Abstract

We calculate the integrated-pulse quantum efficiency of single-photon sources in the cavity quantum electrodynamics (QED) strong-coupling regime. An analytical expression for the quantum efficiency is obtained in the Weisskopf-Wigner approximation. Optimal conditions for a high quantum efficiency and a temporally localized photon emission rate are examined. We show the condition under which the earlier result of Law and Kimble [J. Mod. Opt. 44, 2067 (1997)] can be used as the first approximation to our result.

© 2005 Optical Society of America

1. Introduction

Various implementations of single-photon sources (SPS) based on atom-like emitters have been reported based on different systems in the last three decades, such as calcium atoms [2], single ions in traps [3], single molecules [4], a color center in diamond[5], and semiconductor nanocrystals [6] or quantum dots (QD) [7, 8]. The need for efficient single-photon sources, however, is still a major challenge in the context of quantum information processing [9, 10]. In order to efficiently produce single photons on demand, the single quantum emitter is coupled to a resonant high-finesse optical cavity. A cavity can channel the spontaneously emitted photons into a well-defined spatial mode and in a desired direction to improve the collection efficiency, and can alter the spectral width of the emission. It can also provide an environment where dissipative mechanisms are overcome so that a pure-quantum-state emission takes place. A major question is what is the quantum efficiency (QE) of the emission from such systems.

Depending on the ratios of the coherent interaction rate g 0 between the quantum-emitter and cavity, to the intracavity field decay rate 2κ, and to the emitter population decay rate 2γ, we can distinguish two regimes of coupling between the emitter and the cavity: strong coupling for g 0 > κ,γ and weak coupling for g 0 < κ,γ. The realizations of cavity-QED strong coupling in the atom-cavity [11] and QD-cavity systems [12–14] allow researchers to deterministically generate single photons [15, 16]. Single-atom lasers in the strong-coupling regime have also been studied [17]. While not in the strong-coupling regime, Santori et al. [18] showed the ability to produce largely indistinguishable photons by a semiconductor QD in a microcavity using a large Purcell effect [19]. The QE (ηq ) of SPS, which is intrinsic to the composite quantum system, can be different in these two regimes because the dynamics of the composite system is different. The overall efficiency of SPS will also depend on the excitation efficiency, collection efficiency and detection efficiency, which are not intrinsic to the composite quantum system; however, they can be greatly affected by the energy structure of the quantum emitter and the geometry of the cavity. Qualitative discussions of different efficiencies based on a particular system in the Purcell (bad-cavity) regime have been reported in the literature elsewhere [20].

In this paper we calculate the integrated-pulse QE of SPS in the cavity QED strong-coupling regime based on the solutions of the probability amplitudes in the Weisskopf-Wigner approximation (WWA) [21]. We find that the QE equals

ηq=[g02(g02+κγ)]·[κ(κ+γ)].

We show the condition under which earlier result associated with Law and Kimble et al. in [1] can be used as the first approximation to this more complete result. We also establish the connection between our analytical results and the qualitative discussions of Pelton et al. in [20].

2. Probability-amplitude method in the Weisskopf-Wigner approximation

Consider the interaction of a quantized radiation field with a two-level emitter located at an antinode of the field in an optical microcavity, as in Fig. 1. M1 is a perfect 100%-reflecting mirror and M2 is a partially transparent one, from which a sequence of single photons-on-demand emerges.

 

Fig. 1. Schematic description of a lossy two-level emitter interacting with a single mode in a leaky optical cavity. g 0 is the coupling constant between the emitter and the cavity field. Ap , Ap* and Bk Bk* are the coupling constants between the emitter, a single photon and their respective reservoir (R 1, R 2) fields.

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The interaction Hamiltonian ĤI in the interaction picture for this system in the dipole approximation and rotating-wave approximation is [22],

ĤI(t)=ħg0(σ̂+âeiΔt+h.c.)+ħp(Ap*σ̂d̂p+eiδpt+h.c.)+ħk(Bk*âb̂k+eiδkt+h.c.)

where Δ = ω 0 - ωc , δp = ωp - ω 0, δk = ωk - ωc are the detunings of the emitter-cavity, emitter-reservoir, and cavity-reservoir. â and â + are the annihilation and creation operators for the single cavity mode under consideration, while σ^z and σ^ ± are the Pauli operators for the emitter population inversion, raising, and lowering, respectively.

At arbitrary time t, the state vector can be written as

ψ(t)=E(t)e,00R10R2+C(t)g,10R10R2+
pSp(t)g,01pR10R2+kOk(t)g,00R11kR2

where |m, n〉 (m = e,g, n = 0,1) denotes the emitter state |m〉 (excited state |e〉, ground state |g〉) with n photons in the cavity. |jpR1 |lkR2 (j,l = 0,1) corresponds to j photons in the p mode (other than the privileged cavity mode) of the emitter reservoir R 1 and l photons in a single-mode (k ) traveling wave of the one-dimensional photon reservoir R 2 (output beam). E(t), C(t), Sp (t) and Ok (t) are complex probability amplitudes.

The equations of motion for the probability amplitudes are obtained by substituting |ψ(t)〉 and ĤI (t) into the Schrödinger equation and then projecting the resulting equations onto different states respectively. In the WWA [21, 22], we obtain

Ė(t)=ig0exp(iΔt)C(t)γE(t),Ċ(t)=ig0exp(iΔt)E(t)κC(t)
Sp(t)=iAp*0tdtexp(iδpt)E(t),Ok(t)=iBk*0tdtexp(iδkt)C(t)

where γ and κ are one-half the radiative decay rates of the emitter population (other than the privileged cavity mode) and the intracavity field, respectively.

Consider the case that the emitter and cavity are at resonance, Δ = ω 0 - ωc = 0. By using the initial conditions that at time t 0 = 0 the quantum emitter is prepared in its excited state E(0) = 1, C(0) = 0, we obtain the solutions to Eq. (4),

E(t)=exp[(K2)t]·[cos(gt)+Γ2gsin(gt)]
C(t)=exp[(K2)t]·[ig0gsin(gt)]

where K = κ + γ, Γ = κ - γ, and g ≡ [g02 - (Γ/2)2]1/2 is the generalized vacuum Rabi frequency. Sp (t) and Ok (t) can be obtained by carrying out the integrations in Eq. (5).

3. Quantum efficiency of SPS in the cavity QED strong-coupling regime

A single photon will certainly be emitted from the excited emitter, but it might not be coupled into a single-mode traveling wavepacket because it can also spontaneously decay to the emitter reservoir. Define the emission probability Po (t) to be the probability of finding a single photon in the output mode of the cavity between the initial time t 0 = 0 and a later time t. This equals

Po(t)=2κ0tdtC(t)2=ηq{1exp(Kt)[1+K22g2sin2(gt)+K2gsin(2gt)]}

where ηq is given in Eq. (1), by the single-photon emission probability Po (t) in the sufficiently long-time limit t ≫ K-1. It may be decomposed as ηqηc · ηextr , with

ηc=g02g02+κγ2C02C0+1,ηextr=κκ+γ

where C 0g02/2γκ is the cooperativity parameter per emitter [23].

We define ηq as the quantum efficiency of SPS in the cavity-QED strong-coupling regime, which can be viewed as the product of the coupling efficiency (ηc ) of the emitter to the cavity mode and the extraction efficiency (ηextr ) of the single photon into a single-mode traveling wavepacket. The coupling efficiency characterizes how strong the emitter is coupled to the privileged cavity mode. The extraction efficiency determines how large the fraction of light is coupled to a single wave-packet, outward-traveling-wave mode. We emphasize that the cavity decay is not considered as a loss, but rather as a coherent out-coupling, because our goal is to extract single photons from the cavity.

The photon emission rate n(t), defined as the time derivative of the emission probability, gives the rate of a single photon emerging from the cavity mirror M2 and is

n(t)dPo(t)dt=2κg02g2exp(Kt)sin2(gt)

We expect the shape of n(t) to be sufficiently narrow as to define a well-localized photon wavepacket and a well-specified time interval between successively emitted single photons.

From Eq. (9), we can see that the larger the ratios g02/κγ and κ/γ, the higher the coupling efficiency and the extraction efficiency, respectively. For a given quantum emitter, with no pure dephasing processes, the dipole dephasing rate is limited by its population decay rate. However, we can design a cavity with a proper cavity decay rate κ to optimize the QE of SPS and the shape of the photon-emission rate. Figure 2 shows plots of the emission probabilities and the emission rates for three cavity regimes where we varied the cavity decay rate κ, given realistic parameters (g 0, γ)/2π = (50, 1)GHz in each case.

 

Fig. 2. Plots for the time dependence of (a) the emission probabilities of single photons Po (t), and (b) the emission rates n(t), in three different cavity regimes: optimal cavity regime for κ = g02/ κγ, good cavity regime for g02/κ > κγ, and bad cavity regime for κ > g02/κγ, (red dot, blue square and green triangle, respectively) with κ/2π = (50,20,100)GHz , respectively.

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We find that the optimal condition for a high QE and a temporally narrow emission rate, by optimizing the three parameters in Eq. (1), is κ = g02/ κγ, as shown by the red dotted curves in Fig. 2. The QE is 96%, predicted by Eq. (1) in this example. The photon emission rate is well localized on the time axis. The width of n(t) is about 32ps.

4. Discussion and conclusion

An earlier result obtained in the bad-cavity limit by Law and Kimble is given by [1],

P(t)2C12C1+1

where C 1g02/κγ 1 is the single-atom cooperativity parameter. Note that the γ 1 in definition (11) is the full width of the atomic absorption line. The cooperativity parameter defined in the present context is C 0g02/2γκ because here γ is the half width, so these definitions are the same. Comparing our analytical result with that given by Eq. (11), we see that Eq. (11) is valid in the limit that spontaneous atomic decay is negligible, as treated in [1], or equivalently the extraction efficiency ηextr is unity. This is not necessary for strong coupling and is also not implied by the strong-coupling condition. However, for deterministic production of single photons on demand, we not only require that the coupling of the emitter to the single cavity mode is far stronger than its coupling to all other modes (g02/κγ), but also that there needs to be almost no dephasing of the emitter during the emission process (γ -1κ -1) . This keeps the emission process deterministic and hence guarantees that the consecutively emitted photons are indistinguishable.

The Purcell factor, widely referred to in the weak-coupling regime, is given in [19] by Fp = (3λ 3/4π 2)·(Q/V), which can be shown to be equal to Fp = g02/κγ 0 = 2C 0 · f, where γ 0 is one half the free-space spontaneous decay rate and fγ/γ 0 is the fraction of the spontaneous emission to the modes other than the privileged cavity mode. So our result for QE can also be written as

ηq=FpFp+f·κκ+γ=β·κκ+γ

where βFp (Fp + f) is called the spontaneous-emission coupling factor, the fraction of the light emitted by an emitter that is coupled into one particular mode [24, 25]. In reference [20], the authors discussed the coupling factor and the extraction efficiency in terms of the quality factor of the mode. The result Eq. (12) quantifies this discussion.

To conclude, our result for the QE of SPS in the cavity-QED strong-coupling regime is more general than earlier results in [1, 20]. It can be used to estimate the QE of single photons deterministically generated in the cavity output in the cavity-QED strong-coupling regime, instead of using the Mandel-Q parameter [15]. One can improve the QE and performance of the SPS by optimizing the three parameters in the analytical result Eq. (1). The QE is crucial for a practical use of SPS, for example, a high efficiency is required for implementing the linear-optics quantum computation schemes proposed by Knill et al. in [10]; while a low efficiency will severely limit the practical application of SPS in quantum key distribution, as shown in [26].

Acknowledgments

This work is supported by NSF under Grant ECS 0323141. We thank Justin M. Hannigan for discussions.

References

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

2 . J. F. Clauser , “ Experimental distinction between the quantum and classical field-theoretical prediction for the photoelectric effect ,” Phys. Rev. D 9 , 853 ( 1974 ). [CrossRef]  

3 . F. Diedrich and H. Walther , “ Nonclassical radiation of single stored ion ,” Phys. Rev. Lett. 58 , 203 ( 1987 ). [CrossRef]   [PubMed]  

4 . T. Basche , W. E. Moerner , M. Orrit , and H. Talon , “ Photon antibunching in the fluorescence of a single dye molecule trapped in a solid ,” Phys. Rev. Lett. 69 , 1516 ( 1992 ). [CrossRef]   [PubMed]  

5 . C. Kurtsiefer , S. Mayer , P. Zarda , and H. Weinfurter , “ Stable solid-state source of single photons ,” Phys. Rev. Lett. 85 , 290 ( 2000 ). [CrossRef]   [PubMed]  

6 . P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature 406 , 968 ( 2000 ). [CrossRef]   [PubMed]  

7 . C. Santori , M. Pelton , G. Solomon , Y. Dale , and Y. Yamamoto , “ Triggered single photons from a quantum dot ,” Phys. Rev. Lett. 86 , 1502 ( 2001 ). [CrossRef]   [PubMed]  

8 . Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science 295 , 102 ( 2002 ). [CrossRef]  

9 . C. H. Bennet , G. Brassard , and A. Eckert , “ Quantum cryptography ,” Sci. Am. 267(4) , 50 ( 1992 ).

10 . E. Knill , R. Laflamme , and G. J. Milburn , “ A scheme for efficient quantum computation with linear optics ,” Nature 409 , 46 ( 2001 ). [CrossRef]   [PubMed]  

11 . H. J. Kimble , “ Structure and dynamics in cavity quantum electrodynamics ,” in Cavity Quantum Electrodynamics , P. R. Berman ed. ( Academic Press, Boston , 1994 ), pp 203 – 266 .

12 . J. P. Relthmaier , 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 ( 2004 ). [CrossRef]  

13 . T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature 432 , 200 ( 2004 ). [CrossRef]   [PubMed]  

14 . E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett. 95 , 067401 ( 2005 ). [CrossRef]   [PubMed]  

15 . J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science 303 , 1992 ( 2004 ). [CrossRef]   [PubMed]  

16 . A. Kuhn , M. Hennrich , and G. Rempe , “ Deterministic single-photon source for distributed quantum networking ,” Phys. Rev. Lett. 89 , 067901 ( 2002 ). [CrossRef]   [PubMed]  

17 . S. Y. Kilin and T. B. Karlovich , “ Single-atom laser: coherent and nonclassical effects in the regime of a strong atom-field correlation ,” J. Exp. & Theo. Phys. 95 , 805 ( 2002 ). [CrossRef]  

18 . C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature 419 , 594 ( 2002 ). [CrossRef]   [PubMed]  

19 . E. M. Purcell , “ Spontaneous emission probabilities at radio frequencies (Abstract) ,” Phys. Rev. 69 , 681 ( 1946 ).

20 . 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]  

21 . V. Weisskopf and E. Wigner , “ Berechnung der naturlichen Linienbreite auf Grund der Diracschen Lichttheorie ,” Z. Phys. 63 , 54 ( 1930 ). [CrossRef]  

22 . M. O. Scully and M. S. Zubairy , Quantum Optics ( Cambridge, New York , 1997 ).

23 . L. A. Lugiato , “ Theory of optical bistability ,” in Progress in Optics , XXI , E. Wolf ed. ( Elsevier Science Publishers B. V., New York , 1984 ), pp. 69 – 216 . [CrossRef]  

24 . 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]  

25 . B. Lounis and M. Orrit , “ Single-photon sources ,” Rep. Prog. Phys. 68 , 1129 ( 2005 ). [CrossRef]  

26 . G. Brassard , N. Lutkenhaus , T. Mor , and B. Sanders , “ Limitations on practical quantum cryptography ,” Phys. Rev. Lett. 85 , 1330 ( 2000 ). [CrossRef]   [PubMed]  

References

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  1. C. K. Law and H. J. Kimble , “ Deterministic generation of a bit-stream of single-photon pulses ,” J. Mod. Opt.   44 , 2067 ( 1997 ).
  2. J. F. Clauser , “ Experimental distinction between the quantum and classical field-theoretical prediction for the photoelectric effect ,” Phys. Rev. D   9 , 853 ( 1974 ).
    [Crossref]
  3. F. Diedrich and H. Walther , “ Nonclassical radiation of single stored ion ,” Phys. Rev. Lett.   58 , 203 ( 1987 ).
    [Crossref] [PubMed]
  4. T. Basche , W. E. Moerner , M. Orrit , and H. Talon , “ Photon antibunching in the fluorescence of a single dye molecule trapped in a solid ,” Phys. Rev. Lett.   69 , 1516 ( 1992 ).
    [Crossref] [PubMed]
  5. C. Kurtsiefer , S. Mayer , P. Zarda , and H. Weinfurter , “ Stable solid-state source of single photons ,” Phys. Rev. Lett.   85 , 290 ( 2000 ).
    [Crossref] [PubMed]
  6. P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
    [Crossref] [PubMed]
  7. C. Santori , M. Pelton , G. Solomon , Y. Dale , and Y. Yamamoto , “ Triggered single photons from a quantum dot ,” Phys. Rev. Lett.   86 , 1502 ( 2001 ).
    [Crossref] [PubMed]
  8. Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
    [Crossref]
  9. C. H. Bennet , G. Brassard , and A. Eckert , “ Quantum cryptography ,” Sci. Am.   267(4) , 50 ( 1992 ).
  10. E. Knill , R. Laflamme , and G. J. Milburn , “ A scheme for efficient quantum computation with linear optics ,” Nature   409 , 46 ( 2001 ).
    [Crossref] [PubMed]
  11. H. J. Kimble , “ Structure and dynamics in cavity quantum electrodynamics ,” in Cavity Quantum Electrodynamics , P. R. Berman ed. ( Academic Press, Boston , 1994 ), pp 203 – 266 .
  12. J. P. Relthmaier , 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 ( 2004 ).
    [Crossref]
  13. T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
    [Crossref] [PubMed]
  14. E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
    [Crossref] [PubMed]
  15. J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
    [Crossref] [PubMed]
  16. A. Kuhn , M. Hennrich , and G. Rempe , “ Deterministic single-photon source for distributed quantum networking ,” Phys. Rev. Lett.   89 , 067901 ( 2002 ).
    [Crossref] [PubMed]
  17. S. Y. Kilin and T. B. Karlovich , “ Single-atom laser: coherent and nonclassical effects in the regime of a strong atom-field correlation ,” J. Exp. & Theo. Phys.   95 , 805 ( 2002 ).
    [Crossref]
  18. C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature   419 , 594 ( 2002 ).
    [Crossref] [PubMed]
  19. E. M. Purcell , “ Spontaneous emission probabilities at radio frequencies (Abstract) ,” Phys. Rev.   69 , 681 ( 1946 ).
  20. 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]
  21. V. Weisskopf and E. Wigner , “ Berechnung der naturlichen Linienbreite auf Grund der Diracschen Lichttheorie ,” Z. Phys.   63 , 54 ( 1930 ).
    [Crossref]
  22. M. O. Scully and M. S. Zubairy , Quantum Optics ( Cambridge, New York , 1997 ).
  23. L. A. Lugiato , “ Theory of optical bistability ,” in Progress in Optics , XXI , E. Wolf ed. ( Elsevier Science Publishers B. V., New York , 1984 ), pp. 69 – 216 .
    [Crossref]
  24. 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]
  25. B. Lounis and M. Orrit , “ Single-photon sources ,” Rep. Prog. Phys.   68 , 1129 ( 2005 ).
    [Crossref]
  26. G. Brassard , N. Lutkenhaus , T. Mor , and B. Sanders , “ Limitations on practical quantum cryptography ,” Phys. Rev. Lett.   85 , 1330 ( 2000 ).
    [Crossref] [PubMed]

2005 (2)

E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
[Crossref] [PubMed]

B. Lounis and M. Orrit , “ Single-photon sources ,” Rep. Prog. Phys.   68 , 1129 ( 2005 ).
[Crossref]

2004 (3)

J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
[Crossref] [PubMed]

J. P. Relthmaier , 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 ( 2004 ).
[Crossref]

T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
[Crossref] [PubMed]

2002 (6)

A. Kuhn , M. Hennrich , and G. Rempe , “ Deterministic single-photon source for distributed quantum networking ,” Phys. Rev. Lett.   89 , 067901 ( 2002 ).
[Crossref] [PubMed]

S. Y. Kilin and T. B. Karlovich , “ Single-atom laser: coherent and nonclassical effects in the regime of a strong atom-field correlation ,” J. Exp. & Theo. Phys.   95 , 805 ( 2002 ).
[Crossref]

C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature   419 , 594 ( 2002 ).
[Crossref] [PubMed]

Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
[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]

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]

2001 (2)

C. Santori , M. Pelton , G. Solomon , Y. Dale , and Y. Yamamoto , “ Triggered single photons from a quantum dot ,” Phys. Rev. Lett.   86 , 1502 ( 2001 ).
[Crossref] [PubMed]

E. Knill , R. Laflamme , and G. J. Milburn , “ A scheme for efficient quantum computation with linear optics ,” Nature   409 , 46 ( 2001 ).
[Crossref] [PubMed]

2000 (3)

C. Kurtsiefer , S. Mayer , P. Zarda , and H. Weinfurter , “ Stable solid-state source of single photons ,” Phys. Rev. Lett.   85 , 290 ( 2000 ).
[Crossref] [PubMed]

P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
[Crossref] [PubMed]

G. Brassard , N. Lutkenhaus , T. Mor , and B. Sanders , “ Limitations on practical quantum cryptography ,” Phys. Rev. Lett.   85 , 1330 ( 2000 ).
[Crossref] [PubMed]

1997 (2)

M. O. Scully and M. S. Zubairy , Quantum Optics ( Cambridge, New York , 1997 ).

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

1992 (2)

T. Basche , W. E. Moerner , M. Orrit , and H. Talon , “ Photon antibunching in the fluorescence of a single dye molecule trapped in a solid ,” Phys. Rev. Lett.   69 , 1516 ( 1992 ).
[Crossref] [PubMed]

C. H. Bennet , G. Brassard , and A. Eckert , “ Quantum cryptography ,” Sci. Am.   267(4) , 50 ( 1992 ).

1987 (1)

F. Diedrich and H. Walther , “ Nonclassical radiation of single stored ion ,” Phys. Rev. Lett.   58 , 203 ( 1987 ).
[Crossref] [PubMed]

1974 (1)

J. F. Clauser , “ Experimental distinction between the quantum and classical field-theoretical prediction for the photoelectric effect ,” Phys. Rev. D   9 , 853 ( 1974 ).
[Crossref]

1946 (1)

E. M. Purcell , “ Spontaneous emission probabilities at radio frequencies (Abstract) ,” Phys. Rev.   69 , 681 ( 1946 ).

1930 (1)

V. Weisskopf and E. Wigner , “ Berechnung der naturlichen Linienbreite auf Grund der Diracschen Lichttheorie ,” Z. Phys.   63 , 54 ( 1930 ).
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Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
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C. H. Bennet , G. Brassard , and A. Eckert , “ Quantum cryptography ,” Sci. Am.   267(4) , 50 ( 1992 ).

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J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
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J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
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P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
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P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
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Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
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C. Santori , M. Pelton , G. Solomon , Y. Dale , and Y. Yamamoto , “ Triggered single photons from a quantum dot ,” Phys. Rev. Lett.   86 , 1502 ( 2001 ).
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T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
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C. H. Bennet , G. Brassard , and A. Eckert , “ Quantum cryptography ,” Sci. Am.   267(4) , 50 ( 1992 ).

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T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
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C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature   419 , 594 ( 2002 ).
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J. P. Relthmaier , 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 ( 2004 ).
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E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
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T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
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T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
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A. Kuhn , M. Hennrich , and G. Rempe , “ Deterministic single-photon source for distributed quantum networking ,” Phys. Rev. Lett.   89 , 067901 ( 2002 ).
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J. P. Relthmaier , 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 ( 2004 ).
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E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
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P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
[Crossref] [PubMed]

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Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
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J. P. Relthmaier , 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 ( 2004 ).
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T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
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S. Y. Kilin and T. B. Karlovich , “ Single-atom laser: coherent and nonclassical effects in the regime of a strong atom-field correlation ,” J. Exp. & Theo. Phys.   95 , 805 ( 2002 ).
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J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
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C. K. Law and H. J. Kimble , “ Deterministic generation of a bit-stream of single-photon pulses ,” J. Mod. Opt.   44 , 2067 ( 1997 ).

H. J. Kimble , “ Structure and dynamics in cavity quantum electrodynamics ,” in Cavity Quantum Electrodynamics , P. R. Berman ed. ( Academic Press, Boston , 1994 ), pp 203 – 266 .

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E. Knill , R. Laflamme , and G. J. Milburn , “ A scheme for efficient quantum computation with linear optics ,” Nature   409 , 46 ( 2001 ).
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A. Kuhn , M. Hennrich , and G. Rempe , “ Deterministic single-photon source for distributed quantum networking ,” Phys. Rev. Lett.   89 , 067901 ( 2002 ).
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Kuhn, S.

J. P. Relthmaier , 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 ( 2004 ).
[Crossref]

Kulakovskii, V. D.

J. P. Relthmaier , 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 ( 2004 ).
[Crossref]

Kurtsiefer, C.

C. Kurtsiefer , S. Mayer , P. Zarda , and H. Weinfurter , “ Stable solid-state source of single photons ,” Phys. Rev. Lett.   85 , 290 ( 2000 ).
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J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
[Crossref] [PubMed]

Laflamme, R.

E. Knill , R. Laflamme , and G. J. Milburn , “ A scheme for efficient quantum computation with linear optics ,” Nature   409 , 46 ( 2001 ).
[Crossref] [PubMed]

Law, C. K.

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

Lemaitre, A.

E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
[Crossref] [PubMed]

Lobo, C. J.

Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
[Crossref]

Loffler, A.

J. P. Relthmaier , 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 ( 2004 ).
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Lutkenhaus, N.

G. Brassard , N. Lutkenhaus , T. Mor , and B. Sanders , “ Limitations on practical quantum cryptography ,” Phys. Rev. Lett.   85 , 1330 ( 2000 ).
[Crossref] [PubMed]

Marthou, D.

E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
[Crossref] [PubMed]

Mason, M. D.

P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
[Crossref] [PubMed]

Mayer, S.

C. Kurtsiefer , S. Mayer , P. Zarda , and H. Weinfurter , “ Stable solid-state source of single photons ,” Phys. Rev. Lett.   85 , 290 ( 2000 ).
[Crossref] [PubMed]

McKeever, J.

J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
[Crossref] [PubMed]

Michler, P.

P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
[Crossref] [PubMed]

Milburn, G. J.

E. Knill , R. Laflamme , and G. J. Milburn , “ A scheme for efficient quantum computation with linear optics ,” Nature   409 , 46 ( 2001 ).
[Crossref] [PubMed]

Miller, R.

J. McKeever , A. Boca , A. D. Boozer , R. Miller , J. R. Buck , A. Kuzmich , and H. J. Kimble , “ Deterministic generation of dingle photons from one atom trapped in a cavity ,” Science   303 , 1992 ( 2004 ).
[Crossref] [PubMed]

Moerner, W. E.

T. Basche , W. E. Moerner , M. Orrit , and H. Talon , “ Photon antibunching in the fluorescence of a single dye molecule trapped in a solid ,” Phys. Rev. Lett.   69 , 1516 ( 1992 ).
[Crossref] [PubMed]

Mor, T.

G. Brassard , N. Lutkenhaus , T. Mor , and B. Sanders , “ Limitations on practical quantum cryptography ,” Phys. Rev. Lett.   85 , 1330 ( 2000 ).
[Crossref] [PubMed]

Orrit, M.

B. Lounis and M. Orrit , “ Single-photon sources ,” Rep. Prog. Phys.   68 , 1129 ( 2005 ).
[Crossref]

T. Basche , W. E. Moerner , M. Orrit , and H. Talon , “ Photon antibunching in the fluorescence of a single dye molecule trapped in a solid ,” Phys. Rev. Lett.   69 , 1516 ( 1992 ).
[Crossref] [PubMed]

Pelton, M.

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]

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]

C. Santori , M. Pelton , G. Solomon , Y. Dale , and Y. Yamamoto , “ Triggered single photons from a quantum dot ,” Phys. Rev. Lett.   86 , 1502 ( 2001 ).
[Crossref] [PubMed]

Pepper, M.

Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
[Crossref]

Peter, E.

E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
[Crossref] [PubMed]

Plant, J.

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]

Purcell, E. M.

E. M. Purcell , “ Spontaneous emission probabilities at radio frequencies (Abstract) ,” Phys. Rev.   69 , 681 ( 1946 ).

Reinecke, T. L.

J. P. Relthmaier , 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 ( 2004 ).
[Crossref]

Reitzenstein, S.

J. P. Relthmaier , 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 ( 2004 ).
[Crossref]

Relthmaier, J. P.

J. P. Relthmaier , 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 ( 2004 ).
[Crossref]

Rempe, G.

A. Kuhn , M. Hennrich , and G. Rempe , “ Deterministic single-photon source for distributed quantum networking ,” Phys. Rev. Lett.   89 , 067901 ( 2002 ).
[Crossref] [PubMed]

Ritchie, D. A.

Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
[Crossref]

Rupper, G.

T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
[Crossref] [PubMed]

Sanders, B.

G. Brassard , N. Lutkenhaus , T. Mor , and B. Sanders , “ Limitations on practical quantum cryptography ,” Phys. Rev. Lett.   85 , 1330 ( 2000 ).
[Crossref] [PubMed]

Santori, C.

C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature   419 , 594 ( 2002 ).
[Crossref] [PubMed]

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]

C. Santori , M. Pelton , G. Solomon , Y. Dale , and Y. Yamamoto , “ Triggered single photons from a quantum dot ,” Phys. Rev. Lett.   86 , 1502 ( 2001 ).
[Crossref] [PubMed]

Scherer, A.

T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
[Crossref] [PubMed]

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]

Scully, M. O.

M. O. Scully and M. S. Zubairy , Quantum Optics ( Cambridge, New York , 1997 ).

Sek, G.

J. P. Relthmaier , 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 ( 2004 ).
[Crossref]

Senellart, P.

E. Peter , P. Senellart , D. Marthou , A. Lemaitre , J. Hours , J. M. Gerard , and J. Bloch , “ Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity ,” Phys. Rev. Lett.   95 , 067401 ( 2005 ).
[Crossref] [PubMed]

Shchekin, O. B.

T. Yoshie , A. Scherer , J. Hendrickson , G. Khitrova , H. M. Gibbs , G. Rupper , C. Ell , O. B. Shchekin , and D. G. Deppe , “ Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity ,” Nature   432 , 200 ( 2004 ).
[Crossref] [PubMed]

Shields, A. J.

Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
[Crossref]

Solomon, G.

C. Santori , M. Pelton , G. Solomon , Y. Dale , and Y. Yamamoto , “ Triggered single photons from a quantum dot ,” Phys. Rev. Lett.   86 , 1502 ( 2001 ).
[Crossref] [PubMed]

Solomon, G. S.

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]

C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature   419 , 594 ( 2002 ).
[Crossref] [PubMed]

Stevenson, R. M.

Z. Yuan , B. E. Kardynal , R. M. Stevenson , A. J. Shields , C. J. Lobo , K. Cooper , N. S. Beattie , D. A. Ritchie , and M. Pepper , “ Electrically driven single-photon source ,” Science   295 , 102 ( 2002 ).
[Crossref]

Strouse, G. F.

P. Michler , A. Imamoglu , M. D. Mason , P. J. Carson , G. F. Strouse , and S. K. Buratto , “ Quantum correlation among photons from a single quantum dot at room temperature ,” Nature   406 , 968 ( 2000 ).
[Crossref] [PubMed]

Talon, H.

T. Basche , W. E. Moerner , M. Orrit , and H. Talon , “ Photon antibunching in the fluorescence of a single dye molecule trapped in a solid ,” Phys. Rev. Lett.   69 , 1516 ( 1992 ).
[Crossref] [PubMed]

Vuckovic, J.

C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature   419 , 594 ( 2002 ).
[Crossref] [PubMed]

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]

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]

Walther, H.

F. Diedrich and H. Walther , “ Nonclassical radiation of single stored ion ,” Phys. Rev. Lett.   58 , 203 ( 1987 ).
[Crossref] [PubMed]

Weinfurter, H.

C. Kurtsiefer , S. Mayer , P. Zarda , and H. Weinfurter , “ Stable solid-state source of single photons ,” Phys. Rev. Lett.   85 , 290 ( 2000 ).
[Crossref] [PubMed]

Weisskopf, V.

V. Weisskopf and E. Wigner , “ Berechnung der naturlichen Linienbreite auf Grund der Diracschen Lichttheorie ,” Z. Phys.   63 , 54 ( 1930 ).
[Crossref]

Wigner, E.

V. Weisskopf and E. Wigner , “ Berechnung der naturlichen Linienbreite auf Grund der Diracschen Lichttheorie ,” Z. Phys.   63 , 54 ( 1930 ).
[Crossref]

Yamamoto, Y.

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]

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]

C. Santori , D. Fattal , J. Vuckovic , G. S. Solomon , and Y. Yamamoto , “ Indistinguishable photons from a single-photon device ,” Nature   419 , 594 ( 2002 ).
[Crossref] [PubMed]

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Figures (2)

Fig. 1.
Fig. 1.

Schematic description of a lossy two-level emitter interacting with a single mode in a leaky optical cavity. g 0 is the coupling constant between the emitter and the cavity field. A p , A p * and B k B k * are the coupling constants between the emitter, a single photon and their respective reservoir (R 1, R 2) fields.

Fig. 2.
Fig. 2.

Plots for the time dependence of (a) the emission probabilities of single photons Po (t), and (b) the emission rates n(t), in three different cavity regimes: optimal cavity regime for κ = g02/ κγ, good cavity regime for g02/κ > κγ, and bad cavity regime for κ > g02/κγ, (red dot, blue square and green triangle, respectively) with κ/2π = (50,20,100)GHz , respectively.

Equations (13)

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η q = [ g 0 2 ( g 0 2 + κγ ) ] · [ κ ( κ + γ ) ] .
H ̂ I ( t ) = ħ g 0 ( σ ̂ + a ̂ e i Δ t + h . c . ) + ħ p ( A p * σ ̂ d ̂ p + e i δ p t + h . c . ) + ħ k ( B k * a ̂ b ̂ k + e i δ k t + h . c . )
ψ ( t ) = E ( t ) e , 0 0 R 1 0 R 2 + C ( t ) g , 1 0 R 1 0 R 2 +
p S p ( t ) g , 0 1 p R 1 0 R 2 + k O k ( t ) g , 0 0 R 1 1 k R 2
E ̇ ( t ) = i g 0 exp ( i Δ t ) C ( t ) γE ( t ) , C ̇ ( t ) = i g 0 exp ( i Δ t ) E ( t ) κC ( t )
S p ( t ) = i A p * 0 t dt exp ( i δ p t ) E ( t ) , O k ( t ) = i B k * 0 t dt exp ( i δ k t ) C ( t )
E ( t ) = exp [ ( K 2 ) t ] · [ cos ( gt ) + Γ 2 g sin ( gt ) ]
C ( t ) = exp [ ( K 2 ) t ] · [ i g 0 g sin ( gt ) ]
P o ( t ) = 2 κ 0 t dt C ( t ) 2 = η q { 1 exp ( K t ) [ 1 + K 2 2 g 2 sin 2 ( gt ) + K 2 g sin ( 2 gt ) ] }
η c = g 0 2 g 0 2 + κγ 2 C 0 2 C 0 + 1 , η extr = κ κ + γ
n ( t ) dP o ( t ) dt = 2 κ g 0 2 g 2 exp ( K t ) sin 2 ( gt )
P ( t ) 2 C 1 2 C 1 + 1
η q = F p F p + f · κ κ + γ = β · κ κ + γ

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