Kink bound states in the one dimensional ferromagnetic Ising chain compound CoNb$_2$O$_6$ have been studied using high resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrodinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near two times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states -- two pairs of kinks on neighboring chains.
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