  Combining inelastic neutron scattering and numerical simulations, we study
the quasi-one dimensional Ising anisotropic quantum antiferromagnet \bacovo\ in
a longitudinal magnetic field. This material shows a quantum phase transition
from a N\'eel ordered phase at zero field to a longitudinal incommensurate spin
density wave at a critical magnetic field of 3.8 T. Concomitantly the
excitation gap almost closes and a fundamental reconfiguration of the spin
dynamics occurs. These experimental results are well described by the universal
Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in
one dimension. We especially observe the rise of mainly longitudinal
excitations, a hallmark of the unconventional low-field regime in Ising-like
quantum antiferromagnet chains.
