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arXiv:0909.5642 · Physical Review B

Nonlinear photoluminescence spectra from a quantum-dot–cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED

Peijun Yao, Pradyumna K. Pathak, E. Illes, Stephen Hughes, S. Münch, Stephan Reitzenstein, P. Franeck, A. Löffler, Tobias Heindel, Sven Höfling, L. Worschech, A. Forchel

Published Jan 28, 2010• 38 citations
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Abstract

We investigate the power-dependent photoluminescence spectra from a strongly coupled quantum dot-cavity system using a quantum master equation technique that accounts for incoherent pumping, stimulated emission, pure dephasing, and fermion or boson statistics. Analytical spectra at the one-photon correlation level and the numerically exact multiphoton spectra for fermions are presented. Master equation models that neglect stimulated emission processes are shown to lead to unphysical predictions at high powers, such as negative mean photon numbers. We compare to recent experiments on a quantum dot-micropillar cavity system and show that an excellent fit to the data can be obtained by varying only the incoherent pump rates in direct correspondence with the experiments. Our theory and experiments together show convincing evidence for stimulated-emission induced broadening and anharmonic cavity quantum electrodynamics.

DOI
10.1103/physrevb.81.033309

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We investigate the power-dependent photoluminescence spectra from a strongly coupled quantum dot-cavity system using a quantum master equation technique that accounts for incoherent pumping, stimulated emission, pure dephasing, and fermion or boson statistics. Analytical spectra at the one-photon correlation level and the numerically exact multiphoton spectra for fermions are presented. Master equation models that neglect stimulated emission processes are shown to lead to unphysical predictions at high powers, such as negative mean photon numbers. We compare to recent experiments on a quantum dot-micropillar cavity system and show that an excellent fit to the data can be obtained by varying only the incoherent pump rates in direct correspondence with the experiments. Our theory and experiments together show convincing evidence for stimulated-emission induced broadening and anharmonic cavity quantum electrodynamics.
Theoretical derivation and numerical calculation achieve the quantum dot numerically exact multi-photon emission spectra starting from the interaction of quantum dot and cavity,using the master equation that includes incoherent pumping and pure dephasing and combines with the quantum regression theorem, and considering the relevant initial conditions.Then comparing the multi-photon(fermion statistics) spectra with the one-thoton(boson system) correlation level, our analysis shows that according to the fermion statistics the pure dephasing, and the thermal bath model, an excellent fitting to the data is obtained with the recent experimental of Ref[22] results in a quantum dot-micropiller cavity system. The theory and the recent experiments both show pump-induced stimulated emission and anharmonic cavity-QED in quantum dot-cavity systems.
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-QQQ limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.
We investigate a quantum-dot-based cavity system via the master-equation approach. The dynamics of the system is greatly affected by dissipation and dephasing processes. We include these phenomena to the theory through the master equation. The dissipation effects such as cavity loss, spontaneous recombination of excitons, and incoherent pumping are considered. The dephasing process is included as an electron--acoustic-phonon interaction. An intrinsic feature of solid-state cavity systems is the presence of electron-phonon interaction, which distinguishes this system from atomic cavity quantum electrodynamics. Due to the temperature dependence of phonons we use the complete form of the master equation (temperature dependence of dissipation rates) in this paper. We study the emission spectrum and photon statistics of the system. We show that cavity mode emission depends on temperature, and temperature strongly affects the photon statistics.
We present a semiconductor master equation technique to study the input/output characteristics of coherent photon transport in a semiconductor waveguide-cavity system containing a single quantum dot. We use this approach to investigate the effects of photon propagation and anharmonic cavity-QED for various dot-cavity interaction strengths, including weakly-coupled, intermediately-coupled, and strongly-coupled regimes. We demonstrate that for mean photon numbers much less than 0.1, the commonly adopted weak excitation (single quantum) approximation breaks down, even in the weak coupling regime. As a measure of the multiphoton correlations, we compute the Fano factor and the correlation error associated with making a semiclassical approximation. We also explore the role of electron--acoustic-phonon scattering and find that phonon-mediated scattering plays a qualitatively important role on the light propagation characteristics. As an application of the theory, we simulate a conditional phase gate at a phonon bath temperature of 20 K in the strong coupling regime.
Multi-photon lasing has been realized in systems with strong nonlinear interactions between emitters and cavity modes, where single-photon processes are suppressed. Coherence between the internal states of a quantum emitter, or among multiple emitters, plays a key role. Such continuous nonclassical sources of light can find applications in quantum computation, quantum sensing, quantum metrology, and quantum communication. This thesis explores the multi-photon lasing phenomena in various quantum dot-photonic crystal cavity quantum electrodynamic (QED) setups. Exciton-phonon interactions are inevitable in such systems and are incorporated using the polaron-transformed master equation. The Born-Markov approximation is employed to obtain the reduced density matrix rate equation. Using quantum laser theory, we derived the Scully-Lamb laser rate equations and evaluated the single- and multi-photon excess emission rates defined as the difference between emission and absorption rates into the cavity mode without mean-field approximations. We investigated cooperative two-photon lasing, correlated emission lasing, hyperradiant lasing, non-degenerate two-mode two-photon lasing, and continuous variable entanglement in open quantum systems with single or multiple semiconductor quantum dots (two-level, three-level, and four-level) driven coherently/incoherently and coupled to single/ bimodal cavities.
We study the dynamics of a quantum dot embedded in a three-dimensional microcavity in the strong coupling regime in which the quantum dot exciton has an energy close to the frequency of a confined cavity mode. Under the continuous pumping of the system, the confined electron and hole can recombine either by spontaneous emission through a leaky mode or by stimulated emission of a cavity mode that can escape from the cavity. The numerical integration of a master equation including all these effects gives the dynamics of the density matrix. By using the quantum regression theorem, we compute the first- and second-order coherence functions required to calculate the photon statistics and the spectrum of the emitted light. Our main result is the determination of a range of parameters in which a state of cavity modes with Poissonian or sub-Poissonian (nonclassical) statistics can be built up within the microcavity. Depending on the relative values of pumping and rate of stimulated emission, either one or two peaks close to the excitation energy of the dot and/or to the natural frequency of the cavity are observed in the emission spectrum. The physics behind these results is discussed.