(a),(c) Adapted from J. Struck et al. [1]; (b) Adapted from K. Jiménez-García et al. [2]

Figure 1: (a) Force applied to the optical lattice against time through frequency modulation of a lattice laser beam in Struck et al. [1]. By appropriately choosing times $T1$ and $T2$ the induced Peierls phase is adjusted. (b) The effective magnetic field indicated by the red arrow subtends the solid angle $θ$, shown as light red shading, when an atom hops from site to site in the setup of Jiménez-García et al. [2]. The phase $θ$ is imprinted on the atomic wave function in this process. (c) Measured quasimomenta when adiabatically changing $θ$ as a function of time. The symbol $kFBZ$ indicates the edge of the first Brillouin zone.