Lindblad theory of dynamical decoherence of quantum-dot excitons

TL;DR

This paper develops a Lindblad-based theoretical framework to model phonon-induced decoherence in quantum-dot excitons under laser control, enabling simplified simulations and experimental phonon spectroscopy.

Contribution

It introduces a generalized Lindblad equation capturing phonon effects with time-dependent damping, ensuring positivity and simplifying non-Markovian dynamics modeling.

Findings

The theory accurately models phonon effects at low temperatures.

It enables optimized pulse shaping for exciton creation.

Proposes methods for phonon density of states measurement.

Abstract

We use the Bloch-Redfield-Wangsness theory to calculate the effects of acoustic phonons in coherent control experiments, where quantum-dot excitons are driven by shaped laser pulses. This theory yields a generalized Lindblad equation for the density operator of the dot, with time-dependent damping and decoherence due to phonon transitions between the instantaneous dressed states. It captures similar physics to the form recently applied to Rabi oscillation experiments [A. J. Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)], but guarantees positivity of the density operator. At sufficiently low temperatures, it gives results equivalent to those of fully non-Markovian approaches [S. Luker et al., Phys. Rev. B 85, 121302 (2012)], but is significantly simpler to simulate. Several applications of this theory are discussed. We apply it to adiabatic rapid passage experiments, and show how the pulses can be shaped to maximize the probability of creating a single exciton using a frequency-swept laser pulse. We also use this theory to propose and analyze methods to determine the phonon density of states experimentally, i.e. phonon spectroscopy, by exploring the dependence of the effective damping rates on the driving field.