  We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman
splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard
model using the Kubo formula. We focus on two phenomena: (1) the electric
dipole spin resonance (EDSR) in the metallic regime and (2) the optical
conductivity in the Mott-insulating phase above the optical gap. In both cases,
we calculate qualitatively the effects of SOC and ZS and how they depend on the
relative angle between the SOC vector and the magnetic field direction. First,
we investigate the spin resonance without electron correlation (the Hubbard
parameter $U=0$). Although, neither SOC nor ZS causes any resonance by itself
in the optical conductivity, the EDSR becomes possible when both of them exist.
The resulting contribution to the optical conductivity is analyzed
analytically. The effect of $U$ on the spin resonance is also studied with a
numerical method. It is found that at half-filling, the resonance is first
enhanced for small $U$ and then suppressed when the optical gap is large
enough. In the strong coupling limit $U \rightarrow \infty$ at half-filling, we
also refer to the resonance between the lower and upper Hubbard bands appearing
at $\omega \sim U$, above the optical gap. A large magnetic field tends to
suppress the signal while it is recovered thanks to SOC depending on the
relative angle of the magnetic field.
