  We propose a physical principle for implementation of controllable
interactions of identical electromagnetic bosons (excitons or polaritons) in
two-dimensional (2D) 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 boson scattering
states. As a result, two-body elastic scattering of bosons 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, bosonic fields undergo quantum reaction of fusion
accompanied by their squeezing. For excitons, 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
non-trivial entanglement properties. Our proposal holds promise for the
strongly-correlated photonics and quantum chemistry of light.
