Fig. 1: Chains with synthetic gauge fields and synthetic dimension.
From: Synthetic dimensions for topological and quantum phases
a In a optical 1D chain lattice, three atomic hyperfine levels are coupled through Raman beams with Rabi frequency Ω0 and spatially varying phase xγ. This artificial hopping in the synthetic dimension together with the real-space hopping t mimics the Hamiltonian of a compact 2D square lattice with synthetic magnetic fluxes, in close analogy to the Hofstadter model. Figure taken from ref. 3 with permission of the American Physical Society. b A 1D system with next-nearest-neighbor hopping J can be mapped onto a two-leg ladder. Spatially varying hopping phases (in blue), which can be implemented through Floquet engineering, generate synthetic magnetic fluxes. The additional phase θ provides a cyclic Hamiltonian parameter which can be used to substitute momentum along a second dimension. Figure taken from ref. 15 with permission of the American Physical Society.
