  We investigate an efficient two-photon up-conversion process in more than one
molecule coupled to an optical antenna. In the previous work [Y. Osaka et al.,
PRL 112, 133601 (2014)], we considered the two-photon up-conversion process in
a single molecule within one-dimensional input-output theory, and revealed that
controlling the antenna-molecule coupling enables the efficient up-conversion
with radiative loss in the antenna suppressed. In this work, aiming to propose
a way to enhance the total probability of antenna-photon scattering, we extend
the model to the case of multiple molecules. In general, the presence of more
than one molecule decreases the up-conversion probability because they equally
share the energy of the two photons. However, it is shown that we can overcome
the difficulty by controlling the inter-molecule coupling. Our result implies
that, without increasing the incident photon number (light power), we can
enlarge the net probability of the two-photon up-conversion.
