Emergent Bloch Oscillations in a Kinetically Constrained Rydberg Spin Lattice

Magoni, Matteo; Mazza, Paolo; Lesanovsky, Igor

Abstract

We explore the relaxation dynamics of elementary spin clusters in a kinetically constrained spin system. Inspired by experiments with Rydberg lattice gases, we focus on the situation in which an excited spin leads to a "facilitated" excitation of a neighboring spin. We show that even weak interactions that extend beyond nearest neighbors can have a dramatic impact on the relaxation behavior: they generate a linear potential, which under certain conditions leads to the onset of Bloch oscillations of spin clusters. These hinder the expansion of a cluster and more generally the relaxation of many-body states towards equilibrium. This shows that non-ergodic behavior in kinetically constrained systems may occur as a consequence of the interplay between reduced connectivity of many-body states and weak interparticle interactions. We furthermore show that the emergent Bloch oscillations identified here can be detected in experiment through measurements of the Rydberg atom density, and discuss how spin-orbit coupling between internal and external degrees of freedom of spin clusters can be used to control their relaxation behavior. Introduction.-Kinetically constrained quantum systems have become an important setting for the investigation of complex dynamical many-body phenomena, both from the theoretical and the experimental point of view. In particular, constrained spin systems have turned out to constitute useful models for the study of slow relaxation, ergodicity breaking and the emergence of glassy physics [1-16]. In terms of experimental platforms a significant role is currently being played by Rydberg gases, in which atoms are excited to high-lying and strongly interacting states. This allows to implement effective quantum spin models with highly controllable state-dependent interactions that pave the way towards realizing a host of kinetic constraints [17-28]. Kinetic constraints impose restrictions on the connectiv-ity between many-body states that break the Hilbert space into disconnected sectors [29-32]. Ultimately, this may lead to the absence of thermalization and the emergence of non-ergodic behavior. This mechanism is different to ergodicity breaking stemming from disorder, occurring in many-body localized systems where it is caused by the emergence of local conservation laws [33]. Ergodic-ity breaking (in a disorder-free setting) may also occur when imposing externals fields: Refs. [34-42] show that for the case of a transverse field quantum Ising model, where an additionally applied longitudinal field leads to the confinement of excitations. This inhibits propagation of quasi-particles and thus prevents relaxation towards an ergodic steady state. In this work we investigate the dynamics of a disorder-free, translationally invariant many-body quantum spin system under a so-called facilitation constraint. As shown in Fig. 1, this can be realized with Rydberg atoms held in a lattice. We show that relaxation towards an ergodic stationary state is inhibited by the onset of Bloch oscil

Citation

Magoni, M., Mazza, P., & Lesanovsky, I. (2021). Emergent Bloch Oscillations in a Kinetically Constrained Rydberg Spin Lattice. Physical Review Letters, 126(10), Article 103002. https://doi.org/10.1103/physrevlett.126.103002

• Journal Article Type: Article
• Acceptance Date: Feb 17, 2021
• Online Publication Date: Mar 12, 2021
• Publication Date: Mar 12, 2021
• Deposit Date: Feb 19, 2021
• Publicly Available Date: Mar 15, 2021
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 126
• Issue: 10
• Article Number: 103002
• DOI: https://doi.org/10.1103/physrevlett.126.103002
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/5335392
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.103002