Spin-orbit density dependence and compacton existence in Bose-Einstein condensates.

We investigate binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intra-species Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intra-species scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components and strongly influence the existence of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that while SOC restricts the parameter ranges for stable SOC-compactons existence, it gives more stringent signatures of their occurrence. In particular, SOC-compactons should appear when the intra-species interactions and the number of atoms in the two components are perfectly balanced or close to being balanced for the metastable case. The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intra-species interactions is also suggested.