An ideal source of entangled photon pairs combines the perfect symmetry of an atom with the convenient electrical trigger of light sources based on semiconductor quantum dots. We create a naturally symmetric quantum dot cascade that emits highly polarization entangled photon pairs on demand. The emitted photons strongly violate Bell’s inequality. Our source consists of strain-free GaAs dots grown by Droplet Epitaxy on a triangular symmetric (111)A surface . The remaining decoherence channel of the photon source is ascribed to random charge and nuclear spin fluctuations in and near the dot. We discuss the practical consequences of the nonlinear (quantum) dynamics of the coupled electron-nuclear spin system revealed in quantum dot optics  in these nano-objects with trigonal (C3v) symmetry .
The second part of the talk will be devoted to another degree of freedom : the valley index of electrons in atomically thin two-dimensional crystals. Monolayer MoS2 has emerged as a very promising material for optoelectronic and spin applications for mainly two reasons : First, the indirect bulk semiconductor MoS2 becomes direct when thinned to one monolayer, resulting in efficient optical absorption and emission. Second, the inherent inversion symmetry breaking (usually absent in graphene) together with the strong spin-orbit interaction leads to a coupling of carrier spin and k-space valley physics . The resulting chiral optical selectivity allows exciting one of these non-equivalent K valleys. Both the magnetic field and the temperature dependence of this optical initialization of the valley index will be discussed  in the context of preparing valley-Hall coupled to spin-Hall measurements.
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