Generation of uniform synthetic magnetic fields by split driving of an optical lattice

We describe a method to generate a synthetic gauge potential for ultracold atoms held in an optical lattice. Our approach uses a time-periodic driving potential based on quickly alternating two Hamiltonians to engineer the appropriate Aharonov-Bohm phases, and permits the simulation of a uniform tunable magnetic field. We explicitly demonstrate that our split-driving scheme reproduces the behavior of a charged quantum particle in a magnetic field over the complete range of field strengths, and obtain the Hofstadter butterfly band structure for the Floquet quasienergies.