Prediction of Toric Code Topological Order from Rydberg Blockade

Verresen, Ruben; Lukin, Mikhail D.; Vishwanath, Ashvin

doi:10.1103/PhysRevX.11.031005

Title: Prediction of Toric Code Topological Order from Rydberg Blockade

Journal Article · Thu Jul 08 00:00:00 EDT 2021 · Physical Review. X

DOI:https://doi.org/10.1103/PhysRevX.11.031005· OSTI ID:1806373

; Lukin, Mikhail D.;

The physical realization of $$\mathbb{Z}_2$$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius. First, we show that the blockade model—also known as a “$$\textit{PXP}$$” model—realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term. This model can be interpreted as a $$\mathbb{Z}_2$$ gauge theory whose dynamics is generated by monomer fluctuations. We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln 2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap. Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions $V(r) ~ 1/r^6$ for a choice of lattice parameters. Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter. We show how these can be measured experimentally using a dynamic protocol, providing a “smoking gun” experimental signature of the TQL phase. Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.

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Research Organization:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Simons Foundation; US Army Research Office (ARO); National Science Foundation (NSF)

Grant/Contract Number:: SC0021013; 651440; PHY-1734011; W911NF2010082; PHY-2012023

OSTI ID:: 1806373

Alternate ID(s):: OSTI ID: 1853701

Journal Information:: Physical Review. X, Journal Name: Physical Review. X Vol. 11 Journal Issue: 3; ISSN 2160-3308

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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