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Ultrafast Phenomena and Nanophotonics

Microscopic simulations of the dynamics of excitonic many-body correlations coupled to quantum light

Hendrik Rose, Polina R. Sharapova, T. Meier

Published Mar 8, 2024• 2 citations
Publisher

Abstract

The dynamics of semiconductor quantum wires and wells that are coupled to a single-mode quantum field are analyzed. Within a two-band tight-binding model the Coulomb interaction between electrons and holes is included on a microscopic basis and the light-matter interaction is quantized. The dynamics of the system is described by equations of motion for the relevant set of expectation values of the coupled electronic-photonic system. Starting from the initial condition of a single photon occupying the field mode, we study the dynamics of the mean photon number. To analyze effects arising from the many-body Coulomb interaction, we use an exact truncation of the electronic hierarchy problem by employing the fact that N photons cannot excite more than N electron-hole pairs. We compare Rabi oscillations with and without Coulomb interaction for different excitation conditions. When the quantum field mode is initially occupied by two photons, two interacting electron-hole pairs, i.e., biexcitons, can be generated which characteristically modify the dynamics. Within a consistent and fully-quantized approach we show consequences of biexcitonic many-body correlations that are coupled to a quantum field and discuss the obtained dynamics.

DOI
10.1117/12.2690245

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The dynamics of semiconductor quantum wires and wells that are coupled to a single-mode quantum field are analyzed. Within a two-band tight-binding model the Coulomb interaction between electrons and holes is included on a microscopic basis and the light-matter interaction is quantized. The dynamics of the system is described by equations of motion for the relevant set of expectation values of the coupled electronic-photonic system. Starting from the initial condition of a single photon occupying the field mode, we study the dynamics of the mean photon number. To analyze effects arising from the many-body Coulomb interaction, we use an exact truncation of the electronic hierarchy problem by employing the fact that N photons cannot excite more than N electron-hole pairs. We compare Rabi oscillations with and without Coulomb interaction for different excitation conditions. When the quantum field mode is initially occupied by two photons, two interacting electron-hole pairs, i.e., biexcitons, can be generated which characteristically modify the dynamics. Within a consistent and fully-quantized approach we show consequences of biexcitonic many-body correlations that are coupled to a quantum field and discuss the obtained dynamics.
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.
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.
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.
We present a systematic theory of Coulomb-induced correlation effects in the nonlinear optical processes within the strong-coupling regime. In this paper, we shall set a dynamics controlled truncation scheme microscopic treatment of nonlinear parametric processes in semiconductor microcavities including the electromagnetic field quantization. It represents the starting point for the microscopic approach to quantum optics experiments in the strong-coupling regime without any assumption on the quantum statistics of electronic excitations (excitons) involved. We exploit a previous technique, which was used in the semiclassical context, which, once applied to four-wave mixing in quantum wells, allowed us to understand a wide range of observed phenomena. We end up with dynamical equations for exciton and photon operators, which extend the usual semiclassical description of Coulomb interaction effects in terms of a mean-field term plus a genuine noninstantaneous four-particle correlation to quantum optical effects.