Ba2CuTeO6 is a newly discovered S=1/2 spin ladder material thought to be uniquely close to the theoretically predicted quantum critical point of the coupled two-leg spin ladder system. We have already extensively characterized the material using NMR, magnetic susceptibility, specific heat, torque magnetometry and powder neutron diffraction. Most recently we have performed inelastic neutron scattering measurements using MERLIN and observed key signatures of coupled ladder physics. The MERLIN data investigated the magnetic excitation spectrum above ~2 meV and here we plan to extend the study of the spin excitations with high-resolution measurements at lower energies to test for the presence or absence of a spin gap, as this is a key ingredient required to parameterize how close the system is to the quantum critical point.