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Molecular crystals and liquid crystals science and technology. Section B, Nonlinear optics/Molecular crystals and liquid crystals scienceand technology. Section B, Nonlinear optics/Nonlinear optics

COHERENT DIPOLE OSCILLATION INDUCED BY LOCALIZED PHOTONS

Akira Shojiguchi, Kozo Kobayashi, Suguru Sangu, Kazuo Kitahara, Motoichi Ohtsu

Published Dec 1, 2002• 6 citations
Publisher

Abstract

This paper describes a novel model for the dynamics of the dipole coherence in two-level quantum dots (QDs) interacting with localized photons. The model is based on the fact that the coupling on a nanometer scale between QDs via optical near fields represented by localized photons is much stronger than that via propagating far fields. The model predicts that an intriguing phenomenon such as a collective dipole oscillation occurs if the initial quantum states are locally manipulated. The origin of this kind of collective behaviour is discussed in view of Dicke's superradiance.

DOI
10.1080/1058726021000045414

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This paper describes a novel model for the dynamics of the dipole coherence in two-level quantum dots (QDs) interacting with localized photons. The model is based on the fact that the coupling on a nanometer scale between QDs via optical near fields represented by localized photons is much stronger than that via propagating far fields. The model predicts that an intriguing phenomenon such as a collective dipole oscillation occurs if the initial quantum states are locally manipulated. The origin of this kind of collective behaviour is discussed in view of Dicke's superradiance.
A model is presented for a system of N two-level excitons interacting with each other via optical near fields represented as localized photons. In a low exciton density limit, quantum dynamics of the dipole moments or quantum coherence between any two energy levels is linear. As the exciton density becomes higher, the dynamics becomes nonlinear, and the system has several kinds of quasi-steady states of the dipole distribution depending on the system parameters. These quasi-steady states are classified with the help of the effective Hamiltonian that is derived from the renormalization of degrees of freedom of localized photons with a unitary transformation. Among them there exist a “ferromagnetic” state (dipole-ordered state), in which all electric dipoles are aligned in the same direction, and an “anti-ferromagnetic” state, where all dipoles alternatingly change the direction. In addition, we show that an arbitrary state can be transformed into a dipole-ordered state by manipulating initial values of the population differences appropriately. For example, if we initially prepare a dipole-forbidden state, which is similar to the “anti-ferromagnetic” state and cannot be coupled with propagating far fields, and if we manipulate the distribution of the population differences properly, the initial state evolves into a dipole-ordered state. The radiation property of such dipole-ordered states is examined in detail. Neglecting energy dissipation by radiation, we find that some of the ordered states show strong radiation equivalent to Dicke's superradiance. Then by introducing a radiation reservoir, the dissipative master equation is derived. Solving the equation with and without quantum correlations, we numerically show that multiple peaks in the radiation profile can survive in both cases. The mechanism of this phenomenon is discussed, and a brief comment on an application to photonic devices on a nanometer scale is given.
We investigate the collective spontaneous emission in a system of two identical quantum dots (QDs) strongly coupled through the dipole-dipole ($d\ensuremath{-}d$) interaction. The QDs are modeled as two-level quantum objects, while the $d\ensuremath{-}d$ interaction is described as the exchange of a virtual photon through the photonic reservoir. The master equation approach is used in the analysis. The main attention is focused on antenna characteristics of the two-QD system---the radiation intensity dependence on the meridian and azimuthal angles of observation. We show that the radiation pattern of such a system is nonstationary and its temporal behavior depends on the initial quantum state. In particular, for entangled initial states the radiative pattern exhibits oscillations on the frequency which corresponds to the $d\ensuremath{-}d$ interaction energy. We also analyze spectral properties of the directional diagram. The comparison of radiation patterns is carried out for two QDs and two classical dipoles. The concept of quantum nanoantenna is proposed based on collective spontaneous emission in QD ensembles.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.