  The breathing pyrochlore lattice material Ba$_3$Yb$_2$Zn$_5$O$_{11}$ exists
in the nearly decoupled limit, in contrast to most other well-studied breathing
pyrochlore compounds. As a result, it constitutes a useful platform to
benchmark theoretical calculations of exchange interactions in insulating
Yb$^{3+}$ magnets. Here we study Ba$_3$Yb$_2$Zn$_5$O$_{11}$ at low temperatures
in applied magnetic fields as a further probe of the physics of this model
system. Experimentally, we consider the behavior of polycrystalline samples of
Ba$_3$Yb$_2$Zn$_5$O$_{11}$ with a combination of inelastic neutron scattering
and heat capacity measurements down to 75 mK and up to fields of 10 T.
Consistent with previous work, inelastic neutron scattering finds a level
crossing near 3 T, but no significant dispersion of the spin excitations is
detected up to the highest applied fields. Refinement of the theoretical model
previously determined at zero field can reproduce much of the inelastic neutron
scattering spectra and specific heat data. A notable exception is a low
temperature peak in the specific heat near 0.1 K. This may indicate the scale
of interactions between tetrahedra or may reflect undetected disorder in
Ba$_3$Yb$_2$Zn$_5$O$_{11}$.
