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arXiv:1807.02108 · Physical review. B./Physical review. B

Signatures of integrability in the dynamics of Rydberg-blockaded chains

Vedika Khemani, Chris R. Laumann, Anushya Chandran

Published Apr 3, 2019• 252 citations
arXivHTMLPDF

Abstract

A recent experiment on a 51-atom Rydberg-blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this Rapid Communication, we show that the experimental Hamiltonian exhibits nonthermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The distinctive quench dynamics in the parent model could signal an unconventional class of integrable system.

DOI
10.1103/physrevb.99.161101

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A recent experiment on a 51-atom Rydberg-blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this Rapid Communication, we show that the experimental Hamiltonian exhibits nonthermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The distinctive quench dynamics in the parent model could signal an unconventional class of integrable system.
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Recent experiments on Rydberg-atom quantum simulators have observed surprising signatures of nonergodic quantum dynamics, which has been attributed to the emergence of ``many-body quantum scars.'' Here, the authors present a detailed study of the eigenstate properties of strongly interacting Rydberg-atom chains, identifying distinct families of quantum scarred states that are responsible for the revivals in the quench dynamics. The results show that quantum scarred states have distinct features, such as subthermal entanglement and anomalous expectation values of local observables. The presence of scarred eigenstates leaves an imprint on the rest of the many-body spectrum, leading to a weak breakdown of ergodicity.
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
We show that unconventional relaxation dynamics of special initial states in one-dimensional arrays of Rydberg atoms produce non-generic decay of the initial-state survival probability (SP) at very early times. Using the PXP hamiltonian as a minimal model of the Rydberg blockade, we prove that the early-time SP for states exhibiting quantum many-body scarring (QMBS) decays at a characteristic rate, whose finite-size scaling is determined solely by scars. We numerically investigate the effects of both revival-enhancing and ergodicity-restoring deformations of the PXP hamiltonian and find results consistent with the limiting cases of integrable and ergodic dynamics, respectively. We moreover argue that such unconventional early relaxation of scarred initial states is characteristic of a whole class of QMBS models. Since the SP can be easily measured experimentally, our findings enable us to probe the presence of scars at time scales much shorter than that of thermalization.
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Gaussian correlations emerge in a large class of many-body quantum systems quenched out of equilibrium, as demonstrated in recent experiments on coupled one-dimensional superfluids [Schweigler et al., Nat.Phys.17, 559 (2021)].Here we present a mechanism by which an initial state of a Rydberg atom array can retain persistent non-Gaussian correlations following a global quench.This mechanism is based on an effective kinetic blockade rooted in the ground state symmetry of the system, which prevents thermalizing dynamics under the quench Hamiltonian.We propose how to observe this effect with Rydberg atom experiments and we demonstrate its resilience regarding several types of experimental error.These long-lived non-Gaussian states may have practical applications as quantum memories or stable resources for quantum information protocols due to the protected non-Gaussianity away from equilibrium.