M. Winger | Search arXiv

arXiv2021

Unconditionally energy stable and first-order accurate numerical schemes for the heat equation with uncertain temperature-dependent conductivity

In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving computational efficiency. Both mixed and Robin-type boundary conditions are treated. In contrast with alternative, related methodologies, stability and convergence are unconditional. In particular, we prove unconditional, energy stability and optimal-order error estimates. A battery of numerical tests are presented to illustrate both the theory and application of these algorithms.

math.NA↗

arXiv2006

Quantum nature of a strongly-coupled single quantum dot-cavity system

Cavity quantum electrodynamics (QED) studies the interaction between a quantum emitter and a single radiation-field mode. When an atom is in strong coupling with a cavity mode1,2, it is possible to realize key quantum information processing (QIP) tasks, such as controlled coherent coupling and entanglement of distinguishable quantum systems. Realizing these tasks in the solid state is clearly desirable, and coupling semiconductor self-assembled quantum dots (QDs) to monolithic optical cavities is a promising route to this end. However, validating the efficacy of QDs in QIP applications requires confirmation of the quantum nature of the QD-cavity system in the strong coupling regime. Here we find a confirmation by observing quantum correlations in photoluminescence (PL) from a photonic crystal (PC) nanocavity3-5 interacting with one, and only one, QD located precisely at the cavity electric field maximum. When off-resonance, photon emission from the cavity mode and QD excitons is anti-correlated at the level of single quanta, proving that the mode is driven solely by the QD despite an energy mis-match between cavity and excitons. When tuned into resonance, the exciton and photon enter the strong-coupling regime of cavity-QED and the QD lifetime reduces by a factor of 120. The photon stream from the cavity becomes anti-bunched, proving that the coupled exciton/photon system is in the quantum anharmonic regime. Our observations unequivocally show that QIP tasks requiring the quantum nonlinear regime are achievable in the solid state.

quant-ph↗