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arXiv:cond-mat/0601606 · Physical Review B

Rabi oscillations in the four-level double-dot structure under the influence of the resonant pulse

Alexander V. Tsukanov

Published Feb 9, 2006• 38 citations
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Abstract

We study theoretically the quantum dynamics of an electron in the symmetric four-level double-dot structure under the influence of the monochromatic resonant pulse. The probability amplitudes of the eigenstates relevant for the quantum dynamics are found from the solution of the nonstationary Schr\"odinger equation. The first-order correction term to the solution obtained through the rotating-wave approximation is calculated. The three-level double-dot dynamics and the two-level single-dot dynamics, as well as the off-resonant excitation process, are derived from the general formulas for corresponding choices of the pulse and structure parameters. The results obtained may be applied to the solid-state qubit design.

DOI
10.1103/physrevb.73.085308

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We study theoretically the quantum dynamics of an electron in the symmetric four-level double-dot structure under the influence of the monochromatic resonant pulse. The probability amplitudes of the eigenstates relevant for the quantum dynamics are found from the solution of the nonstationary Schr"odinger equation. The first-order correction term to the solution obtained through the rotating-wave approximation is calculated. The three-level double-dot dynamics and the two-level single-dot dynamics, as well as the off-resonant excitation process, are derived from the general formulas for corresponding choices of the pulse and structure parameters. The results obtained may be applied to the solid-state qubit design.
The oscillation characteristics of populations in two orthogonal energy substates of semiconductor quantum dots (SQDs) excited by linearly polarized monochromatic pulse field were discussed. With rotatingwave approximation, the nondamped solutions of the dynamic population equations with resonance excitation were deduced. The effective transition dipole moments and effective input pulse area were introduced and their expressions were also given. Theoretical analysis showed that the amplitude and frequency of the population oscillation on the substates can be manipulated by adjusting the original conditions and the polarization angle of excitation field.
We study theoretically the quantum dynamics of two interacting electrons in the symmetric double-dot structure under the influence of a bichromatic resonant pulse. The state vector evolution is studied for two different pulse designs. It is shown that the laser pulse can generate an effective exchange coupling between electron spins localized in different dots. Possible applications of this effect to quantum-information processing (entanglement generation, quantum-state engineering) are discussed.
Quantum operations with a charge solid-state qubit whose logical states are formed by two spatially separated localized states of an electron in the double-dot structure are studied theoretically. We show that it is possible to perform various one-qubit rotations making use of the microwave pulses tuned to the resonances between the localized states and the excited state delocalized over the nanostructure. An explicit analytic expression for the time-dependent electron state vector is derived, and the appropriate pulse parameters are determined.
We theoretically investigate the influence of dynamic Coulomb interaction on optical bistability and Rabi oscillations in a driven two-level semiconductor quantum dot system under laser irradiation. Using density matrix equations derived from the Coulomb-interaction model proposed by Lu et al. [Phys. Rev. A 103, 043504 (2021)], we obtain analytical solutions for population inversion under the rotating wave approximation. Our analysis shows that the Coulomb interaction induces optical bistability, governed by a cubic equation. The thresholds and the shapes of the hysteresis loops are tunable and can be controlled by various parameters, including electron density, confinement potential, detuning, and dephasing. Additionally, our numerical simulations demonstrate the potential for achieving high-efficiency population inversion and predicting bifurcation and anharmonic regimes in Rabi oscillations under monochromatic excitation.
The influence of electron-hole dipole-dipole interactions (local fields) on the excitonic Rabi oscillations in an isolated quantum dot (QD) has been theoretically investigated. An analysis for the QD interaction with monochromatic field and ultrashort Gaussian pulse has been performed. On the basis of optical Bloch equations the Rabi oscillation dynamics has been investigated. As a result, the bifurcation and essentially anharmonic regimes in the Rabi oscillations in a QD exposed to the monochromatic field have been predicted. The strong dependence of the period of Rabi oscillations on the QD depolarization has been revealed. For the Gaussian pulse it has been shown that the final state of inversion as a function of the pulse peak strength demonstrates step-like transitions.