Modulational Instabity of Spin-Orbit Coupled Bose-Einstein Condensates in Discrete Media

We address the impact of intra-site spin-orbit (SO) coupling and associated inter-component Rabi coupling on the modulational instability (MI) of plane-wave states in two-component discrete Bose-Einstein condensates (BECs). Conditions for the onset of the MI and the respective instability are found analytically. SO coupling allows us to produce the MI even for a small initial wavenumber (q < {\pi}/2) for miscible states. In particular, SO coupling introduces MI even in the absence of hopping coefficient, a concept which may have wider ramifications in heavy atomic BECs. Our investigations predict that the impact of Rabi coupling is more pronounced compared to the other system parameters. We have also shown how our results of the linear stability analysis can be corroborated numerically. The fact that we have brought out the stability criteria in different domains of system parameters means that our model is tailor made experiments.