Abstract

In this paper, we introduce a hybrid three-dimensional photonic-crystal cavity with an embedded quantum dot, and investigate the dynamics of the cavity-quantum dot system. The general procedure of modelling such a practical structure is presented, where the master equation is solved on the basis of the parameters obtained from defect mode analyses. According to our study, this structure can be engineered to achieve a nearly deterministic single photon gun. The excitation power is found to have an optimal value in terms of photon emission efficiency. Large excitation pulse duration is believed to cause a spurious peak in the second-order coherence measurement.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phy. Rev. Lett. 58, 2059 (1987).
    [CrossRef]
  2. O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O�??Brien, P.D. Dapkus, and I. Kim, �??Two-dimensional photonic band-gap defect mode laser,�?? Science 284, 1819 (1999).
    [CrossRef] [PubMed]
  3. M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G.S. Solomon, J. Plant and Y. Yamamoto, �??Efficient source of single photons: a single quantum dot in a micropost microcavity,�?? Phys. Rev. Lett. 89, 233602 (2002).
    [CrossRef] [PubMed]
  4. C. Santori, D. Fattal, J. Vuckovic, G.S. Solomon, �??Indistinguishable photons from a single-photon device,�?? Nature 419, 594 (2002).
    [CrossRef] [PubMed]
  5. H. Kimble, �??Structures and dynamics,�?? in cavity quantum electrodynamics, P Berman, ed. (Academic press,1994)
  6. O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, �??Regulated and entangled photons from a single quantum dot,�?? Phys. Rev. Lett. 84, 2513 (2000).
    [CrossRef] [PubMed]
  7. J. Vuckovic and Y. Yamamoto, �??Photonic-crystal microcavities for cavity quantum electrodynamics with a single quantum dot,�?? Appl. Phys. Lett. 82, 2374 (2003).
    [CrossRef]
  8. A. Imamoglu, D. Awschalom, G. Burkard, D.P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, �??Quantum information processing using quantum dot spins and cavity QED,�?? Phys. Rev. Lett. 83, 4204 (1999).
    [CrossRef]
  9. M. Pelton, J. Vuckovic, G. Solomon, A. Scherer, and Y. Yamamoto, �??Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,�?? IEEE J. Quantum. Electron. 38, 170 (2002).
    [CrossRef]
  10. O. Painter, J. Vuckovic, and A. Scherer, �??Defect modes of a two-dimensional photonic-crystal in an optically thin dielectric slab,�?? J. Opt. Soc. Am. B 16, 275 (1999).
    [CrossRef]
  11. 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]
  12. G. Solomon, M. Pelton, and Y. Yamamoto, �??Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity,�?? Phys. Rev. Lett. 86, 3903 (2001).
    [CrossRef] [PubMed]
  13. A. Kiraz, C. Reese, B. Gayral, L. Zhang, W. Schoenfeld, B. Gerardot, P. Petroff, E. Hu, and A. Imamoglu, �??Cavity-quantum electrodynamics with quantum dots,�?? J. Opt. B 5, 129 (2003).
    [CrossRef]
  14. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, �??Design of photonic-crystal microcavities for cavity QED,�?? Phys. Rev. E 65, 016608 (2001).
    [CrossRef]
  15. J. Vuckovic, M. Pelton, A. Scherer, and Y. Yamamoto, �??Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,�?? Phys. Rev. A 66, 023808 (2002).
    [CrossRef]
  16. S. Guo and S. Albin, �??Numerical techniques for excitation and analysis of defect modes in photoniccrystals,�?? Opt. Express 11, 1080 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1080">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1080.</a>
    [CrossRef] [PubMed]
  17. D. Walls and G. Milburn, Quantum Optics (Springer, 1994).
  18. C.K. Law and H.J. Kimble, �??Deterministic generation of a bit-stream of single-photon pulses,�?? J. Mod. Opt. 44, 2067 (1997).
  19. M.B. Plenio and P.L. Knight, �??The quantum-jump approach to dissipative dynamics in quantum optics,�?? Rev. Mod. Phys. 70, 101 (1998).
    [CrossRef]
  20. E. Purcell, �??Spontaneous emission probabilities at radio frequencies,�?? Phys. Rev. 69, 681 (1946).
  21. 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]
  22. J. Gerard and B. Gayral, �??Strong Purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities,�?? J. Light. Tech. 17, 2089 (1999).
    [CrossRef]
  23. Ph. Lalanne, S. Mias, and J.P. Hugonin, �??Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic-crystal microcavities,�?? Opt. Express 12, 458 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-458.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-458.</a>
    [CrossRef] [PubMed]
  24. S. Johnson, S. Fan, A. Mekis, and J. Joannopoulos, �??Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,�?? Appl. Phys. Lett. 78, 3388 (2001).
    [CrossRef]
  25. P. Grangier, G. Reymond, and Schlosser, �??Implementations of quantum computing using cavity quantum electrodynamics schemes,�?? Fortschr. Phys. 48, 859 (2000).
    [CrossRef]

Appl. Phys. Lett. (2)

J. Vuckovic and Y. Yamamoto, �??Photonic-crystal microcavities for cavity quantum electrodynamics with a single quantum dot,�?? Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

S. Johnson, S. Fan, A. Mekis, and J. Joannopoulos, �??Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,�?? Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

Fortschr. Phys. (1)

P. Grangier, G. Reymond, and Schlosser, �??Implementations of quantum computing using cavity quantum electrodynamics schemes,�?? Fortschr. Phys. 48, 859 (2000).
[CrossRef]

IEEE J. Quantum. Electron. (1)

M. Pelton, J. Vuckovic, G. Solomon, A. Scherer, and Y. Yamamoto, �??Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors,�?? IEEE J. Quantum. Electron. 38, 170 (2002).
[CrossRef]

J. Light Tech. (1)

J. Gerard and B. Gayral, �??Strong Purcell effect for InAs quantum boxes in three-dimensional solid-state microcavities,�?? J. Light. Tech. 17, 2089 (1999).
[CrossRef]

J. Mod. Opt. (1)

C.K. Law and H.J. Kimble, �??Deterministic generation of a bit-stream of single-photon pulses,�?? J. Mod. Opt. 44, 2067 (1997).

J. Opt. B (1)

A. Kiraz, C. Reese, B. Gayral, L. Zhang, W. Schoenfeld, B. Gerardot, P. Petroff, E. Hu, and A. Imamoglu, �??Cavity-quantum electrodynamics with quantum dots,�?? J. Opt. B 5, 129 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

C. Santori, D. Fattal, J. Vuckovic, G.S. Solomon, �??Indistinguishable photons from a single-photon device,�?? Nature 419, 594 (2002).
[CrossRef] [PubMed]

Opt. Express (2)

Phy. Rev. Lett. (1)

E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phy. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Phys. Rev. (1)

E. Purcell, �??Spontaneous emission probabilities at radio frequencies,�?? Phys. Rev. 69, 681 (1946).

Phys. Rev. A (1)

J. Vuckovic, M. Pelton, A. Scherer, and Y. Yamamoto, �??Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,�?? Phys. Rev. A 66, 023808 (2002).
[CrossRef]

Phys. Rev. E (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, �??Design of photonic-crystal microcavities for cavity QED,�?? Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

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]

G. Solomon, M. Pelton, and Y. Yamamoto, �??Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity,�?? Phys. Rev. Lett. 86, 3903 (2001).
[CrossRef] [PubMed]

A. Imamoglu, D. Awschalom, G. Burkard, D.P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, �??Quantum information processing using quantum dot spins and cavity QED,�?? Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G.S. Solomon, J. Plant and Y. Yamamoto, �??Efficient source of single photons: a single quantum dot in a micropost microcavity,�?? Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, �??Regulated and entangled photons from a single quantum dot,�?? Phys. Rev. Lett. 84, 2513 (2000).
[CrossRef] [PubMed]

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]

Rev. Mod. Phys. (1)

M.B. Plenio and P.L. Knight, �??The quantum-jump approach to dissipative dynamics in quantum optics,�?? Rev. Mod. Phys. 70, 101 (1998).
[CrossRef]

Science (1)

O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O�??Brien, P.D. Dapkus, and I. Kim, �??Two-dimensional photonic band-gap defect mode laser,�?? Science 284, 1819 (1999).
[CrossRef] [PubMed]

Other (2)

H. Kimble, �??Structures and dynamics,�?? in cavity quantum electrodynamics, P Berman, ed. (Academic press,1994)

D. Walls and G. Milburn, Quantum Optics (Springer, 1994).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

The schematic view of the photonic-crystal. The darker regions represent GaAs, and the brighter ones represent AlAs. Both a complete photonic-crystal (a) and the photonic-crystal cavity (b) are shown.

Fig. 2.
Fig. 2.

Normalized amplitude of Ex of x-dipole mode in the central xy-plane where the quantum dot is located (a) and in a vertical slice with respect to y axis (b). The frequency of the mode is a/λ=0.263. The structural parameters are as follows: p=8a/15, s=16a/15, the refractive index nGaAs=3.57 and nAlAs=2.94.

Fig. 3.
Fig. 3.

The average photon number detected during time interval from 0 to t. The parameters are (g, κ, γ0 , r 0)=(441,1678,0.56,500) GHz and 2T 0=3 ps.

Fig. 4.
Fig. 4.

Dependence of the saturation value p(+∞) on peak pump rate r 0 with 2T 0=3 ps and 6 ps.

Fig. 5.
Fig. 5.

The pulse duration dependence of P max

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

V = ∫∫∫ ε ( r ) E ( r ) 2 d 3 r max [ ε ( r ) E ( r ) 2 ] ,
g = μ ħ ħ ω 2 εV = γ 0 2 V 0 V ,
H = ħ g ( σ a + a σ ) + ħ r ( t ) ( σ + σ ) ,
d dt ρ = i ħ [ H , ρ ] + κ ( 2 a ρ a a ρ a a ) + γ 2 ( 2 σρ σ σ σρ ρσ σ )
P ( t ) 2 κ 0 t a ( τ ) a ( τ ) d τ
r ( t ) = r 0 exp { ( t 3 T 0 ) 2 T 0 2 }
H = H iħκ a a γ 0 2 σ σ .
ψ ( t ) = a 1 ( t ) G , 0 + a 2 ( t ) X , 0 + a 3 ( t ) G , 1 ,
i a ˙ 1 = r ( t ) a 2
i a ˙ 2 = r ( t ) a 1 + g a 3 i γ 0 2 a 2
i a ˙ 3 = g a 2 i κ a 3 ,
a 3 g a 2
a 2 { sin ( r 0 t ) t < T sin ( r 0 T ) exp { ( g 2 κ + γ 0 2 ) t } t T
a 1 i 0 t r ( t ) a 2 ( t ) d t .
P ( t ) 2 κ 0 t a 3 ( t ) 2 d t sin 2 ( r 0 T ) F F + 1 { 1 exp [ ( 2 g 2 κ + γ 0 ) t ] }
P ( t ) g 2 (κ γ 0 )1 t+ sin 2 ( r 0 T )

Metrics