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Physical Review B

Mixed states in Rabi waves and quantum nanoantennas

Gregory Ya. Slepyan, Yauhen Yerchak, С. А. Максименко, A. Hoffmann, F. G. Bass

Published Jun 28, 2012• 22 citations
Publisher

Abstract

The mixed states of Rabi waves in a one-dimensional chain of two-level quantum dots (QDs) with tunnel coupling between neighbor QDs are theoretically considered. The propagation of Rabi waves is described by a $2\ifmmode\times\else\texttimes\fi{}2$ statistical operator depending on two spatial and one temporal variables. For a statistical operator the generalized Bloch equations are derived. The eigenmodes of the statistical operator are considered, the general solution of the initial problem is obtained, and the frequency spectrum of the induced current is investigated. The high-frequency part of the spectrum corresponds to a Mollow triplet, but is distinct from the last one as it is the continuous spectral band located on both sides of the transition frequency. The low-frequency part is caused by tunnel current and includes a dc-component and continuous ac-band in the vicinity of the Rabi oscillation frequency. The application of Rabi waves to the electrically controlled quantum nanoantennas of terahertz range is considered.

DOI
10.1103/physrevb.85.245134

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The mixed states of Rabi waves in a one-dimensional chain of two-level quantum dots (QDs) with tunnel coupling between neighbor QDs are theoretically considered. The propagation of Rabi waves is described by a 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 statistical operator depending on two spatial and one temporal variables. For a statistical operator the generalized Bloch equations are derived. The eigenmodes of the statistical operator are considered, the general solution of the initial problem is obtained, and the frequency spectrum of the induced current is investigated. The high-frequency part of the spectrum corresponds to a Mollow triplet, but is distinct from the last one as it is the continuous spectral band located on both sides of the transition frequency. The low-frequency part is caused by tunnel current and includes a dc-component and continuous ac-band in the vicinity of the Rabi oscillation frequency. The application of Rabi waves to the electrically controlled quantum nanoantennas of terahertz range is considered.
We consider one-dimensional chains of two-level quantum systems coupled via tunneling. The chain is driven by the superposition of dc and ac fields in the strong coupling regime. Based on the fundamental principles of electrodynamics and quantum theory, we have developed a generalized model of quantum dynamics for such interactions, free of rotating-wave approximation. The system of equations of motion was studied numerically. We analyzed the dynamics and spectra of the inversion density, dipole current density, and tunneling current density. In the case of resonant interaction with the ac component, the particle dynamics exhibits itself in the oscillatory regime, which may be interpreted as a combination of Rabi and Bloch oscillations with their strong mutual influence. Such scenario for an obliquely incident ac field dramatically differs from the individual picture of both types of oscillations due to the interactions. This effect is counterintuitive because of the existence of markedly different frequency ranges for such two types of oscillations. These dynamics manifest themselves in multiline spectra in different combinations of Rabi and Bloch frequencies. The effect is promising as a framework of a new type of spectroscopy in nanoelectronics and electrical control of nanodevices.
We theoretically investigate the spatial propagation of Rabi oscillations (Rabi waves) in one-dimensional inhomogeneous quantum dot (QD) chain. QD-chain is modeled by the set of two-level quantum systems with tunnel coupling between neighboring QDs. The space propagation of Rabi waves in the form of traveling waves and localized wave packets is considered. It is shown, that the propagation of Rabi waves is accompanied by the transfer of the inversion and quantum correlations along the QD-chain and by their reflection and mutual transformations at the spatial inhomogeneities of QE-chain. The effect is potentially applicable in quantum nanooptics and quantum informatics.
We predict and theoretically investigate the new coherent effect of nonlinear quantum optics---spatial propagation of Rabi oscillations (Rabi waves) in one-dimensional quantum dot (QD) chain. QD chain is modeled by the set of two-level quantum systems with tunnel coupling between neighboring QDs. The space propagation of Rabi waves in the form of traveling waves and wave packets is considered. It is shown, that traveling Rabi waves are quantum states of QD chain dressed by radiation. The dispersion characteristics of traveling Rabi waves are investigated and their dependence on average number of photons in wave is demonstrated. The propagation of Rabi wave packets is accompanied by the transfer of the inversion and quantum correlations along the QD chain and by the transformation of quantum light statistics. The conditions of experimental observability are analyzed. The effect is potentially useful for quantum computing and quantum informatics.
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.