We report the observation of tunable spin-orbit coupling (SOC) for ultracold $^{87}$Rb atoms in hyperfine spin-1 states. Different from most earlier experiments where atomic SOC of pseudo-spin-1/2 are synthesized with Raman coupling lasers, the schem
e we demonstrate employs a gradient magnetic field (GMF) with ground state atoms and is immune to atomic spontaneous emission. The effect of the SOC is confirmed through the studies of: 1) the collective dipole oscillation of an atomic condensate in a harmonic trap after the synthesized SOC is abruptly turned on; and 2) the minimum energy state at a finite adiabatically adjusted momentum when the SOC strength is slowly ramped up. The coherence properties of the spinor condensates remain very good after interacting with modulating GMFs, which prompts the enthusiastic claim that our work provides a new repertoire for synthesized gauge fields aimed at quantum simulation studies with cold atoms.
We present a general scheme for synthesizing a spatially periodic magnetic field, or a magnetic lattice (ML), for ultracold atoms using pulsed gradient magnetic fields. Both the period and the depth of the artificial ML can be tuned, immune to atomic
spontaneous emission often encountered in optical lattices. The effective Hamiltonian for our 2-dimensional ML has not been discussed previously in condensed matter physics. Its band structures show interesting features which can support topologically nontrivial phases. The technical requirements for implementing our protocol are readily available in todays cold atom experiments. Realization of our proposal will significantly expand the repertoire for quantum simulation with ultracold atoms.
