Real-time-dynamics quantum simulation of (1+1)-dimensional lattice QED with Rydberg atoms

Abstract

We show how to implement a Rydberg-atom quantum simulator to study the non-equilibrium dynamics of an Abelian (1+1)-D lattice gauge theory. The implementation locally codifies the degrees of freedom of a Z3 gauge field, once the matter field is integrated out by means of the Gauss' local symmetries. The quantum simulator scheme is based on current available technology and scalable to considerable lattice sizes. It allows, within experimentally reachable regimes, to explore different string dynamics and to infer information about the Schwinger U (1) model.

Real Time Dynamics and Confinement in the Zn Schwinger-Weyl lattice model for 1+1 QED

“…In particular, by means of simulations based on the Density Matrix Renormalization Group (DMRG) algorithm, we will examine the evolution of the system for a wide range of the parameters, showing that the dynamical behaviour of the model strongly deviates from the usual relaxation properties which are expected to be found in a manybody non-integrable system, resulting in stable and/or recurrent evolution of interesting physical quantities. This shows that confinement and a slow dynamics are not specific features of the U (1) Schwinger model, but of the whole class of discrete lattice models we consider in this paper, which might be relevant for the description of future experiments with Rydberg atoms [43]. We remark also that similar results have been obtained in different many-body systems, such as non-integrable spin-chain models [62] or constrained Hamiltonians [38] .…”

“…It is interesting to notice that, in the two latter cases, the physical states of the system under consideration are constrained to lie in a restricted subspace of the total Hilbert space, a fact that is shared by our model, where the role of Gauss's law constraint is crucial. This is also at the heart of the recent proposal to experimentally implement these Hamiltonians with Rydberg atomic systems in the Rydberg-blockade regime [43]. We plan to further investigate the role of the gauge constraint in future work.…”

“…In spite of its simplicity, the model shares many phenomenological features with more complicated theories, such as QCD, thus representing an interesting instance to test quantum field theory and quantum simulations. The model has been widely investigated since the 70's [6,7,8,9] and has been recently proposed as a possible viable experimental option in the not-too-distant future [39,40,41,42,43]. Indeed, a first experiment reproducing such a model with few qubits in a ion trap has already been reported [27] and new ideas have been proposed for possible experimental realizations with Rydberg atoms [44,43].…”

Simulating lattice gauge theories within quantum technologies

“…Closer to an atomic physics implementation with Rydberg atoms is the work [168] where different string dynamics are explored to infer information about the Schwinger model.…”

“…For instance, in [238], it was shown how recent experiments in Rydberg atoms arrays have already realised [41] quantum simulations of gauge theories at large scales. In [168], it is shown how to implement a Rydberg-atom quantum simulator to study the nonequilibrium dynamics of an Abelian (1+1)-d lattice gauge theory, the implementation locally codifies the degrees of freedom of a Z(3) gauge field, once the matter field is integrated out by means of the Gauss local symmetries.…”