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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 7002–7009
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Effect of pure dephasing on the Jaynes-Cummings nonlinearities

A. Gonzalez-Tudela, E. del Valle, E. Cancellieri, C. Tejedor, D. Sanvitto, and F. P. Laussy  »View Author Affiliations


Optics Express, Vol. 18, Issue 7, pp. 7002-7009 (2010)
http://dx.doi.org/10.1364/OE.18.007002


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Abstract

We study the effect of pure dephasing on a two-level system in strong coupling in the nonlinear regime with the single mode of a cavity. The photoluminescence spectrum of the cavity has a robust tendency to display triplet structures, instead of the expected Jaynes-Cummings pairs of doublets at the incommensurate frequencies ± ( n ± n 1 ) for integer n. We discuss recent experimental works that may already manifest signatures of single photon nonlinearities.

© 2010 Optical Society of America

1. Introduction

The most basic and fundamental representation of the QD is that of a two-level atomic-like system [20

20. P. Michler, A. Ĭmamoḡlu, 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]

]. Dressing this fermionic system (i.e., coupling it strongly) with more than one photon yields a splitting of 2√ng when n quanta are involved (g is the interaction strength, we take h̄ = 1). Transitions between these dressed states provide spectral lines at incommensurate energies ±(n±n1)g, which are a direct manifestation of full-field quantization, as predicted by one of the most important theoretical model of quantum physics, the Jaynes-Cummings Hamiltonian [21

21. E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theory with application to the beam maser,” Proc. IEEE 51, 89 (1963). [CrossRef]

]. Evidencing these nonlinearities is a chief goal of quantum optics. It has been fulfilled with atoms [22

22. M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800 (1996). [CrossRef] [PubMed]

] and more recently with superconducting circuits [23

23. J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes-Cummings ladder and observing its √n nonlinearity in a cavity QED system,” Nature 454, 315 (2008). [CrossRef] [PubMed]

], but a direct spectral signature remains elusive for semiconductor QDs, although compelling indirect evidences have been reported [5

5. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fălt, E. L. Hu, and A. Ĭmamoḡlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896 (2007). [CrossRef] [PubMed]

,24

24. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859 (2008). [CrossRef]

]. We have predicted that they could be observed with a careful control (or lucky encounter) of the effective quantum state [25

25. E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009). [CrossRef]

]. In this text, in the light of the importance of pure dephasing in semiconductors, we revisit our claims taking it into account. We show that due to dephasing, single-photon nonlinearities manifest through a triplet at resonance in the photoluminescence spectrum, rather than a quadruplet as expected previously.

2. Formalism

The Jaynes-Cummings Hamiltonian, that describes the strong coupling of a two-level QD with the single mode of a microcavity, reads H = ωa a a + ωσ σ σ + g(a σ + ) with a the photon annihilation operator (following Bose statistics) and σ the material excitation annihilation operator (following Fermi statistics). The two modes are coupled with interaction strength g and close enough to resonance (with small detuning Δ = ωa - ωa) to allow for the rotating wave approximation. A Liouvillian ℒ is used to describe the system in the framework of a quantum dissipative master equation, tρ = ℒρ, taking into account decay γc and incoherent pumping Pc, with c = a, σ (referred to as cavity and electronic pumping, respectively) [25

25. E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009). [CrossRef]

]. Pure dephasing enters as an additional source of decoherence ℒγϕσρ: [13

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

]

ρ=i[ρ,H]+c=a,σγc2(2ccρcc)+c=a,σPc2(2cρcccρρcc)+γσϕρ.

Mmnμνmnμν=iωa(mn)+iωσ(μν)γaPa2(m+n)γσ+Pσ2(μ+ν)γσϕ2(μν)2.

Other elements Mmnμνpqθϑ are as given in Ref. [25

25. E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009). [CrossRef]

]. In the following, we study the effect of nonzero γϕσ on the spectral shape of the cavity photoluminescence spectrum, under various cases of particular experimental relevance.

3. Results

Fig. 1. (Colour online) Loss of the Jaynes-Cummings quadruplet and emergence of a triplet with dephasing, for a system well into strong coupling (γa/g = 0.1 and γσ/g = 0.001). Values of dephasing are γϕσ/g = 0 (dotted), 0.75 (dashed) and 1.5 (solid). Panel (a) [resp., (b)] is for Pσ/g = 0.02 [resp., 0.1]. In inset (c), the level structure (Jaynes-Cummings ladder) at γϕσ = 0, from the vacuum up to 5 excitations, and the transitions between its rungs that give rise to the dressed states resonances ωp/g. These appear below for the parameters of (b) and show the impact of dephasing on strong coupling: inner transitions (blue) melt into a common line while outer transitions (red) remain well apart.

Dephasing is not a parameter that is easy to control directly. In an attempt to probe the nonlinearities of the system, a natural experiment is to increase the pumping power, so as to populate more the higher excited states. The evolution of the Rabi doublet with increasing electronic pumping is shown on Fig. 2(a), for parameters from state-of-the art experimental systems (cf. caption). In this case, a triplet is also formed at resonance, but without any direct manifestation of the Jaynes-Cumming quadruplets, owing to the poor splitting to broadening ratio, even in the best systems available so far. The observation of this trend has been recently reported by Ota et al. [28

28. Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system,” Appl. Phys. Express 2, 122301 (2009). [CrossRef]

], who attribute it to “pumping processes” restoring the bare cavity emission. We have indeed considered parameters from this work to show that our effect is within the reach of today technology. As the strong-coupling system is pushed more into the nonlinear regime with pumping, a transition to lasing occurs [33

33. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. (2010). AOP doi:10.1038/nphys1518. [CrossRef]

,34

34. S. Strauf, “Lasing under strong coupling,” Nat. Phys. (2010). AOP doi:10.1038/nphys1600. [CrossRef]

]. In panels (b), we follow this evolution in presence of dephasing, from the vacuum Rabi doublet (Pσ/g ≈ 0.001) towards a lasing single peak (Pσ/g ≈ 5) and eventually to a quenched system recovering the bare cavity emission (Pσ/g ≈ 500). This is matched by (c), the cavity population na (becoming > 1 with lasing and ≪C 1 in the quantum/quenched regions), (d), the dot population (showing population inversion with lasing and being empty or saturated in the quantum/quenched regions) and, (e), the two-photon coincidence g (2)(0) (showing poissonian fluctuation at lasing, and antibunching/bunching in the quantum/quenched regions).

Fig. 2. Evolution of strong-coupling with increasing electronic pumping. Parameters are those of state of the art systems from the literature [7,9,28]: g = 120μeV, γa = 38μeV, γσ = 1μeV, γϕσ = g, at resonance, Pσ varying as indicated, without cavity pumping and with detector resolution of 46μeV. (a) The system evolves from the vacuum Rabi doublet into a triplet, similarly to the experiment of Ota et al. [28]. (b) At much higher pumpings, the system goes to lasing then to quenching. These transitions are shown in (c) cavity and (d) dot population, and (e) g (2) (0).

In Fig. 3, we display other manifestations of nonlinearities in the luminescence spectrum of a strongly-coupled QD/microcavity system, with the intent of showing the wide range of phenomenologies that are accessible in different configurations, as well as the strong similarities with other experiments that have so far eluded a definite theoretical explanation [5

5. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fălt, E. L. Hu, and A. Ĭmamoḡlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896 (2007). [CrossRef] [PubMed]

,35

35. D. Sanvitto, F. P. Laussy, F. Bello, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Single-photon nonlinearity of a semiconductor quantum dot in a cavity,” arXiv:condmat/0612034 (2006).

]. In these cases, we focus more on the similar general behavior than on a tight numerical agreement with the experimental values claimed in these works, although our parameters remain within the possible margins for such systems (for instance, we have considered an ideal detector in the cases of Figs. 3, whereas we included the detector resolution of Ref. [28

28. Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system,” Appl. Phys. Express 2, 122301 (2009). [CrossRef]

] in our reproduction of their experiment in Fig. 2). In the quest for strong-coupling in semiconductors, one typically performs an anticrossing experiment, where the dot and the cavity are brought to resonance to exhibit level-repulsion (maintaining their line splitting). Figure 3 shows the situation with detuning for two sets of parameters (cf. caption). In the first case, (a), well identified dot and cavity emission lines approach in the expected way but grow a central peak. This situation is similar to the one reported by Hennessy et al. [5

5. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fălt, E. L. Hu, and A. Ĭmamoḡlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896 (2007). [CrossRef] [PubMed]

], where the authors have attributed the central peak to pure cavity emission due to fluctuation in energy of the emitter (thereby not staying all the time in strong-coupling). In the second case, (b), a doublet is now produced at resonance and a triplet is observed in its vicinity and only at negative detunings. This situation is similar to the one reported by Sanvitto et al. [35

35. D. Sanvitto, F. P. Laussy, F. Bello, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Single-photon nonlinearity of a semiconductor quantum dot in a cavity,” arXiv:condmat/0612034 (2006).

] (that has remained unexplained–and unpublished–so far). In the first case, dephasing is constant, the cavity has a higher quality factor and electronic pumping is moderate. These considerations match the experimental situation of a single QD detuned from the cavity by a thin-film condensation technique. The triplet then arises for the same reasons as those explained for the phenomenology of Fig. 1. A slightly better system (either from system parameters or with less dephasing) would grow a quadruplet at resonance, if dephasing is indeed the cause for the central peak in this case as well. In the second case, the experimental situation varies in a few ways that would appear unimportant for the physics investigated, but that turn out to produce very different qualitative results: the dephasing has been correlated with the detuning (we have used a sigmoid shape to reflect that detuning is changed with temperature, resulting in a nonlinear dependence of dephasing with detuning [9

9. A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, “Electrical control of spontaneous emission and strong coupling for a single quantum dot,” New J. Phys. 11, 023034 (2009). [CrossRef]

]), cavity photon has smaller lifetime and pumping is much stronger. This results in the emergence of a triplet outside of the resonance. In this later case, rather than superimposing a central peak, the non-commensurable transitions placed at ±(nn1) at resonance produce the multiplet out of resonance, owing to their virtue of being stationary with detuning [25

25. E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009). [CrossRef]

]. The dephasing here serves the purpose of levelling the quadruplet predicted in Ref. [25

25. E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009). [CrossRef]

] for such a structure at nonzero detuning, into a triplet.

Fig. 3. Strong-coupling in the nonlinear regime in presence of dephasing as detuning is varied. Parameters are γσ/g - 0.001 and Pa/g = 0.011 for both panels, and for (a) [resp., (b)], γϕσ/g = 1 [resp., sigmoid function of Δ], γa/g - 0.35 [resp., 0.5] and Pσ/g = 0.1 [resp., 0.3]. Instead of the usual anticrossing, triplets are observed in slightly varying configurations: (a) A triplet is grown as the dot enters in resonance similarly to the experiment of Hennessy et al. [5]. (b) As detuning varies with temperature, a triplet is observed out of resonance with an asymmetry with detuning caused by the temperature-dependent dephasing similarly to the experiment of Sanvitto et al. [35].

4. Conclusion

We have shown that nonlinearities of the Jaynes-Cummings Hamiltonian—the pinnacle of full-field quantization in cavity Quantum Electrodynamics—have a robust tendency to manifest as triplet structures in presence of a non-negligible dephasing (such as is the case in semiconductors), rather than the expected Jaynes-Cummings quadruplets with no emission at the cavity (central) mode. We have shown that various parameters (corresponding to slightly different experimental situations) result in strong qualitative differences, such as observation of a triplet at—or out of—resonance. In our interpretation, in contrast to those previously speculated in the literature [5

5. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fălt, E. L. Hu, and A. Ĭmamoḡlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896 (2007). [CrossRef] [PubMed]

,28

28. Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system,” Appl. Phys. Express 2, 122301 (2009). [CrossRef]

], the triplet arises from Jaynes-Cummings nonlinearities in presence of de-phasing or detuning, in a system that is always in strong-coupling. Although this mechanism reproduces remarkably various experimental findings, on the basis of a clear physical picture and with the expected experimental parameters, a quantitative analysis is needed to bring a definite proof of which effect is responsible for the observed phenomenology. Experiments typically come with additional complications of their own. For instance, a non-negligible drift in detuning in Ota et al. ’s experiment is making their triplet markedly more visible even at smaller values of the dephasing. Such a compelling proof, however, is outside the scope of this text and a challenge for the microcavity QED community at large. In the meantime, our work shows the considerable conceptual novelties added to the basic picture of cavity QED by bringing together the two crucial agents that are dephasing and nonlinearities.

Acknowledgments

La Caixa, the Newton fellowship & Ramony Cajal programs, Spanish MEC (MAT2008-01555, QOIT-CSD2006-00019) & CAM (S2009/ESP-1503), and EPSRC are acknowledged.

References and links

1.

E. del Valle, Microcavity Quantum Electrodynamics (VDM Verlag, 2009).

2.

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42, 24 (1989). [CrossRef]

3.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162 (2004). [CrossRef] [PubMed]

4.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724 (2009). [CrossRef] [PubMed]

5.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fălt, E. L. Hu, and A. Ĭmamoḡlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896 (2007). [CrossRef] [PubMed]

6.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. 98, 117402 (2007). [CrossRef] [PubMed]

7.

M. Nomura, Y. Ota, N. Kumagai, S. Iwamoto, and Y. Arakawa, “Large vacuum Rabi splitting in single self-assembled quantum dot-nanocavity system,” Appl. Phys. Express 1, 072102 (2008). [CrossRef]

8.

C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16, 15006 (2008). [CrossRef] [PubMed]

9.

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, “Electrical control of spontaneous emission and strong coupling for a single quantum dot,” New J. Phys. 11, 023034 (2009). [CrossRef]

10.

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senel-lart, “Scalable implementation of strongly coupled cavity-quantum dot devices,” Appl. Phys. Lett. 94, 121102 (2009). [CrossRef]

11.

G. Cui and M. G. Raymer, “Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime,” Phys. Rev. A 73, 053807 (2006). [CrossRef]

12.

F. P. Laussy, E. del Valle, and C. Tejedor, “Strong coupling of quantum dots in microcavities,” Phys. Rev. Lett. 101, 083601 (2008). [CrossRef] [PubMed]

13.

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

14.

A. Naesby, T. Suhr, P. T. Kristensen, and J. Mork, “Influence of pure dephasing on emission spectra from single photon sources,” Phys. Rev. A 78, 045802 (2008). [CrossRef]

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M. Yamaguchi, T. Asano, and S. Noda, “Photon emission by nanocavity-enhanced quantum anti-Zeno effect in solid-state cavity quantum-electrodynamics,” Opt. Express 16, 118067 (2008). [CrossRef]

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J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, “Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems,” Phys. Rev. Lett. 103, 027401 (2009). [CrossRef] [PubMed]

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P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement,” Phys. Rev. B 71, 115328 (2005). [CrossRef]

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I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, P. Roussignol, R. Ferreira, and J. M. Gérard, “Temperature dependence of the zero-phonon linewidth in quantum dots: An effect of the fluctuating environment,” Phys. Rev. B 75, 073308 (2007). [CrossRef]

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Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations,” Phys. Rev. Lett. 64, 2499 (1990). [CrossRef] [PubMed]

20.

P. Michler, A. Ĭmamoḡlu, 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]

21.

E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theory with application to the beam maser,” Proc. IEEE 51, 89 (1963). [CrossRef]

22.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800 (1996). [CrossRef] [PubMed]

23.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes-Cummings ladder and observing its √n nonlinearity in a cavity QED system,” Nature 454, 315 (2008). [CrossRef] [PubMed]

24.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859 (2008). [CrossRef]

25.

E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009). [CrossRef]

26.

G. S. Agarwal and S. Dutta Gupta, “Steady states in cavity QED due to incoherent pumping,” Phys. Rev. A 42, 1737 (1990). [CrossRef] [PubMed]

27.

F. P. Laussy and E. del Valle, “Optical spectra of the Jaynes-Cummings ladder,” AIP Conference Proceedings 1147, 46 (2009). [CrossRef]

28.

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, “Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system,” Appl. Phys. Express 2, 122301 (2009). [CrossRef]

29.

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B 80, 155326 (2009). [CrossRef]

30.

S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express 17, 3322 (2009). [CrossRef] [PubMed]

31.

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32.

A. Auffèves, J.-M. Gérard, and J.-P. Poizat, “Pure emitter dephasing: A resource for advanced solid-state single-photon sources,” Phys. Rev. A 79, 053838 (2009). [CrossRef]

33.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. (2010). AOP doi:10.1038/nphys1518. [CrossRef]

34.

S. Strauf, “Lasing under strong coupling,” Nat. Phys. (2010). AOP doi:10.1038/nphys1600. [CrossRef]

35.

D. Sanvitto, F. P. Laussy, F. Bello, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Single-photon nonlinearity of a semiconductor quantum dot in a cavity,” arXiv:condmat/0612034 (2006).

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(270.5580) Quantum optics : Quantum electrodynamics
(140.3945) Lasers and laser optics : Microcavities

ToC Category:
Quantum Optics

History
Original Manuscript: February 24, 2010
Revised Manuscript: March 9, 2010
Manuscript Accepted: March 11, 2010
Published: March 19, 2010

Citation
A. Gonzalez-Tudela, E. del Valle, E. Cancellieri, C. Tejedor, D. Sanvitto, and F. P. Laussy, "Effect of pure dephasing on the Jaynes-Cummings nonlinearities," Opt. Express 18, 7002-7009 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7002


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References

  1. E. del Valle, Microcavity Quantum Electrodynamics (VDM Verlag, 2009).
  2. S. Haroche and D. Kleppner, "Cavity quantum electrodynamics," Phys. Today 42, 24 (1989). [CrossRef]
  3. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature 431, 162 (2004). [CrossRef] [PubMed]
  4. S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724 (2009). [CrossRef] [PubMed]
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