The nature and spectrum of elementary excitations are defining features of a many-body system. In this study, we used a Rydberg quantum simulator to demonstrate a form of spectroscopy, called quench spectroscopy, that probes these low-energy excitations. We illustrated the method on a two-dimensional simulation of the spin-1/2 dipolar XY model. Through microscopic measurements of the spatial spin correlation dynamics following a quench, we extracted the dispersion relation of the elementary excitations for both ferro- and antiferromagnetic couplings. The ferromagnet exhibits elementary excitations behaving as linear spin waves, whereas in the antiferromagnet, spin waves appear to decay, suggesting the presence of strong nonlinearities. Our demonstration highlights the importance of power-law interactions on the excitation spectrum of a many-body system.
The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasiparticles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional
S=1/2 Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the nonlocal nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed-matter physics. Here, we show theoretically that quench spectroscopy for synthetic quantum matter---which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions---can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure nonlocal spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on exact results for the quench dynamics of quantum spin chains, and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.
The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasi-particles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional
S=1/2 Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the non-local nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed matter physics. Here we show theoretically that \emph{quench spectroscopy} for synthetic quantum matter -- which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions -- can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure non-local spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on new exact results for the quench dynamics of quantum spin chains; and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.