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Physical Review Letters

Nonmonotonic Field Dependence of Damping and Reappearance of Rabi Oscillations in Quantum Dots

Alexei Vagov, Mihail D Croitoru, V. M. Axt, T. Kühn, François Maria Peeters

Published Jun 1, 2007• 114 citations
Publisher

Abstract

The dynamics of strongly confined laser driven semiconductor quantum dots coupled to phonons is studied theoretically by calculating the time evolution of the reduced density matrix using a numerical path integral method. We explore the cases of long pulses, strong dot-phonon and dot-laser coupling, and high temperatures, which, up to now, have been inaccessible. We find that the phonon-induced damping of Rabi rotations is a nonmonotonic function of the laser field that is increasing at low fields and decreasing at high fields. This results in a reappearance of Rabi rotations at high fields. This phenomenon is of a general nature which occurs for all temperatures and carrier-phonon coupling strengths.

DOI
10.1103/physrevlett.98.227403

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The dynamics of strongly confined laser driven semiconductor quantum dots coupled to phonons is studied theoretically by calculating the time evolution of the reduced density matrix using a numerical path integral method. We explore the cases of long pulses, strong dot-phonon and dot-laser coupling, and high temperatures, which, up to now, have been inaccessible. We find that the phonon-induced damping of Rabi rotations is a nonmonotonic function of the laser field that is increasing at low fields and decreasing at high fields. This results in a reappearance of Rabi rotations at high fields. This phenomenon is of a general nature which occurs for all temperatures and carrier-phonon coupling strengths.
We study the dynamics of strongly confined semiconductor quantum dots coupled to acoustic phonons and driven by external laser pulses by a numerical path integral method. The field-dependent damping, caused by the non-Markovian processes of pure dephasing and manifesting itself in the peculiar decay and reappearance phenomenon of Rabi rotations is found to depend notably on the dot size and the shape of the applied laser pulses. In the limit of strong fields rectangular pulses yield a significant weaker damping than Gaussian or other bell-shaped profiles. As a consequence, the undamping of Rabi rotations at high pulse areas is most clearly visible for rectangular pulses.
Phonons in solid-state quantum emitters play a crucial role in their performance as photon sources in quantum technology. For resonant driving, phonons dampen the Rabi oscillations, resulting in reduced state-preparation fidelities. The phonon spectral density, which quantifies the strength of the carrier-phonon interaction, is nonmonotonic as a function of energy. As one of the most prominent consequences, this should lead to the reappearance of Rabi rotations for increasing pulse power, according to the theoretical predictions in Vagov et al. [Phys. Rev. Lett. 98, 227403 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.227403]. In this Letter, we present the experimental demonstration of the reappearance of Rabi rotations for a resonantly driven quantum dot.
We study optically driven Rabi rotations of a quantum dot exciton transition between 5 and 50 K, and for pulse areas of up to 14π. In a high driving field regime, the decay of the Rabi rotations is nonmonotonic, and the period decreases with pulse area and increases with temperature. By comparing the experiments to a weak-coupling model of the exciton-phonon interaction, we demonstrate that the observed renormalization of the Rabi frequency is induced by fluctuations in the bath of longitudinal acoustic phonons, an effect that is a phonon analogy of the Lamb shift.
Abstract We have simulated coherent control signals from quantum dots for carrier phonon interactions covering the low as well as the strong coupling limit. Calculations using the correlation expansion for phonon assisted density matrices are compared with numerically exact results obtained from a time dependent path‐integral approach. Even at elevated coupling strengths both calculations agree well for not too high temperatures. For pulse lengths and delay times shorter than the phonon induced memory time the correlation expansion gives good results in almost all cases. For strong coupling and/or high temperatures drastic discrepancies emerge. Interestingly, the correlation expansion works better at high pulse areas, which is related to a dynamic decoupling of electron and phonon dynamics in strongly confined systems.
We show that the interaction between carriers confined in a quantum dot and the surrounding lattice under external driving of carrier dynamics has a dynamical, resonant character. The quality of Rabi oscillations in such a system depends on the relation between nonlinear spectral characteristics of the driven dynamics and the spectral density of effectively coupled lattice modes (phonon frequencies and density of states). For a large number of Rabi oscillations within a fixed time (allowed by, e.g., exciton recombination) the spectrum of the dynamics extends towards high frequencies, coming into resonance with acoustic and optical phonons. Thus, this resonant lattice response strongly restricts the possibility of fully coherent control over the charge state in a quantum dot.
Electron-phonon interaction is a major source of optical dephasing in semiconductor quantum dots. Within a density matrix theory the electron-phonon interaction is considered up to the second order of a correlation expansion, allowing the calculation of the quantum kinetic dephasing dynamics of optically induced nonlinearities in GaAs quantum dots for arbitrary pulse strengths and shapes. We find Rabi oscillations renormalized and a damping that depends on the input pulse strength, a behavior not known from exponential dephasing mechanisms.