Digital Quantum Simulation of Z_{2} Lattice Gauge Theories with Dynamical Fermionic Matter.

We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2+1) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z_{2} model in (2+1) dimensions.

Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices.

Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.

Simulating (2+1)-dimensional lattice QED with dynamical matter using ultracold atoms.

We suggest a method to simulate compact quantum electrodynamics using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows us to test the dynamical effects of confinement as well as the deformations and breaking of two-dimensional flux loops, and to observe the Wilson-loop area law.

Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory.

Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory-SU(2) Yang-Mills in (1 + 1) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations.

Simulating compact quantum electrodynamics with ultracold atoms: probing confinement and nonperturbative effects.

Recently, there has been much interest in simulating quantum field theory effects of matter and gauge fields. In a recent work, a method for simulating compact quantum electrodynamics (CQED) using Bose-Einstein condensates has been suggested. We suggest an alternative approach, which relies on single atoms in an optical lattice, carrying 2l + 1 internal levels, which converges rapidly to CQED as l increases. That enables the simulation of CQED in 2 + 1 dimensions in both the weak and the strong coupling regimes, hence, allowing us to probe confinement as well as other nonperturbative effects of the theory. We provide an explicit construction for the case l = 1 which is sufficient for simulating the effect of confinement between two external static charges.

Confinement and lattice quantum-electrodynamic electric flux tubes simulated with ultracold atoms.

We propose a method for simulating (2+1)D compact lattice quantum-electrodynamics, using ultracold atoms in optical lattices. In our model local Bose-Einstein condensates' (BECs) phases correspond to the electromagnetic vector potential, and the local number operators represent the conjugate electric field. The well-known gauge-invariant Kogut-Susskind Hamiltonian is obtained as an effective low-energy theory. The field is then coupled to external static charges. We show that in the strong coupling limit this gives rise to "electric flux tubes" and to confinement. This can be observed by measuring the local density deviations of the BECs, and is expected to hold even, to some extent, outside the perturbative calculable regime.

Classical analog to topological nonlocal quantum interference effects.

The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and nonlocality-local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and nonlocal features of the Aharonov-Bohm effect can be manifested in a classical model that incorporates random noise. The model also suggests new types of multiparticle topological nonlocal effects which have no quantum analog.