  We study a new effect of Cooper-pair-based two-photon gain in
semiconductor-superconductor structures, showing broadband enhancement of
ultrafast two-photon amplification. We further show that with the
superconducting enhancement, at moderately high seed intensities the two-photon
gain contribution approaches that of the one-photon gain. A full
quantum-optical model of singly- and fully-stimulated two-photon emission is
developed. Our results provide new insights on nonlinear light-matter
interaction in the superconducting state, including the possibility of coherent
control in two-photon semiconductor-superconductor devices. The theoretically
demonstrated effects can have important implications in optoelectronics and in
coherent control applications.
