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Optics and Spectroscopy

Entanglement of electronic states of impurities in a nanocrystal

Ashat M. Basharov, В. Н. Горбачев, N. V. Znamenskiı̆

Published Aug 1, 2007• 2 citations
Publisher

Abstract

It is shown that the dynamics of electronic states of impurities in a nanocrystal embedded in a bulk matrix can be described with the help of the model of a single-mode microcavity with quasi-resonant atoms and losses at the mirrors. In the proposed model, the dynamics of impurities is similar to the collective decay of atoms in a common bath. In the case of a nanocrystal, matrix phonons represent this bath. Impurities interact with the localized phonon mode of the nanocrystal owing to the electron-phonon interaction. The localized phonon mode is coupled with bath phonons at the nanocrystal boundary. In the dispersive limit, the standard model of collective relaxation appears, within the framework of which, different types of many-particle entangled electronic states of impurities are described. In the case of exact resonance, similar entangled states also appear, which are discussed for two impurities in a nanocrystal.

DOI
10.1134/s0030400x07080085

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It is shown that the dynamics of electronic states of impurities in a nanocrystal embedded in a bulk matrix can be described with the help of the model of a single-mode microcavity with quasi-resonant atoms and losses at the mirrors. In the proposed model, the dynamics of impurities is similar to the collective decay of atoms in a common bath. In the case of a nanocrystal, matrix phonons represent this bath. Impurities interact with the localized phonon mode of the nanocrystal owing to the electron-phonon interaction. The localized phonon mode is coupled with bath phonons at the nanocrystal boundary. In the dispersive limit, the standard model of collective relaxation appears, within the framework of which, different types of many-particle entangled electronic states of impurities are described. In the case of exact resonance, similar entangled states also appear, which are discussed for two impurities in a nanocrystal.
We investigate the dynamical behavior of entanglement in a system made of two solid-state emitters, as two quantum dots, embedded in two separated microcavities. In these solid-state systems, in addition to the coupling with the cavity mode, the emitter is coupled to a continuum of leaky modes providing additional losses and is also subjected to a phonon-induced pure dephasing mechanism. We model this physical configuration as a multipartite system composed of two independent parts each containing a qubit embedded in a single-mode cavity, exposed to cavity losses, spontaneous emission and pure dephasing. We study the time evolution of entanglement of this multipartite open system, finally applying this theoretical framework to the case of currently available solid-state quantum dots in microcavities.
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.
We investigate a simple surface hopping (SH) approach for modeling a single impurity level coupled to a single phonon and an electronic (metal) bath (i.e., the Anderson-Holstein model). The phonon degree of freedom is treated classically with motion along--and hops between--diabatic potential energy surfaces. The hopping rate is determined by the dynamics of the electronic bath (which are treated implicitly). For the case of one electronic bath, in the limit of small coupling to the bath, SH recovers phonon relaxation to thermal equilibrium and yields the correct impurity electron population (as compared with numerical renormalization group). For the case of out of equilibrium dynamics, SH current-voltage (I-V) curve is compared with the quantum master equation (QME) over a range of parameters, spanning the quantum region to the classical region. In the limit of large temperature, SH and QME agree. Furthermore, we can show that, in the limit of low temperature, the QME agrees with real-time path integral calculations. As such, the simple procedure described here should be useful in many other contexts.
We numerically study the relaxation dynamics of impurity-host systems, focusing on the presence of long-lived metastable states in the nonequilibrium dynamics after an initial excitation of the impurities. In generic systems, an excited impurity coupled to a large bath at zero temperature is expected to relax and approach its ground state over time. However, certain exceptional cases exhibit metastability, where the system remains in an excited state on timescales largely exceeding the typical relaxation time. We study this phenomenon for three prototypical impurity models: a tight-binding quantum model of independent spinless fermions on a lattice with two stub impurities, a classical-spin Heisenberg model with two weakly coupled classical impurity spins, and a tight-binding quantum model of independent electrons with two classical impurity spins. Through numerical integration of the fundamental equations of motion, we find that all three models exhibit similar qualitative behavior: complete relaxation for nearest-neighbor impurities and incomplete or strongly delayed relaxation for next-nearest-neighbor impurities. The underlying mechanisms leading to this behavior differ between models and include impurity-induced bound states, emergent approximately conserved local observables, and exact cancellation of local and nonlocal dissipation effects. Published by the American Physical Society 2024