  Galactic centers are very dynamically active environments, often harbouring a
nuclear star cluster and supermassive black hole at their cores. Binaries in
these environments are subject to strong tidal fields that can efficiently
torque its orbit, exciting near unity eccentricities that ultimately lead to
their merger. In turn, frequent close interactions with passing stars
impulsively perturb the orbit of the binary, generally softening their orbit
until their evaporation, potentially hindering the role of tides to drive these
mergers. In this work, we study the evolution of compact object binaries in the
galactic center and their merger rates, focusing for the first time on the
combined effect of the cluster's tidal field and flyby interactions. We find a
significant synergy between both processes, where merger rates increase by a
factor of ~10-30 compared to models in which only flybys or tides are taken
into account. This synergy is a consequence of the persistent tides-driven
eccentricity excitation that is enhanced by the gradual diffusion of $j_z$
driven by flybys. The merger efficiency peaks when the diffusion rate is
~10-100 slower than the tides-driven torquing. Added to this synergy, we also
find that the gradual softening of the binary can lift the relativistic
quenching of initially tight binaries, otherwise unable to reach extreme
eccentricities, and thus expanding the available phase-space for mergers.
Cumulatively, we conclude that despite the gradual softening of binaries due to
flybys, these greatly enhance their merger rates in galaxy centers by promoting
the tidal field-driven eccentricity excitation.
