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.
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