  Confining light in open structures is a long-sought goal in nanophotonics and
cavity quantum electrodynamics. Embedded eigenstates provide infinite lifetime
despite the presence of available leakage channels, but in linear
time-invariant systems they cannot be excited from the outside, due to
reciprocity. Here, we investigate how atomic nonlinearities may support
single-photon embedded eigenstates, which can be populated by a multi-photon
excitation followed by internal relaxation. We calculate the system dynamics
and show that photon trapping, as well as the reverse release process, can be
achieved with arbitrarily high efficiencies. We also discuss the impact of
loss, and a path towards the experimental verification of these concepts.
