  We study the single-particle dispersion of a spin-orbit coupled (SOC)
Bose-Einstein condensate (BEC) under the periodical modulation of the Raman
coupling. This modulation introduces a further coupling of the SOC dressed
eigenlevels, thus creating a second generation of modulation-dressed
eigenlevels. Theoretical calculations show that these modulation-dressed
eigenlevels feature a pair of avoided crossings and a richer spin-momentum
locking, which we observe using BEC transport measurements. Furthermore, we use
the pair of avoided crossings to engineer a tunable Stueckelberg interferometer
that gives interference fringes in the spin polarization of BECs.
