Greatly enhanced absorption of nonresonant microwave fields by ultracold molecules near a Feshbach resonance

We show that the probability of the collision-induced absorption of nonresonant microwave photons by a gas of ultracold molecules is dramatically enhanced near a Feshbach scattering resonance. This can be used for detecting Feshbach resonances of ultracold molecules by measuring the microwave field absorption and for tuning the elastic scattering cross sections of ultracold molecules by varying the frequency and intensity of the microwave field in a wide range of the field parameters.