Theory of Cavity Quantum Electrodynamics with solid-state emitters and cavities

People : Alexia Auffèves, Jean-Philippe Poizat, Jean-Michel Gérard

1. Spontaneous emission of a quantum dot in a semi-conducting cavity

Our aim is to study how the results of Cavity Quantum Electrodynamics (CQED) are modified when one replaces an isolated two-level atom by a solid-state atom like a quantum dot (QD). To a large extent, one can consider a QD as an artificial two-level atom. Rabi oscillations have been induced between the ground state and the excitonic state of a QD [1,2], and the Mollow triplet, which is the spectral counterpart of these oscillations, has been observed [2]. Impressive progresses have been witnessed in the production of semi-conducting cavities too : ultra-small modal volumes and very high quality factors have been achieved, allowing to observe CQED effects like Purcell effect [3], strong coupling [4,5] and more recently QD induced transparency [6], which have been demonstrated for QDs coupled to solid-state cavities. Experiments previously realized in atomic physics can thus be realized using solid-state devices, holding the promise to realize scalable coherent tasks.

Nevertheless, recent experimental results show that the modelling of a QD as a two-level system reaches its limits. In particular, it has been observed that a QD strongly coupled to a detuned cavity emits photons at the cavity mode frequency with a significant probability [5]. This process is allowed by strong coupling but its efficiency remains very poor in the case of an isolated atom [7]. This apparently puzzling feature requires thus an advanced modelling of the spontaneous emission properties of a quantum dot (QD) in a cavity. An important difference between an isolated atom and a QD resides in the fact that QDs interact with phonons of the crystalline matrix they are embedded in. At low temperature and low pumping rate, collisions with phonons lead to a dephasing of the excitonic dipole of the QD, without reducing its lifetime (pure dephasing). Because of this effect, photons emitted by solid-state emitters are spectrally broadened, which puts an upper bound to their rate of indistinguishability. We have pointed out recently that pure dephasing has a crucial influence on the shape of the emission spectra of QD-cavity systems [9] and leads to a strong increase of the emission at the cavity energy for detuned systems, in qualitative agreement with the experimental trend.

Our results highlight appealing novel opportunities for the development of novel advanced single photon sources exploiting both quantum microcavity effects and pure dephasing. In the case of emitters displaying spectral diffusion, pure emitter dephasing could be exploited to build a wavelength stabilized single photon source, whose emission wavelength is only defined by the cavity mode. Amazingly, it could also be exploited to prepare single photons displaying a high degree of indistinguishability. From a more fundamental point of view, these results show that dealing with artificial atoms leads to entirely new physics and unexpected phenomena. They open a new field of research at the boundary between quantum optics and solid-state physics, namely CQED of solid state systems. In the future we will work at the interface between the two communities, to model existing experiments as well as to imagine new photonic devices based on the specificity of semi-conducting emitters and cavities.

This project has obtained the financial support of the RTRA “Nanosciences aux limites de la nanoélectronique”. It will give rise to a collaboration with the Federal University of Minas Gerais (Brazil).

[1] R. Melet et al, arXiv : 0707.3061 (2007).
[2] A. Muller et al, Phys. Rev. Lett 99, 187402 (2007).
[3] J. M. Gérard et al, Phys. Rev. Lett. 81, 1110 (1998).
[4] J.P. Reithmaier et al., Nature 432, 197 (2004), T. Yoshie et al., Nature 432, 200 (2004), E. Peter et al., Phys. Rev. Lett. 95, 067401 (2005).
[5] K. Hennessy et al., Nature 445, 896 (2007). D. Press et al., Phys. Rev. Lett. 98, 117402 (2007).
[6] D. Englund et al, Nature 450, 857 (2007).
[7] A. Auffèves, B. Besga, J.M. Gérard and J. P. Poizat, Phys. Rev. A 77, 063833 (2008).
[8] C. Santori, D. Fattal, J. Vuckovic, G.S. Solomon, Y. Yamamoto , Nature \textbf419, 594 (2002) ; S. Varoutsis et al, Phys. Rev. B \textbf72, 041303(R) (2005).
[9] A. Auffèves, J. M. Gérard and J. P. Poizat, arXiv : 0808.0820, accepted in PRA

2. N emitters in a cavity, from lasing to superradiance

Post-doc required

This topics is funded within the frame of the NanoSciEra project "Lasing of Erbium in Crystalline Silicon Photonic Nanostructures" LECSIN. The project focuses on the control of radiative emission of Erbium ions embedded in photonic crystal cavities made of Silicon, with the aim to achieve Silicon-based laser emission at 1.54 micron wavelength. A collection of N Erbium ions in a solid-state cavity provides an original model system that joints the advantages of atomic physics, as the emitters are indistinguishable, and of solid state physics, as light-matter coupling is constant and the density of emitters may be high. This system is very promising for cavity-QED based effects, in particular low-threshold lasing and superradiance. We aim at building the theoretical frame and the numerical tools necessary to model the experiments conducted within this project.

To be more specific, superradiance is observable when N indistinguishable 2-level systems are pumped in the excited level, equally coupled to the EM field, and confined in a volume small compared to λ3, where λ is the wavelength of light. It can thus be shown that the system relaxes by emitting a short pulse of coherent light during a radiative cascade [1]. This collective behavior is quite different from the spontaneous emission of N independent emitters, and is expected to be enhanced by the coupling to a cavity mode [2]. The transition between the spontaneous emission and the superradiance regime will be analytically and/or numerically studied as a function of the relevant parameters, namely the cavity coupling and linewidth. If the medium is incoherently pumped, the stimulated emission regime, giving rise to a lasing effect, can be reached. We will estimate the lasing threshold, and compare the lasing condition to the superradiance condition. The same equations and code will be used to describe the two phenomena, lasing corresponding to the permanent regime under continuous pumping, and superradiance the transient after a single incoherent excitation of the N emitters.

The theoretical and numerical tools will be exploited to model ongoing experiments performed in the project. From a fundamental point of view, the question of the boundary between lasing and superradiance will be addressed.

[1] Gross and Haroche, Phys. Reports 93, 301 (1982).
[2] Temnov and Woggon, PRL 95, 243602 (2005).

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