Correspondence Principle for Many-Body Scars in Ultracold Rydberg Atoms

• Published in: Physical review. X Vol. 11; no. 2; p. 021021
• Main Authors: Turner, C. J., Desaules, J.-Y., Bull, K., Papić, Z.
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 01-04-2021
• Subjects: Chains; Chaos theory; Correspondence; Eigenvectors; Mathematical analysis; Orbits; Quantum computers; Qubits (quantum computing); Scars; Standing waves; Thermalization (energy absorption); Wave functions
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.11.021021

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.