  We study the quasiparticle excitation and quench dynamics of the
one-dimensional transverse-field Ising model with power-law ($1/r^{\alpha}$)
interactions. We find that long-range interactions give rise to a confining
potential, which couples pairs of domain walls (kinks) into bound
quasiparticles, analogous to mesonic bound states in high-energy physics. We
show that these quasiparticles have signatures in the dynamics of order
parameters following a global quench and the Fourier spectrum of these order
parameters can be expolited as a direct probe of the masses of the confined
quasiparticles. We introduce a two-kink model to qualitatively explain the
phenomenon of long-range-interaction induced confinement, and to quantitatively
predict the masses of the bound quasiparticles. Furthermore, we illustrate that
these quasiparticle states can lead to slow thermalization of one-point
observables for certain initial states. Our work is readily applicable to
current trapped-ion experiments.
