  We apply input-output theory with quantum pulses [AH Kiilerich, K M\o lmer,
Phys. Rev. Lett. {\bf 123}, 123604 (2019)] to a model of a new type of
two-photon detector consisting of one molecule that can detect two photons
arriving sequentially in time. The underlying process is distinct from the
usual two-photon absorption process where two photons arriving simultaneously
and with frequencies adding up to the resonance frequency are absorbed by a
single molecule in one quantum jump. Our detector model includes a Hamiltonian
description of the amplification process necessary to convert the microscopic
change in the single molecule to a macroscopic signal.
