  Spin-orbit coupling (SOC) plays an essential role in many exotic and
interesting phenomena in condensed matter physics. In neutral-atom-based
quantum simulations, synthetic SOC constitutes a key enabling element. The
strength of SOC realized so far is limited by various reasons or constraints.
This work reports tunable SOC synthesized with a gradient magnetic field (GMF)
for atoms in a harmonic trap. Nearly ten-fold enhancement is observed when the
GMF is modulated near the harmonic-trap resonance in comparison with free-space
atoms. A theory is developed that well explains the experimental results. Our
work offers a clear physical insight into and analytical understanding of how
to tune the strength of atomic SOC synthesized with GMF using harmonic trap
resonance.
