Controllable fusion of electromagnetic bosons in two-dimensional semiconductors

We propose a physical principle for implementation of controllable interactions of excitons in two-dimensional semiconductors. The key ingredients are tightly bound biexcitons and in -plane anisotropy of the host structure due to, e.g., a uniaxial strain. We show that anisotropy -induced splitting of the radiative exciton doublet couples the biexciton state to continua of exciton scattering states. As a result, two -body elastic scattering of excitons may be resonantly amplified when energetically tuned close to the biexciton by applying a transverse magnetic field or tuning the coupling with the microcavity photon mode. At the resonance excitonic fields may undergo quantum reaction of fusion. The fusion and a reverse reaction of biexciton disintegration may be used for efficient generation of squeezed light. For "bright" excitons in the absence of a microcavity, we predict giant molecules (Feshbach dimers) which can be obtained from a biexciton via rapid adiabatic sweeping of the magnetic field across the resonance. The molecules possess nontrivial entanglement properties. Our proposal holds promise for the strongly correlated photonics and quantum chemistry of light.