Correspondence principle for many-body scars in ultracold Rydberg atoms

The theory of quantum scarring – a remarkable violation of quantum unique ergodicity – rests on two complementary pillars: the existence of unstable classical periodic orbits and the so-called quasimodes, i.e., the non-ergodic states that strongly overlap with a small number of the system’s eigenstates. Recently, interest in quantum scars has been revived in a many-body setting of Rydberg atom chains. While previous theoretical works have identified periodic orbits for such systems using time-dependent variational principle (TDVP), the link between periodic orbits and quasimodes has been missing. Here we provide a conceptually simple analytic construction of quasimodes for the non-integrable Rydberg atom model, and prove that they arise from a “requantisation” of previously established periodic orbits when quantum fluctuations are restored to all orders. Our results shed light on the TDVP classical system simultaneously playing the role of both the mean-field approximation and the system’s classical limit, thus allowing us to establish a rigorous link between the eigenstate scarring in the Rydberg atom chains and the single-particle quantum systems.