We describe a simple technique for generating a cold-atom lattice pierced by a uniform magnetic field. Our method is to extend a one-dimensional optical lattice into the "dimension" provided by the internal atomic degrees of freedom, yielding a synthetic 2D lattice. Suitable laser-coupling between these internal states leads to a uniform magnetic flux within the 2D lattice. We show that this setup reproduces the main features of magnetic lattice systems, such as the fractal Hofstadter butterfly spectrum and the chiral edge states of the associated Chern insulating phases.PACS numbers: 37.10. Jk, 03.75.Hh, 05.30.Fk Intense effort is currently devoted to the creation of gauge fields for electrically neutral atoms [1][2][3][4]. Following a number of theoretical proposals in presence [5][6][7][8][9][10][11][12][13] or in absence of optical lattices [14][15][16][17][18][19][20], synthetic magnetic fields have been engineered both in vacuum [21][22][23][24][25] and in periodic lattices [26][27][28][29]. The addition of a lattice offers the advantage to engineer extraordinarily large magnetic fluxes, typically of the order of one magnetic flux quantum per plaquette [5-7, 10, 11], which are out of reach using real magnetic fields in solid-state systems (e.g. artificial magnetic fields recently reported in graphene [30][31][32]). Such cold-atom lattice configurations will enable one to access striking properties, such as Hofstadter-like fractal spectra [33] and Chern insulating phases, in a controllable manner. Existing schemes for creating uniform magnetic fluxes require several laser fields and/or additional ingredients, such as tilted potentials [6,10], superlattices [11], or lattice-shaking methods [9,13,[34][35][36][37]. Experimentally, strong staggered magnetic flux configurations have been reported [26,27], and very recently also uniform ones [28,29]. Besides, an alternative route is offered by optical flux lattices [38][39][40][41].In all of these lattice schemes, the sites are identified by their location in space. This need not be the case: the available spatial degrees of freedom can be augmented by employing the internal atomic "spin" degrees of freedom as an extra, or synthetic, lattice-dimension [42]. Here we demonstrate that this extra dimension can support a uniform magnetic flux, and we propose a specific scheme using a 1D optical lattice along with Raman transitions within the atomic ground state manifold (Fig. 1). The flux is produced by a combination of ordinary tunneling in real space and laser-assisted tunneling in the extra dimension creating the necessary Peierls phases. Our proposal therefore extends the toolbox of existing techniques to create gauge potentials for cold atoms.The proposed scheme distinguished by the naturally sharp boundaries in the extra dimension, a feature which greatly simplifies the detection of chiral edge states resulting from the synthetic magnetic flux [43][44][45][46][47]. We demonstrate that the chiral motion of these topological edge states can be directly visualiz...

Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagome lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-abelian gauge fields.

Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented-a classical simulation approachapplied to the study of lattice gauge theories together with some results on