Dynamical generation of arbitrary spin-orbit couplings for neutral atoms

Spin-orbit coupling (SOC) can give rise to interesting physics, from spin Hall to topological insulators, in condensed matter systems. Recently, this topical area has extended into atomic quantum gases in searching for artificial or synthetic gauge potentials. The prospects of tunable interaction and quantum state control promote neutral atoms as nature's quantum emulators for SOC. Lin et al. recently demonstrated a special form of the SOC kₗₘ, which they interpret as an equal superposition of Rashba and Dresselhaus couplings in Bose-condensed atoms Lin, Jim\'enez-Garc\'a, and Spielman, Nature (London) 471, 83 (2011). This work reports a method of implementing arbitrary forms of SOC by switching between two pairs of Raman laser pulses like the method used by Lin et al. While one pair affects kₗₘ for some time, a second pair creates kₘₘ at other times with Raman pulses from different directions and a subsequent spin rotation into kₘₗ. With a sufficient number of pulses, the effective actions from different durations are small and accumulate in the same exponent despite the fact that kₗₘ and kₘₗ do not commute. Our scheme involves no added complication and can be demonstrated within current experiments. It applies equally to bosonic or fermionic atoms.