Long-range quantum coherence in electronic dot–cavity systems

We present a theoretical analysis of coherent electronic transport across a mesoscopic dot--cavity system and extensions thereof. Such coherent transport has been recently demonstrated in an experiment with a dot--cavity hybrid implemented in a high-mobility two-dimensional electron gas [PRL 115, 166603 (2015)] and its spectroscopic signatures have been interpreted in terms of a competition between Kondo-type dot-lead and molecular-type dot--cavity singlet-formation. We analyze the system in a progressive fashion, starting with a single particle numerical investigation of the 2D geometry which allows us to postulate an effective 1D model with a local impurity. We then address this model using many body techniques, from exact diagonalisation to Fermi liquid theory through an equation of motion approach for Green's functions, to predict the system's transport properties. Our analysis brings forward all the transport features observed in the experiments and supports the claim that a spin-coherent molecular singlet forms across the full extent of the dot--cavity device. We then propose a new experimental setup which paves the way for an all electronic, long range entangling gate and could be used to study a delocalised impurity in a Kondo system, the Kondo cat.