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arXiv:2112.04217

Effects of spatial quantization and Rabi-shifted resonances in single and double excitation of quantum wells and wires induced by few-photon optical field

А. Н. Васильев, Olga V. Tikhonova

Published Dec 8, 2021• 0 citations
arXivHTMLPDF

Abstract

We develop a fully quantum theoretical approach which describes the dynamics of Frenkel excitons and bi-excitons induced by few photon quantum light in a quantum well or wire (atomic chain) of finite size. The eigenenergies and eigenfunctions of the coupled exciton-photon states in a multiatomic system are found and the role of spatial confinement as well as the energy quantization effects in 1D and 2D cases is analyzed. Due to the spatial quantization, the excitation process is found to consist in the Rabi-like oscillations between the collective symmetric states characterized by discrete energy levels and arising in the picture of the ladder bosonic operators. At the same time, the enhanced excitation of additional states with energy close to the upper polariton branch is revealed. The found new effect is referred to as the formation of Rabi-shifted resonances and is analyzed in details. Such states are shown to influence dramatically on the dynamics of excitation especially in the limit of large times.

DOI
10.48550/arxiv.2112.04217

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We develop a fully quantum theoretical approach which describes the dynamics of Frenkel excitons and bi-excitons induced by few photon quantum light in a quantum well or wire (atomic chain) of finite size. The eigenenergies and eigenfunctions of the coupled exciton-photon states in a multiatomic system are found and the role of spatial confinement as well as the energy quantization effects in 1D and 2D cases is analyzed. Due to the spatial quantization, the excitation process is found to consist in the Rabi-like oscillations between the collective symmetric states characterized by discrete energy levels and arising in the picture of the ladder bosonic operators. At the same time, the enhanced excitation of additional states with energy close to the upper polariton branch is revealed. The found new effect is referred to as the formation of Rabi-shifted resonances and is analyzed in details. Such states are shown to influence dramatically on the dynamics of excitation especially in the limit of large times.
We develop a fully quantum theoretical approach which describes the dynamics of Frenkel excitons and bi-excitons induced by few photon quantum light in a quantum well or wire (atomic chain) of finite lateral size. The excitation process is found to consist in the Rabi-like oscillations between the collective symmetric states characterized by discrete energy levels. At the same time, the enhanced excitation of high-lying free exciton states being in resonance with these 'dressed' polariton eigenstates is revealed. This found new effect is referred to as the formation of Rabi-shifted resonances and appears to be the most important and new feature established for the excitation of 1D and 2D nanostructures with final lateral size. The found new physics changes dramatically the conventional concepts of exciton formation and play an important role for the development of nanoelectronics and quantum information protocols involving manifold excitations in nanosystems.
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 study the resonant electronic excitation dynamics for ultracold atoms trapped in a deep optical lattice prepared in a Mott-insulator state. Excitons in these artificial crystals are similar to Frenkel excitons in noble atom or molecular crystals. They appear when the atomic excited state linewidth is smaller than the exciton bandwidth generated by dipole-dipole coupling. When the atoms are placed within a cavity the electronic excitations and the quantized cavity mode get coupled. In the collective strong coupling regime excitations form two branches of cavity polaritons with Rabi splitting larger than the atomic and the cavity linewidth. To demonstrate their properties we calculate the transmission, reflection, and absorption spectra for an incident weak probe field, which show resonances at the polariton frequencies.
The optical response of radiatively coupled semiconductor multiple-quantum-well structures is investigated theoretically. It is shown that the transverse optical field leads to a coupling of exciton states within each well which causes a radiative decay and a mixing of excitonic resonances. Simultaneously, the field-induced long-ranged coupling between different wells leads to collective effects that are very sensitive to the detailed geometry of the structure. For a quantum-well spacing equal to an integer multiple of half the optical wavelength inside the medium, it is predicted that the collective effects cause a stimulated decay of electronic excitations that should be observable in either transmission or reflection geometry. On the other hand, in a quarter wavelength structure, the light-induced coupling causes an interwell energy transport and a splitting of the excitonic resonances, that should be observable as quantum beats in the time-resolved transmitted or reflected signal.
This dissertation addresses both fundamental aspects of the coherent exciton kinetics in single semiconductor quantum wells and more application-oriented aspects of the collective excitonic optical properties in quantum well Bragg structures. We use a bosonic theory to investigate the ultrafast coherent exciton dynamics after an optical excitation in a single semiconductor quantum well. It is shown that, on intermediate time scales, nonlinear mean-field interactions between excitons lead to a coherent, wave-like evolution in the momentum distribution of optically inactive excitons, which can survive for some time before dephasing sets in. Driven by two-exciton correlations, this coherent quantum kinetic effect bridges the well-known kinetics associated with optical excitation on the one hand and incoherent relaxation on the other. We also study more general dynamical properties of bosonic mean field systems with N-species of excitons (in a single semiconductor quantum well). We find that the momentum-conserving exciton mean field equations, including the coupling to external fields and fermionic corrections, have the dynamical structure su(N,N). We show that one can define a non-real generalized "Bloch vector" and a non-hermitian "density matrix" description, which allow us to explicitly obtain all the constants of motion associated with the su(N,N) symmetry. The many-body effects and correlations of excitons in a single quantum well are mainly induced by the Coulomb interactions. In the case of a semiconductor quantum well Bragg structure, the light induced coupling between different quantum wells also dramatically affects the excitons' behavior, especially through the collective excitations of excitons in the whole structure. We investigate the linear excitonic optical properties of the quantum well Bragg structure induced by the collective excitations using the transfer matrix approach. We show that the so called "intermediate band" (IB) created by the exciton resonance, which does not exist in conventional photonic crystals, can be used for the stopping, storing and releasing of light, which is important in information processing devices. We also discuss the compensation of the dispersive distortion in the light delay process through reversing the IB band structure. Other conceptual and practical issues such as the decay rate of the IB modes and the generalized anti-reflection coating are also investigated.
A theoretical study of excitonic Rabi oscillations in semiconductor quantum wells is presented. Fundamental differences between excitonic Rabi oscillations and optical Rabi oscillations in ideal atomic or molecular 2-level systems are due to the existence of the continuous 1-particle spectrum in solids (energy bands) and the resulting strong effects of the Coulomb interaction, such as the attractive electron-hole interaction and the repulsive exchange interaction. In spite of these fundamental differences, Rabi-like oscillations of the excited electron-hole densities are computed for the case of resonant optical pumping of excitons. We compare our theoretical results with our recent experimental observation of excitonic Rabi oscillations.