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Physical Review A

Microscopic theory of squeezed-light emission in strong-coupling semiconductor quantum-dot systems

L. Schneebeli, M. Kira, S. W. Koch

Published Sep 28, 2009• 5 citations
Publisher

Abstract

Resonance fluorescence equations are derived and solved for strong-coupling semiconductor quantum-dot systems using a fully quantized multimode theory and a cluster-expansion approach. A reduced model is developed to explain the origin of autocorrelation and cross-correlation resonances in the two-photon emission spectrum of the fluorescent light. These resonances are traced back to the two-photon strong-coupling states of Jaynes-Cummings ladder. The accuracy of the reduced model is verified via numerical solution of the resonance fluorescence equations. The analysis reveals the direct relation between the squeezed-light emission and the strong-coupling states in optically excited semiconductor systems.

DOI
10.1103/physreva.80.033843

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Resonance fluorescence equations are derived and solved for strong-coupling semiconductor quantum-dot systems using a fully quantized multimode theory and a cluster-expansion approach. A reduced model is developed to explain the origin of autocorrelation and cross-correlation resonances in the two-photon emission spectrum of the fluorescent light. These resonances are traced back to the two-photon strong-coupling states of Jaynes-Cummings ladder. The accuracy of the reduced model is verified via numerical solution of the resonance fluorescence equations. The analysis reveals the direct relation between the squeezed-light emission and the strong-coupling states in optically excited semiconductor systems.
It is shown that spectrally resolved photon-statistics measurements of the resonance fluorescence from realistic semiconductor quantum-dot systems allow for high contrast identification of the two-photon strong-coupling states. Using a microscopic theory, the second-rung resonance of Jaynes-Cummings ladder is analyzed and optimum excitation conditions are determined. The computed photon-statistics spectrum displays gigantic, experimentally robust resonances at the energetic positions of the second-rung emission.
Quantum optics provides a fundamental framework for understanding the interaction between light and matter at the quantum level. Recently, it has been shown that under incoherent pumping, the resonance fluorescence spectrum dramatically changes. Engineering the resonance fluorescence spectrum paves the way towards solid-state-based single-photon sources. In this paper, we start by reviewing and reproducing some of the results concerning the resonance fluorescence spectrum, single-photon sources, dressed-state lasers, and luminescence spectrum of a quantum dot in a microcavity. Photon correlations in quantum optical systems and spectral properties of radiation emitted by atomic and semiconductor systems interacting with external fields are investigated. The well known Mollow triplet structure of the emission spectrum is discussed, together with the role of dressed states in explaining the origin of the three spectral peaks. Furthermore, the luminescence spectra of quantum emitters coupled to microcavities are reviewed. The numerical results presented here contribute to the theoretical understanding of resonance fluorescence, photon correlations, and engineered emission in quantum optical systems. These studies highlight the rich physical properties arising from light matter interaction at the quantum level and demonstrate their relevance for emerging quantum technologies.
The Jaynes-Cummings model provides a well established theoretical framework for single electron two level systems in a radiation field. Similar exactly solvable models for semiconductor light emitters such as quantum dots dominated by many particle interactions are not known. We access these systems by a generalized cluster expansion, the photon-probability cluster expansion: a reliable approach for few-photon dynamics in many body electron systems. As a first application, we discuss vacuum Rabi oscillations and show that their amplitude determines the number of electrons in the quantum dot.
We show that resonance fluorescence, i.e., the resonant emission of a coherently driven two-level system, can be realized with a semiconductor quantum dot. The dot is embedded in a planar optical microcavity and excited in a waveguide mode so as to discriminate its emission from residual laser scattering. The transition from the weak to the strong excitation regime is characterized by the emergence of oscillations in the first-order correlation function of the fluorescence, g(tau), as measured by interferometry. The measurements correspond to a Mollow triplet with a Rabi splitting of up to 13.3 microeV. Second-order correlation measurements further confirm nonclassical light emission.
The build-up dynamics of quantum-optical correlations in a Jaynes–Cummings model for semiconductor quantum-dot systems is characterized using the cluster-expansion scheme. Assuming an excitation with a coherent state source under strong- and weak-coupling conditions, it is found that higher-order correlations are sequentially generated. Even though the influence of dephasing hinders their development, significant correlations build up even in the presence of strong dissipation showing that quantum-spectroscopy studies are possible even in interacting many-body systems like semiconductors.
We theoretically study quantum-optical properties of one- and two-dimensional semiconductor nanostructures, where the electronic band structure is described by a two-band tight-binding model. Since the focus of our work is on analyzing quantum-optical effects of systems with a continuous band structure, many-body processes like electron-electron and electron-phonon interactions are neglected. The quantum-optical interband excitations are fully incorporated and described by a Jaynes-Cummings-type model. The exciting quantum light can be a state with arbitrary photon statistics. For simplicity, the results discussed here are limited to single-photon and two-photon Fock states. Our analytical approach is based on the eigenvalue problem and can be utilized to obtain explicit expressions for the steady-state properties of the system. Numerical simulations are based on solutions of the equations of motion and allow for a more precise analysis of the dynamics and nonresonant excitations of the system. We demonstrate that during the interaction process, a collective excitation of the conduction band is formed. For nonresonant excitations, this collective dynamics results in interesting steady states, in which the resonantly addressed eigenstates are occupied. The presented model provides a framework for microscopic simulations of quantum-optically excited extended semiconductor nanostructures.