Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations

We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept is finer than dissipative solutions and satisfies the weak-strong uniqueness property. For a certain choice of the regularity weight, the existence of energy-variational solutions implies the existence of measure-valued solutions and for a different choice, we construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm

Coherent and robust high-fidelity generation of a biexciton in a quantum dot by rapid adiabatic passage

A biexciton in a semiconductor quantum dot is a source of polarization-entangled photons with high potential for implementation in scalable systems. Several approaches for non-resonant, resonant and quasi-resonant biexciton preparation exist, but all have their own disadvantages, for instance low fidelity, timing jitter, incoherence or sensitivity to experimental parameters. We demonstrate a coherent and robust technique to generate a biexciton in an InGaAs quantum dot with a fidelity close to one. The main concept is the application of rapid adiabatic passage to the ground state-exciton-biexciton system. We reinforce our experimental results with simulations which include a microscopic coupling to phonons.Comment: Main manuscript 5 pages and 4 figures, Supplementary Information 5 pages and 3 figures, accepted as a Rapid Communication in PRB. arXiv admin note: text overlap with arXiv:1701.0130