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Physical Review A

Quantum-optical spectroscopy of semiconductors

M. Kira, S. W. Koch

Published Jan 18, 2006• 124 citations
Publisher

Abstract

The microscopic foundation of quantum-optical spectroscopy is presented. It is proposed to use this technique to generate and detect quasiparticle states in semiconductors whose quantum-statistical properties are governed by that of the exciting light. While resonant classical excitation induces an optical interband polarization, low-intensity quantum excitation directly seeds a quantum-degenerate exciton state which is characterized by long-range order, anomalous reduction of Coulomb and phonon scattering, as well as strongly enhanced and directional quantum emission.

DOI
10.1103/physreva.73.013813

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The microscopic foundation of quantum-optical spectroscopy is presented. It is proposed to use this technique to generate and detect quasiparticle states in semiconductors whose quantum-statistical properties are governed by that of the exciting light. While resonant classical excitation induces an optical interband polarization, low-intensity quantum excitation directly seeds a quantum-degenerate exciton state which is characterized by long-range order, anomalous reduction of Coulomb and phonon scattering, as well as strongly enhanced and directional quantum emission.
Conceptually, a single-mode laser light may be perceived as a quantum-degenerate state because all of its photons occupy one and the same light-mode state. One can utilize this property in direct-gap semiconductor in order to excite, e.g., quantum-degenerate excitons that are Coulomb-bound electronhole pairs. For example, if a classical laser resonant with an exciton resonance, the resulting excitation injects a quantum-degenerate state of coherent excitons. This process is fully explained by the semiconductor Bloch equations [1] where the quantum-degenerate coherent excitons are simply described by a polarization. One can rigorously generalize [2] this state-injection concept to realize quantum-optical spectroscopy beyond simple excitons because also laser’s quantum fluctuations are injected as such to the quantumdegenerate electron-hole pairs, before the onset of Coulomb and phonon-induced scattering. More explicitly, the quantum aspects of a single-mode pump laser are defined by a boson operator B while the Coulomb-bound electron-hole pairs are described by an exciton operator X that is bosonic only approximately. When the pump laser has quantum-optical correlations †J K
Quantum spectroscopy utilizes the quantum fluctuations of the light source to characterize and control matter. More specifically, desired many-body states can be directly excited to the semiconductor by adjusting light source's quantum fluctuations. The method is experimentally realizable by projecting an extensive set of classical measurements into a quantum-optical response resulting from any possible quantum source. In this work, quantum spectroscopy is used to identify new classes of many-body states and quantum processes in semiconductor nanostructures. In the first part of this Thesis, the optical properties of semiconductor quantum wells are analyzed with quantum spectroscopy by projecting high-precision optical measurements into quantum-optical responses. It is shown that quantum spectroscopy can characterize the properties of specific stable electron-hole cluster – called quasiparticles – much more sensitively than traditional ultrafast laser spectroscopy. In particular, unambiguous evidence is demonstrated for the identification of a new highly correlated quasiparticle in direct-gap Galliumarsenide quantum wells, the dropleton, that is a quantum droplet consisting of four-to-seven electron-hole pairs. To determine the detectable excitation energetics of such correlated quasiparticles in optically excited semiconductor quantum wells, a new theoretical framework is presented which allows for the computation of the excitation spectrum based on a pair-correlation function formulation of the quasiparticle state. Another study in this Thesis deals with the emission properties of optically pumped quantum-dot microcavities. Experimental and theoretical evidence is shown for a new intriguing quantum-memory effect that is controllable by adjusting pump source's quantum fluctuations. The last part of this Thesis presents a fundamental study about the general applicability of quantum spectroscopy in dissipative systems.
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.
A microscopic many-body theory for the optical and electronic properties of semiconductors is reviewed with an emphasis on the role of correlation effects. At the semiclassical level, the semiconductor Bloch equations include many-body effects via bandgap and field renormalization as well as correlation contributions representing two electron-hole pair amplitudes, excitonic populations, and coupled interband and intraband coherences. These Coulomb interaction induced carrier correlations lead to characteristic signatures in nonlinear semiconductor spectroscopy. At the fully quantum mechanical level the dominant light-matter correlations are described by coupled semiconductor Bloch and luminescence equations. Excitonic emission properties of quantum well and microcavity systems are discussed, including effects such as coherent signatures in the secondary emission and coherent control of the emitted light.