  Quasi-one-dimensional systems exhibit many-body effects elusive in higher
dimensions. A prime example is spin-orbital separation, which has been measured
by resonant inelastic X-ray scattering (RIXS) in Sr$_2$CuO$_3$. Here, we
theoretically analyze the time-resolved RIXS spectrum of Sr$_2$CuO$_3$ under
the action of a time-dependent electric field. We show that the external field
can reversibly modify the parameters in the effective $t-J$ model used to
describe spinon and orbiton dynamics in the material. For strong driving
amplitudes, we find that the spectrum changes qualitatively as a result of
reversing the relative spinon to orbiton velocity. The analysis shows that in
general, the spin-orbital dynamics in Mott insulators in combination with
time-resolved RIXS should provide a suitable platform to explore the reversible
control of many-body physics in the solid with strong laser fields.
