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Physical Review Letters

Photon-Mediated Stroboscopic Quantum Simulation of a Z 2 Lattice Gauge Theory

Tsafrir Armon, Shachar Ashkenazi, Gerardo García-Moreno, Alejandro González-Tudela, Erez Zohar

Published Dec 15, 2021• 35 citations
Publisher

Abstract

Quantum simulation of lattice gauge theories, aiming at tackling nonperturbative particle and condensed matter physics, has recently received a lot of interest and attention, resulting in many theoretical proposals as well as several experimental implementations. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. In this Letter, we propose a method to obtain them based on a combination of stroboscopic optical atomic control and the nonlocal photon-mediated interactions appearing in nanophotonic or cavity QED setups. We illustrate the method for a Z_{2} lattice gauge theory. We also show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.

DOI
10.1103/physrevlett.127.250501

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Photon-mediated Stroboscopic Quantum Simulation of a Z2\mathbb{Z}_{2}Z2​ Lattice Gauge Theory
Quantum simulation of lattice gauge theories (LGTs), aiming at tackling non-perturbative particle and condensed matter physics, has recently received a lot of interest and attention, resulting in many theoretical proposals, as well as several experimental implementations. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. In this Letter, we propose a method to obtain them based on a combination of stroboscopic optical atomic control and the non-local photon-mediated interactions appearing in nanophotonic or cavity QED setups. We illustrate the method for a Z2\mathbb{Z}_{2}Z2​ lattice Gauge theory. We also show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.
Lattice gauge theories form a very successful framework for studying nonperturbative gauge field physics, in particular in quantum chromodynamics. Recently, their quantum simulation on atomic and solid-state platforms has been discussed, aiming at overcoming some of the difficulties still faced by the conventional approaches (such as the sign problem and real time evolution). While the actual implementations of a lattice gauge theory on a quantum simulator may differ in terms of the simulating system and its properties, they are all directed at studying similar physical phenomena, requiring the measurement of nonlocal observables, due to the local symmetry of gauge theories. In this work, general schemes for measuring such nonlocal observables (Wilson loops and mesonic string operators) in general lattice gauge theory quantum simulators that are based merely on local operations are proposed.
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.
Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on [Formula: see text] dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue 'Quantum technologies in particle physics'.
In the present work, we propose a scheme for the digital formulation of lattice gauge theories with dynamical fermions in 3 + 1 dimensions. All interactions are obtained as a stroboscopic sequence of two-body interactions with an auxiliary system. This enables quantum simulations of lattice gauge theories where the magnetic four-body interactions arising in two and more spatial dimensions are obtained without the use of perturbation theory, thus resulting in stronger interactions compared with analogue approaches. The simulation scheme is applicable to lattice gauge theories with either compact or finite gauge groups. The required bounds on the digitization errors in lattice gauge theories, due to the sequential nature of the stroboscopic time evolution, are provided. Furthermore, an implementation of a lattice gauge theory with a non-abelian gauge group, the dihedral group D 3 , is proposed employing the aforementioned simulation scheme using ultracold atoms in optical lattices.