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arXiv:2011.01500

Floquet Engineering of a Dynamical $Z_{2}$ Lattice Gauge Field with Ultracold Atoms

Wei Zheng, Pengfei Zhang

Published Nov 3, 2020• 2 citations
arXivHTMLPDF

Abstract

In this paper, we propose that a simple model, in which fermions coupled to a dynamical lattice gauge field, can be engineered via the Floquet approach. The model possess both a independent Maxwell term and the local $Z_{2}$ gauge symmetry. Our proposal relies on a species dependent optical lattice, and can be achieved in one, two or three dimension. By an unitary transformation, this model can be mapped into a non-interacting composite Fermion system with fluctuating back ground charge. With the help of this composite Fermion picture, two characteristic observations are predicted. One is the radio-frequency spectroscopy, which exhibits no dispersion in all parameter regimes. Second is the the dynamical localization, which depends on the structure of the initial states.

DOI
10.48550/arxiv.2011.01500

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We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2+12+12+1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3{\mathbb{Z}}_{3}Z3​ lattice gauge theory with dynamical fermionic matter in 2+12+12+1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
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