Abstract
The physical realization of Z2 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 Z2 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/r6 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.12 MoreReceived 24 November 2020Accepted 19 May 2021DOI:https://doi.org/10.1103/PhysRevX.11.031005Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasTopological phases of matterTopological quantum computingPhysical SystemsRydberg atoms & moleculesCondensed Matter, Materials & Applied Physics
Highlights
Five decades ago, Anderson [1] proposed that quantum fluctuations could lead to a liquid of resonating valence bonds, stimulating a vast theoretical effort that continues to this day
We introduce a new approach for realizing a Z2 topologically ordered state as the ground state of a 2D Rydberg atom array. We show that this approach does not require careful engineering or fine-tuning of the constraints, enabling the first realization and direct probing of a timereversal- and parity-invariant topological order and of emergent deconfined gauge fields in a quantum model on a near-term quantum device
The Rydberg blockade implies that any two sites within this distance cannot both be occupied [Fig. 1(b)], which we can interpret as a dimer state on the kagome lattice if the system is at maximal filling [see Fig. 1(c)]
Summary
Anderson [1] proposed that quantum fluctuations could lead to a liquid of resonating valence bonds, stimulating a vast theoretical effort that continues to this day. The special features of the Rydberg atom interactions make them attractive platforms for realizing emergent lattice gauge theories and quantum dimer models [57,58,59,60,61,62]. We introduce a new approach for realizing a Z2 topologically ordered state as the ground state of a 2D Rydberg atom array We show that this approach does not require careful engineering or fine-tuning of the constraints, enabling the first realization and direct probing of a timereversal- and parity-invariant topological order and of emergent deconfined gauge fields in a quantum model on a near-term quantum device. We show that, for a particular choice of two-dimensional atom arrangement, Rydberg blockade radius, and laser detuning, a Z2 spin liquid is stabilized as the ground state of this model. IV C gives examples of how this realization can be applied
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