  The Ising chain realizes the fundamental paradigm of spin fractionalization,
where locally flipping a spin creates two domain walls (spinons) that can
separate apart at no energy cost. In a quasi-one-dimensional system, the
mean-field effects of the weak three-dimensional couplings confine the spinons
into a Zeeman ladder of two-spinon bound states. Here, we experimentally tune
the confinement potential between spinons in the quasi-one-dimensional Ising
ferromagnet CoNb2O6 by means of an applied magnetic field with a large
component along the Ising direction. Using high-resolution single crystal
inelastic neutron scattering, we directly observe how the spectrum evolves from
the limit of very weak confinement at low field (with many closely-spaced bound
states with energies scaling as the field strength to the power 2/3) to very
strong confinement at high field (where it consists of a magnon and a
dispersive two-magnon bound state, with a linear field dependence). At
intermediate fields, we explore how the higher-order bound states disappear
from the spectrum as they move to higher energies and overlap with the
two-particle continuum. By performing a global fit to the observed spectrum in
zero field and high field applied along two orthogonal directions, combined
with a quantitative parameterization of the interchain couplings, we propose a
refined single chain and interchain Hamiltonian that quantitatively reproduces
all observed dispersions and their field dependence.
