  Feshbach resonance occurs when a pair of free particles is resonantly coupled
to a molecular bound state. In the field of ultracold quantum gases, atomic
Feshbach resonances became a usual tool for tailoring atomic interactions
opening up many new applications in this field. In a semiconductor microcavity,
the Feshbach resonance appears when two lower polaritons are coupled to the
molecular biexciton state. Here, we demonstrate the existence of a cross
Feshbach resonance for which a pair of polaritons, lower together with upper,
effectively couples to the biexciton state. This demonstration is a crucial
step towards the efficient generation of entangled photon pairs in a
semiconductor microcavity. The existence of a Cross Feshbach resonance
establishes the condition to convert a pair of upper and lower polaritons via
the biexciton state into two lower polaritons, paving the way for the
generation of momentum and polarization entangled photons.
