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 nonergodic 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 nonintegrable Rydberg atom model and prove that they arise from a requantization 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 firm up the analogy between the eigenstate scarring in the Rydberg atom chains and the single-particle quantum systems.

Automated summary

The text explains key concepts and findings in the theory of quantum scarring, demonstrating that quasimodes arise from previously established periodic orbits when quantum fluctuations are restored. The results shed light on the role of the TDVP classical system in Rydberg atom chains and its impact on the system.