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Journal of the Optical Society of America B

Sequential build-up of quantum-optical correlations

Martin Mootz, M. Kira, S. W. Koch

Published Jan 25, 2012• 9 citations
Publisher

Abstract

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.

DOI
10.1364/josab.29.000a17

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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.
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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.
The optically generated excitations in semiconductors constitute a genuine many-body system. To describe its quantum-optical features, we have to expand significantly the theoretical models used so far. However, the important insights of Chapters 16–23 are already presented in a form in which most of them can directly be used and generalized to analyze central properties of the optical excitations in solids. As for atoms, the optical transitions in semiconductors are induced via dipole interaction between photons and electrons. We can thus efficiently construct a systematic quantum-optical theory for semiconductors by following the cluster-expansion approach. One of the main differences from atoms is that the electronic excitations in semiconductors form a strongly interacting many-body system. Thus, we must systematically treat the arising Coulomb-induced hierarchy problem together with the quantum-optical one. Moreover, the coupling of electrons to lattice vibrations, i.e., the phonons, produces yet another hierarchy problem. In addition, in solid-state spectroscopy one often uses multimode light fields such that one cannot rely on the single-mode simplifications to study semiconductor quantum optics. As shown in Chapter 15, the Coulomb-, phonon-, and photon-induced hierarchy problems have formally an identical structure. Thus, we start the analysis by investigating how semiconductor quantum optics emerges from the dynamics of correlated clusters. We first focus on the basic properties of the optical transitions in the classical regime. This means investigating the fundamental optical phenomena resulting from the singlets. The full singlet–doublet approach is presented in Chapters 28–30.
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.
The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an NNN-qubit chain quantum Rabi models.