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Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model
Journal article   Open access   Peer reviewed

Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model

Yannick Meurice
Physical review. D, Vol.104(9), 094513
11/01/2021
DOI: 10.1103/PhysRevD.104.094513
url
https://arxiv.org/pdf/2107.11366View
Open Access

Abstract

The lattice compact Abelian Higgs model is a nonperturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1 + 1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms [J. Zhanget al., Phys. Rev. Lett. 121, 223201 (2018)]. In this setup, one spatial dimension is used to carry the angular momentum of the quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to build local Hilbert spaces associated with the links of the lattice. We argue that ladder-shaped configurable arrays of Rydberg atoms can be used for the same purpose. We make concrete proposals involving two and three Rydberg atoms to build one local spin-1 space (a qutrit). We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We compare target and simulators using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the one-spin model while the three-atom setup involves solving nonlinear equations. We discuss approximate methods to couple two spin-1 spaces. The article provides analytical and numerical tools necessary to design and build the proposed simulators with current technology.
 Physical Sciences Physics Astronomy & Astrophysics Physics, Particles & Fields Science & Technology

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