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arXiv:2010.07825 · Physical Review Letters

Emergent Bloch Oscillations in a Kinetically Constrained Rydberg Spin Lattice

Matteo Magoni, Paolo P. Mazza, Igor Lesanovsky

Published Mar 12, 2021• 28 citations
arXivHTMLPDF

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 toward equilibrium. This shows that nonergodic 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.

DOI
10.1103/physrevlett.126.103002

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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 toward equilibrium. This shows that nonergodic 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.
We study the dynamics of a one-dimensional Rydberg lattice gas under facilitation (anti-blockade) conditions which implements a so-called kinetically constrained spin system. Here an atom can only be excited to a Rydberg state when one of its neighbors is already excited. Once two or more atoms are simultaneously excited mechanical forces emerge, which couple the internal electronic dynamics of this many-body system to external vibrational degrees of freedom in the lattice. This electron-phonon coupling results in a so-called phonon dressing of many-body states which in turn impacts on the facilitation dynamics. In our theoretical study we focus on a scenario in which all energy scales are sufficiently separated such that a perturbative treatment of the coupling between electronic and vibrational states is possible. This allows to analytically derive an effective Hamiltonian for the evolution of clusters of consecutive Rydberg excitations in the presence of phonon dressing. We analyze the spectrum of this Hamiltonian and show --- by employing Fano resonance theory --- that the interaction between Rydberg excitations and lattice vibrations leads to the emergence of slowly decaying bound states that inhibit fast relaxation of certain initial states.
Rydberg lattice under facilitation conditions can feature kinetic constraints, leading to ballistic and nonergodic behavior at different detuning intensities. Here, we demonstrate that a resonant driving field can achieve effects similar to those under facilitation conditions. We focus on the relaxation dynamics of spin clusters in a periodically driven Rydberg spin lattice. Through an effective Hamiltonian for the domain walls of the spin cluster, it is shown that when the driving frequency is resonant with the Rydberg interaction, the spin cluster exhibits ballistic expansion with half the spreading rate compared to the case of facilitation conditions. However, near the resonant point, the spin cluster displays confinement behavior of the Bloch-like oscillations. These results demonstrate the rich dynamic behaviors in the driven Rydberg spin lattices and may find applications in quantum state manipulation.
Lattice spin models featuring kinetic constraints constitute a paradigmatic setting for the investigation of glassiness and localization phenomena. The intricate dynamical behavior of these systems is a result of the dramatically reduced connectivity between many-body configurations. This truncation of transition pathways often leads to a fragmentation of the Hilbert space, yielding highly collective and therefore often slow dynamics. Moreover, this mechanism supports the formation of characteristic elementary excitations, which we investigate here theoretically in a two-dimensional Rydberg lattice gas. We explore their properties as a function of interaction strength and range, and illustrate how they can be experimentally probed via sideband spectroscopy. Here, we show that the transition rate to certain delocalized superposition states of elementary excitations displays collective many-body enhancement.
Quantum spin systems with kinetic constraints have become paradigmatic for exploring collective dynamical behavior in many-body systems. Here we discuss a facilitated spin system which is inspired by recent progress in the realization of Rydberg quantum simulators. This platform allows to control and investigate the interplay between facilitation dynamics and the coupling of spin degrees of freedom to lattice vibrations. Developing a minimal model, we show that this leads to the formation of polaronic quasiparticle excitations which are formed by many-body spin states dressed by phonons. We investigate in detail the properties of these quasiparticles, such as their dispersion relation, effective mass, and the quasiparticle weight. Rydberg lattice quantum simulators are particularly suited for studying this phonon-dressed kinetically constrained dynamics as their exaggerated length scales permit the site-resolved monitoring of spin and phonon degrees of freedom.
We investigate the interplay between mechanical forces and the internal-state dynamics of Rydberg excitations in atom-tweezer arrays. Dipole interactions between Rydberg atoms facilitate excitation spreading, but at the same time couple electronic (spin) degrees of freedom with motional (phonon) states. With increasing spin-phonon coupling, the growth dynamics of a cluster of excited Rydberg atoms changes from ballistic spreading to Bloch-like oscillations and eventually to Anderson-like localization. We show that these effects are caused by quantum fluctuations in the phonon field: The dynamics of a Rydberg cluster can be mapped to a single particle in a semi-infinite lattice subject to phonon-induced energy shifts. The mean-field contribution of this energy shift leads to a linear potential gradient, resulting into Bloch-like oscillations. In addition, quantum fluctuations of phonons create a random local potential causing a transition from a regime of Bloch oscillations to localization. The spin-phonon coupling leads furthermore to highly correlated and non-classical phonon states in the form of squeezed states of the position of the Rydberg atoms. Depending on the form of the dipolar interaction potential, either in- or out-of-phase correlated oscillations of atoms emerge.
In a strongly interacting Rydberg atom array, the dynamics are often constrained to the decoupled Hilbert subspaces, representing an intriguing paradigm for nonergodicity. By considering a variable detuning of the global Rydberg coupling, we show that, not only is the existence of these Hilbert subspaces dependent on the interplay of detuning and interaction, but they are also strongly fragmented, with the fragment dimensions exhibiting various scaling behaviors with increasing system size. The resulting constrained dynamics of the system are thus governed by the dimension and connectivity of these fragments. We then adopt an auxiliary fermion description to reveal the underlying emergent kinetic constraints for the subspace fragmentation and fragment-confined dynamics. Our results provide a systematic understanding of Hilbert-space fragmentation in Rydberg arrays, and shed light on engineering nonergodic many-body dynamics beyond the PXP model.