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arXiv:0907.3191 · Physical Review B

Strong electron-photon coupling in a one-dimensional quantum dot chain: Rabi waves and Rabi wave packets

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

Published Feb 22, 2010• 39 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.81.085115

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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.
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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 $2\ifmmode\times\else\texttimes\fi{}2$ 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.
We present a model of one-dimensional chain of two-level artificial atoms driven with DC field and quantum light simultaneously in a strong coupling regime. The interaction of atoms with light leads to electron-photon entanglement (dressing of the atoms with light). The driving via dc field leads to the Bloch oscillations (BO) in the chain of dressed atoms. We consider the mutual influence of dressing and BO and show that scenario of oscillations dramatically differs from predicted by the Jaynes-Cummings and Bloch-Zener models. We study the evolution of the population inversion, tunneling current, photon probability distribution, mean number of photons, and photon number variance, and show the influence of BO on the quantum-statistical characteristics of light. For example, the collapse-revivals picture and vacuum Rabi-oscillations are strongly modulated with Bloch frequency. As a result, quantum properties of light and degree of electron-photon entanglement become controllable via adiabatic dc field turning. On the other hand, the low-frequency tunneling current depends on the quantum light statistics (in particular, for coherent initial state it is modulated accordingly the collapse-revivals picture). The developed model is universal with respect to the physical origin of artificial atom and frequency range of atom-light interaction. The model is adapted to the 2D-heterostructures (THz frequencies), semiconductor quantum dots (optical range), and Josephson junctions (microwaves). The data for numerical simulations are taken from recently published experiments. The obtained results open a new way in quantum state engineering and nano-photonic spectroscopy.
The influence of local fields on the excitonic Rabi oscillations in isolated, arbitrary shaped quantum dot (QD) has been theoretically investigated. Hamiltonian of the system "QD+electromagnetic field" has been obtained. Both QD interaction with classical electromagnetic field and ultrashort optical pulse has been considered. As a result, the bifurcation and anharmonism in the Rabi oscillations in a QD exposed to the monochromatic field have been predicted. The dependence of Rabi oscillations period on the QD depolarization parameter, which characterize local field has been obtained. It has been shown, that for the Gaussian pulse the final state of inversion as a function of peak pulse strength demonstrates step-like transitions.
A theory of the nonlinear interaction between a single quantum dot (QD) and electromagnetic fields, accounting the QD-depolarization (local-field) has been developed. QD excitation by classical and quantum electromagnetic fields such as coherent state of light, Fock qubit and gaussian excitation has been considered. As a result, for the case of the QD illuminated by coherent states of light, we predict the appearance of two oscillatory regimes in the Rabi oscillations. In the first one, signatures of Rabi oscillations are found to be suppressed: the population inversion is negative and the conventional collapse-revivals phenomenon is absent, while in the second one the collapse and revivals are appeared, showing significant difference as compared to those predicted within the standard Jaynes-Cummins theory. Under the pulsed excitation, Rabi oscillation dynamics is found to be strongly depended on the input pulse area and duration.