BCS Pairing Detection by Electromagnetically Induced Transparency

We seek a new application of electromagnetically induced transparency (EIT), a well-known phenomena in quantum optics; to detect the onset of the BCS transition to superfluidity in a degenerate atomic fermi gas involving a pump and a copropagating probe laser field. We show that when a BCS pairing emerges, the EIT spectrum makes a qualitative change, which can be traced to the two-photon resonance condition being momentum-independent for a normal gas but momentum-dependent for a BCS paring phase. We will calculate and discuss the EIT spectrum under different situations including when the pseudo gap cannot be ignored.