Controllable fusion of excitons in two-dimensional semiconductors

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 stable 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. 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 the quantum chemistry of light.