Multiphoton controllable transport between remote resonators

We develop a novel method for multiphoton controllable transport between remote resonators. Specifically, an auxiliary resonator is used to control the coherent long-range coupling of two spatially separated resonators, mediated by a coupled-resonator chain of arbitrary length. In this manner, an arbitrary multiphoton quantum state can be either transmitted through or reflected off the intermediate chain on demand, with very high fidelity. We find, on using a time-independent perturbative treatment, that quantum information leakage of an arbitrary Fock state is limited by two upper bounds, one for the transmitted case and the other for the reflected case. In principle, the two upper bounds can be made arbitrarily small, which is confirmed by numerical simulations.Comment: 16 pages, 7 figure

On blowup formulae for the S-duality conjecture of Vafa and Witten

This is the first part of two papers. In this part, we prove the blowup formulae for virtual Hodge polynomials of Gieseker moduli spaces of rank-2 stable sheaves and Uhlenbeck compactification spaces over algebraic surfaces. In particular, we verify the blowup formulae for the S-duality conjecture of Vafa-Witten, i.e. the blowup formulae for the Euler numbers of instanton moduli spaces over algebraic surfaces.Comment: 24 page