Observation of Magnon Bound States in the Long-Range, Anisotropic Heisenberg Model

Since the 1930s, researchers have known that magnons—collective excitations of quantum spins propagating through a lattice—can exist as bound states. For short-range spin interactions, the dynamics of these bound states are well understood. But long-range interactions can significantly change this picture. Here, we present experimental tools to detect these bound states and show that they indeed exist in an experimental system. In our work, we experimentally probe the quantum dynamics of 20 individually controlled trapped ions. Using periodic driving, we realize a tunable, long-range, anisotropic Heisenberg model—a model of quantum spins—and characterize the excitations of the spin chain that are stabilized by the spin interactions. In particular, we demonstrate that the spectrum consists not only of single spin flips, or magnons, but also of bound states, provided the interactions between magnons are sufficiently strong. Interestingly, the long-range interactions lead to a divergent group velocity of the single magnons, while the bound states possess a well-defined, nondivergent velocity. These are striking features of the unconventional long-range interactions of our system. We elucidate these effects by developing new tools for measuring the dispersion of the magnon bound states and show their striking signature on the real-time spreading of correlations and entanglement. Our observations provide key insights into the peculiar role of composite excitations in the nonequilibrium dynamics of quantum many-body systems.