Phys. Rev. B84, 075328 (2011). [CrossRef]
- A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics4, 302–306 (2010). [CrossRef]
- E. Stock, T. Warming, I. Ostapenko, S. Rodt, A. Schliwa, J. A. Töfflinger, A. Lochmann, A. I. Toropov, S. A. Moshchenko, D. V. Dmitriev, V. A. Haisler, and D. Bimberg, “Single-photon emission from InGaAs quantum dots grown on (111) GaAs,” Appl. Phys. Lett.96, 093112 (2010). [CrossRef]
- L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an efficient on-demand entangled 1.55 – μm photon emitter,” Phys. Rev. Lett.101, 157405 (2008). [CrossRef] [PubMed]
- B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, D. Granados, J. M. Garcia, K. Kowalik, O. Krebs, K. Karrai, A. Badolato, and P. M. Petroff, “Manipulating exciton fine structure in quantum dots with a lateral electric field,” Appl. Phys. Lett.90, 041101 (2007). [CrossRef]
- R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature439, 179–182 (2006). [CrossRef] [PubMed]
- S. Seidl, M. Kroner, A. Högele, K. Karrai, R. J. Warburton, A. Badolato, and P. M. Petroff, “Effect of uniaxial stress on excitons in a self-assembled quantum dot,” Appl. Phys. Lett.88, 203113 (2006). [CrossRef]
- E. del Valle, A. Gonzalez-Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a quantum dot in a microcavity,” New J. Phys.13, 113014 (2011). [CrossRef]
- U. Hohenester, T. Volz, M. Winger, and A. Imamoglu, “Cavity-assisted two-photon decay of biexcitons,” OECS12 Conference Proceedings, page 110 (2011).
- Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a single quantum dot,” Phys. Rev. Lett.107, 233602 (2011). [CrossRef] [PubMed]
- G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys.48, 119–130 (1976). [CrossRef]
- A. Laucht, N. Hauke, J. M. Villas-Boas, F. Hofbauer, M. Kaniber, G. Böhm, and J. J. Finley, “Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities,” Phys. Rev. Lett.103, 087405 (2009). [CrossRef] [PubMed]
- G. Pfanner, M. Seliger, and U. Hohenester, “Entangled photon sources based on semiconductor quantum dots: the role of pure dephasing,” Phys. Rev. B78, 195410 (2008).
- H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, 2002), 2nd ed.
- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys.81, 865–942 (2009). [CrossRef]
- T. Flissikowski, A. Betke, I. A. Akimov, and F. Henneberger, “Two-photon coherent control of a single quantum dot,” Phys. Rev. Lett.92, 227401 (2004). [CrossRef] [PubMed]

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