Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator

We use a Rydberg quantum simulator to demonstrate a new form of
spectroscopy, called quench spectroscopy, which probes the low-energy
excitations of a many-body system. We illustrate the method on a
two-dimensional simulation of the spin-1/2 dipolar XY model. Through
micro- scopic measurements of the spatial spin correlation dynamics
following a quench, we extract the dispersion relation of the elementary
excitations for both ferro- and anti-ferromagnetic cou- plings. We observe
qualitatively different behaviors between the two cases that result from
the long-range nature of the interactions, and the frustration inherent in
the antiferromagnet. In particular, the ferromagnet exhibits elementary
excitations behaving as linear spin waves. In the anti-ferromagnet, spin
waves appear to decay, suggesting the presence of strong nonlinear- ities.
Our demonstration highlights the importance of power-law interactions on
the excitation spectrum of a many-body system.