Prediction of Toric Code Topological Order from Rydberg Blockade

The physical realization of 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...

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Autores principales:	Ruben Verresen, Mikhail D. Lukin, Ashvin Vishwanath
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/2b375a53c3d04ebb8e446183052c7acc
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spelling	oai:doaj.org-article:2b375a53c3d04ebb8e446183052c7acc2021-12-02T15:07:25ZPrediction of Toric Code Topological Order from Rydberg Blockade10.1103/PhysRevX.11.0310052160-3308https://doaj.org/article/2b375a53c3d04ebb8e446183052c7acc2021-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.031005http://doi.org/10.1103/PhysRevX.11.031005https://doaj.org/toc/2160-3308The physical realization of 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 “PXP” model—realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term. This model can be interpreted as a 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 ln2 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.Ruben VerresenMikhail D. LukinAshvin VishwanathAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 3, p 031005 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Ruben Verresen Mikhail D. Lukin Ashvin Vishwanath Prediction of Toric Code Topological Order from Rydberg Blockade
description	The physical realization of 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 “PXP” model—realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term. This model can be interpreted as a 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 ln2 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.
format	article
author	Ruben Verresen Mikhail D. Lukin Ashvin Vishwanath
author_facet	Ruben Verresen Mikhail D. Lukin Ashvin Vishwanath
author_sort	Ruben Verresen
title	Prediction of Toric Code Topological Order from Rydberg Blockade
title_short	Prediction of Toric Code Topological Order from Rydberg Blockade
title_full	Prediction of Toric Code Topological Order from Rydberg Blockade
title_fullStr	Prediction of Toric Code Topological Order from Rydberg Blockade
title_full_unstemmed	Prediction of Toric Code Topological Order from Rydberg Blockade
title_sort	prediction of toric code topological order from rydberg blockade
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/2b375a53c3d04ebb8e446183052c7acc
work_keys_str_mv	AT rubenverresen predictionoftoriccodetopologicalorderfromrydbergblockade AT mikhaildlukin predictionoftoriccodetopologicalorderfromrydbergblockade AT ashvinvishwanath predictionoftoriccodetopologicalorderfromrydbergblockade
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Prediction of Toric Code Topological Order from Rydberg Blockade

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