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Kink bound states in the one dimensional ferromagnetic Ising chain compoundCoNb$_2$O$_6$ have been studied using high resolution time-domain terahertzspectroscopy in zero applied magnetic field. When magnetic order develops atlow temperature, nine bound states of kinks become visible. Their energies canbe modeled exceedingly well by the Airy function solutions to a 1DSchr\"odinger equation with a linear confining potential. This sequence ofbound states terminates at a threshold energy near two times the energy of thelowest bound state. Above this energy scale we observe a broad featureconsistent with the onset of the two particle continuum. At energies just belowthis threshold we observe a prominent excitation that we interpret as a novelbound state of bound states -- two pairs of kinks on neighboring chains.

A hierarchy of bound states in the 1D ferromagnetic Ising chain CoNb$_2$O$_6$ investigated by high resolution time-domain terahertz spectroscopy