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arXiv:1111.3995 · Physical Review B

Nonlinear photon transport in a semiconductor waveguide-cavity system containing a single quantum dot: Anharmonic cavity-QED regime

Stephen Hughes, C. Roy

Published Jan 17, 2012• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.85.035315

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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.
We have studied the characteristic feature of coherent photon transport in a semiconductor waveguide. We have presented a semiconductor master equation formalism that accurately simulated coherent input or output coupling of semiconductor cavity quantum electrodynamics systems such as planar photonic crystals and micropillar cavities. The role of quantized multiphoton effects pointed out the possible failure of weak excitation approximation, which was found to fail even for low input powers and small mean cavity photon numbers. For increasing field strengths, possible failure of the semiclassical approach was taken into account. In the weak coupling regime, higher order quantum correlation effects, were shown to be significant. We have introduced the general theoretical technique to simulate coherent photon transport outside both the weak excitation approximation and the semi classical approximation. Electron-phonon interactions at a microscopic level were derived using polaron transformation. We have demonstrated that substantial deviations from the weak excitation approximation resulted for very small mean photon numbers. We have modified the master equation approach to include the mechanism of electron-acoustic scattering and studied the impact of electron-phonon interaction on incoherent scattering and coherent renormalization of the exciton cavity coupling rate, qualitative differences from simple Lorentzian decay model containing quantum dot were found. We have also studied the transmission of light in the strong coupling regime and simulated a phase gate. We have found that coupling to an acoustic phonon bath caused considerable qualitative changes in light propagation characteristics modeled by a simple pure dephasing process. We have used the model to simulate a conditional phasegate. The obtained results were found in good agreement with previously obtained results.
We present a semiconductor quantum optics formalism to study the dynamics of a coherently-driven semiconductor quantum dot interacting with an acoustic phonon bath and a high Q microcavity. A quantum master equation is derived in the polaron frame, where multiphoton and multiphoton effects are included to all orders. As applications of the theory, we study the Mollow triplet of a driven quantum dot in the regime of semiconductor cavity-QED. Pronounced signatures of electron-phonon-photon scattering are observed through excitation-induced dephasing and off-resonant cavity coupling. We also present an effective phonon master in Lindblad form and show example quantum trajectory simulations that help one to understand the features in the Mollow triplet spectra.
We investigate the effect of electron-phonon interactions on the coherence properties of single photons emitted from a semiconductor cavity QED (quantum electrodynamics) system, i.e., a quantum dot embedded in an optical cavity. The degree of indistinguishability, governing the quantum mechanical interference between two single photons, is calculated as a function of important parameters describing the cavity QED system and the phonon reservoir, e.g., cavity quality factor, light-matter coupling strength, temperature, and phonon lifetime. We show that non-Markovian effects play an important role in determining the coherence properties for typical parameter values and establish the conditions under which a Markovian approximation may be applied. The calculations are performed using a recently developed second-order perturbation theory, and the limits of validity are established by comparing to an exact diagonalization approach. We find that for large cavity decay rates the perturbation theory may break down.
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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.