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Oxford University Press eBooks

QUANTUM DESCRIPTION OF LIGHT-MATTER COUPLING IN SEMICONDUCTORS

Alexey Vitalievich Kavokin, Jeremy J. Baumberg

Published Dec 20, 2007• 0 citations
Publisher

Abstract

This chapter starts from description of Rabi and Bloch-oscillations in semiconductors. It introduces the exciton-light coupling Hamiltonian in terms of the secondary quantization theory, and considers different approaches to quantum description of light-matter coupling, including the Jaynes-Cummings model and the Dicke model. The crossover from bosonic to fermionic statistics for excitons is then discussed. Finally, the dispersion of exciton-polaritons in microcavities is obtained and the polariton Hamiltonian is constructed.

DOI
10.1093/acprof:oso/9780199228942.003.0005

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This chapter starts from description of Rabi and Bloch-oscillations in semiconductors. It introduces the exciton-light coupling Hamiltonian in terms of the secondary quantization theory, and considers different approaches to quantum description of light-matter coupling, including the Jaynes-Cummings model and the Dicke model. The crossover from bosonic to fermionic statistics for excitons is then discussed. Finally, the dispersion of exciton-polaritons in microcavities is obtained and the polariton Hamiltonian is constructed.
Abstract In this chapter we study with the tools developed in Chapter 3 the basic models that are the foundations of light–matter interaction. We start with Rabi dynamics, then consider the optical Bloch equations that add phenomenologically the lifetime of the populations. As decay and pumping are often important, we cover the Lindblad form, a correct, simple and powerful way to describe various dissipation mechanisms. Then we go to a full quantum picture, quantizing also the optical field. We first investigate the simpler coupling of bosons and then culminate with the Jaynes–Cummings model and its solution to the quantum interaction of a two-level system with a cavity mode. Finally, we investigate a broader family of models where the material excitation operators differ from the ideal limits of a Bose and a Fermi field.
Polaritons, in particular microcavity exciton-polaritons, have attracted much attention in recent years, as the phenomena of Bose-Einstein condensation and superfluidity have been observed for these quasiparticles. While the basic physics of these systems is well understood, there has been confusion over the connection of these systems to other phenomena, namely the Jaynes-Cummings Hamiltonian, Rabi flopping, and the vacuum Rabi splitting of atoms in a cavity. This paper reviews the basic theory of polaritons and shows these connections explicitly.
We present a microscopic and fully quantized model to investigate the interaction between semiconductor nanostructures and quantum light fields including the many-body Coloumb interaction between photoexcited electrons and holes. Our approach describes the coupled dynamics of the quantum light field and single and double electron-hole pairs, i.e., excitons and biexcitons, and exactly accounts for Coulomb many-body correlations and carrier band dispersions. Using a straightforward yet exact approach, we study a one-dimensional two-band system interacting with a single-mode, two-photon quantum state within a Tavis-Cummings framework. By employing an exact coherent factorization scheme, the computational complexity is reduced significantly enabling numerical simulations. We also derive a simplified model that includes only the bound 1s1s1s-exciton and biexciton states for comparison. Our simulations reveal distinct single- and two-photon Rabi oscillations, corresponding to photon-exciton and exciton-biexciton transitions. We demonstrate, in particular, that biexciton continuum states significantly modify the dynamics in a way that cannot be captured by simplified models that consider only bound states. Our findings emphasize the importance of a comprehensive microscopic modeling in order to accurately describe quantum optical phenomena of interacting electronic many-body systems.
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.
This chapter presents the basic principles of quantum optics. It starts from recalling the main elements of quantum mechanics in Heisenberg and Schroedinger interpretations, then the creation and annihilation operators are introduced, and bosonic and fermionic commutation rules are discussed. The secondary quantization theory is used to show differences between coherent, thermal, and Fock states of light; introduce squeezing and antisqueezing; and discuss the statistics of photons. Finally, the polarization and second-order coherence of light are discussed from the point of view of the quantum optics.
We discuss the Jaynes–Cummings–Hubbard model describing the superfluid–Mott insulator transition of polaritons (i.e., dressed photon–qubit states) in coupled qubit–cavity arrays in the crossover from strong to weak correlations. In the strongly correlated regime the phase diagram and the elementary excitations of lattice polaritons near the Mott lobes are calculated analytically using a slave-boson theory (SBT). The opposite regime of weakly interacting polariton superfluids is described by a weak-coupling mean-field theory for a generalized multi-mode Dicke model. We show that a remarkable relation between the two theories exists in the limit of large photon bandwidth and large negative detuning, i.e., when the nature of polariton quasiparticles becomes qubit-like. In this regime, the weak-coupling theory predicts the existence of a single Mott lobe with a change of the universality class of the phase transition at the tip of the lobe, in perfect agreement with the SBT. Moreover, the spectra of low energy excitations, i.e., the sound velocity of the Goldstone mode and the gap of the amplitude mode match exactly as calculated from both theories.