  In this article we use time-dependent Josephson coupling to enhance
unconventional photon blockade in a system of two coupled nonlinear bosonic
modes which are initially loaded with weakly populated coherent states, so the
evolution is restricted to the manifold of up to two field quanta. Using
numerical optimal control, we find the optimal coupling which minimizes the
two-photon occupation of one mode, which is actually transferred to the other,
while maintains a non-zero one-photon occupation in the same mode. Moreover, we
choose the continuous coupling to vanish after the transfer between the modes
such that they are decoupled and one of them is left only with some one-photon
population which can be observed upon its decay. We numerically find lower
values of the second-order correlation function obtained at earlier times than
with constant coupling, with larger one-photon populations and for longer time
windows, corresponding thus to higher emission efficiency and easier detection.
The presented methodology is not restricted to the system under study, but it
can also be transferred to other related frameworks, to find the optimal
driving fields which can improve the single-photon emission statistics from
these systems.
