  Low temperature optical spectroscopy in applied magnetic fields provides
clear evidence of magnetoelastic coupling in the spin ice material
Ho$_2$Ti$_2$O$_7$. In far-IR reflectometry measurements, we observe field
dependent features around 30, 61, 72 and 78~meV, energies corresponding to
crystal electronic field (CEF) doublets. The calculations of the crystal-field
Hamiltonian model confirm that the observed features in IR spectra are
consistent with magnetic-dipole-allowed excitations from the ground state to
higher $^5$I$_8$ CEF levels. We present the CEF parameters that best describe
our field-dependent IR reflectivity measurements. Additionally, we identify a
weak field-dependent shoulder near one of the CEF doublets. This indicates that
this level is split even in zero-field, which we associate with a vibronic
bound state. Modeling of the observed splitting shows that the phonon resides
at slightly lower energy compared to the CEF level that it couples to, which is
in contrast with previously published inelastic neutron measurements. The
magnetic field dependence of the vibronic state shows a gradual decoupling of
the phonon with the CEF level as it shifts. This approach should work in
pyrochlores and other systems that have magnetic dipole transitions in the IR
spectroscopic range, which can elucidate the presence and the ability to tune
the nature of vibronic states in a wide variety of materials.
