Toolbox for Abelian lattice gauge theories with synthetic matter

Dutta, Omjyoti; Tagliacozzo, Luca; Lewenstein, Maciej; Zakrzewski, Jakub

doi:10.1103/physreva.95.053608

Cited by 48 publications

(43 citation statements)

References 69 publications

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“…Lattice gauge theories can be interpreted as the natural next step after synthetic gauge fields, where the phases representing the classical gauge fields are promoted to operators acting on the gauge degrees of freedom living on the links of the lattice. By adopting convenient gauge invariant truncations of such degrees of freedom, one can design simulators of both Abelian [31][32][33][34][35][36][37] and non-Abelian gauge theories [38][39][40] capable to probe confinement, string breaking, and to study the dynamics of charges as in the first proof-of-principle experimental realization of the Schwinger model with four ions [41,42]. Together with the new classical simulation approach based on tensor networks, e.g.…”

Section: Introductionmentioning

confidence: 99%

Unruh effect for interacting particles with ultracold atoms

2018

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Section: Introductionmentioning

confidence: 99%

Unruh effect for interacting particles with ultracold atoms

2018

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“…Any attempt to simulate theses theories must take these facts into account [70,71].Some examples of simulation proposals for gauge theories using ultracold atoms include both the continuous [72] and lattice version of QED, focusing especially on the latter case. In particular, analog simulations for cQED were proposed both in the absence [73,74] and presence of dynamical matter [75][76][77][78], where gauge invariance emerges as an effective symmetry. Realizations of U(1) gauge theories with dynamical or background Higgs fields, using effective gauge invariance, were discussed in [79][80][81].…”

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confidence: 99%

Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

2017

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We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time. allows us to obtain information about systems that cannot be accessed experimentally, by investigating others for which state preparation and measurements are much easier tasks.Among the relevant platforms that can serve as quantum simulators, both analog and digital, many atomic and optical systems stand out due to their remarkable experimental controllability. Some examples include ultracold atoms [5][6][7][8][9], trapped ions [10][11][12][13][14], photonic systems [15] and Rydberg atoms [16]. Ultracold atoms in optical lattices, in particular, present the possibility of recreating many different interactions-such as nearestneighbor, long-range forces, on-site interactions, etc-allowing for the simulation of both condensed matter and high energy physics models. Solid-state systems, such as quantum dots [17][18][19] or superconducting circuits [20,21], also show prominent results that make them interesting candidates to perform quantum simulations.Using these ideas, many condensed matter Hamiltonians have been considered for quantum simulations, some of them even realized experimentally. Some examples include spin systems [14,[22][23][24], such as the Ising or Heisenberg models; the Bose-Hubbard model [5,25]; the Tonks-Girardeau gas [26], or copper-oxide superconductors [18]. External gauge potentials can be simulated as well, allowing for the study of the fractional quantum Hall effect [27] and other topological phenomena [28-31]. Quantum simulations of high energy physics models, although more demanding than their condensed matter counterparts, are also possible. Some examples include the simulation of the Dirac [32-34] and Majorana equations [35], the Casimir force [36], the Schwinger mechanism [37] or the oscillations of neutrinos [38, 39]. Simulations of quantum field theories [40, 41], gravitational theories [42] and black holes [43, 44] have been proposed in recent years, some of them realized experimentally as well [45].Within high energy physics, gauge theories are particularly relevant, since they lie in the core of the Standard Model of particle physics [46][47][48][49]; dyn...

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“…Another proposal in which the gauge theory is obtained as the low-energy limit of the atomic interactions was introduced by Dutta et al [405], who proposed a setup to realize different gauge theories using two atomic species trapped in a two-dimensional optical lattice. One of the atoms acts as an ancilla, while the other is a boson trapped at large filling.…”

Section: Analog Proposals: Different Strategies For Gauge Invariancementioning

confidence: 99%

Review on novel methods for lattice gauge theories

2020

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Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem.In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

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Toolbox for Abelian lattice gauge theories with synthetic matter

Cited by 48 publications

References 69 publications

Unruh effect for interacting particles with ultracold atoms

Unruh effect for interacting particles with ultracold atoms

Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

Review on novel methods for lattice gauge theories

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