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arXiv:2204.05380 · Nature

Realizing a 1D topological gauge theory in an optically dressed BEC

Anika Frölian, C. S. Chisholm, E. Neri, Cesar R. Cabrera, Ramón Ramos, Alessio Celi, Leticia Tarruell

Published Aug 10, 2022• 76 citations
arXivHTMLPDF
DOI
10.1038/s41586-022-04943-3

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Topological gauge theories constitute a framework for understanding strongly correlated quantum matter in terms of weakly interacting composite degrees of freedom. Their topological properties become evident when these theories are realized on a space of nontrivial topology. Here, we propose a scheme to realize a one-dimensional topological gauge theory, the so-called chiral BF theory, on a ring geometry. We obtain such a theory by dimensionally reducing Chern-Simons theory on a disk to the chiral BF theory defined on the ring. Then, we encode the theory into a Hamiltonian with a coupling between angular momentum and density, and we propose and numerically benchmark its realization in an optically dressed Bose gas confined in a ring-shaped trap. There, the topological properties of the underlying theory manifest themselves through a magnetic flux variable that is density dependent. We quantify such density-dependent magnetic flux in terms of the ground-state angular momentum and the chiral properties of the system through a Bogoliubov analysis. Our proposal enables the observation of topological features of the chiral BF theory that become manifest due to the nontrivial topology of the ring geometry.
Abstract Simulating U(1) quantum gauge theories with spatial dimensions greater than one is of great physical significance. Here we propose a simple realization of U(1) gauge theory with Rydberg and Rydberg-dressed atom arrays. Within the experimentally accessible range, we find that the various aspects of the U(1) gauge theory can be well simulated, such as the emergence of topological sectors, incommensurability, and the Rokhsar–Kivelson point that hosts deconfined charge excitations and degenerate topological sectors. Our proposal is promising to implement experimentally and exhibits pronounced quantum dynamics.
Symmetry-protected topological (SPT) states have boundary 't Hooft anomalies that obstruct the effective boundary theory realized in its own dimension with UV completion and with an on-site G-symmetry.In this work, yet we show that a certain anomalous non-on-site G-symmetry along the boundary becomes on-site when viewed as an extended H-symmetry, via a suitable group extension 1 → K → H → G → 1. Namely, a nonperturbative global (gauge or gravitational) anomaly in G becomes anomaly free in H.This guides us to construct an exactly soluble lattice path integral and Hamiltonian of symmetric gapped boundaries applicable to any SPT state of any finite symmetry group, including on-site unitary and antiunitary time-reversal symmetries.The resulting symmetric gapped boundary can be described either by an H-symmetry extended boundary in any spacetime dimension or, more naturally, by a topological emergent K-gauge theory with a global symmetry G on a 3 þ 1D bulk or above.The excitations on such a symmetric topologically ordered boundary can carry fractional quantum numbers of the symmetry G, described by representations of H. (Applying our approach to a 1 þ 1D boundary of 2 þ 1D bulk, we find that a deconfined gauge boundary indeed has spontaneous symmetry breaking with long-range order.The deconfined symmetry-breaking phase crosses over smoothly to a confined phase without a phase transition.)In contrast to known gapped boundaries or interfaces obtained via symmetry breaking (either global symmetry breaking or the Anderson-Higgs mechanism for gauge theory), our approach is based on symmetry extension.More generally, applying our approach to SPT states, topologically ordered gauge theories, and symmetry enriched topologically ordered (SET) states leads to generic boundaries or interfaces constructed with a mixture of symmetry breaking, symmetry extension, and dynamical gauging.