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The phase boundaries of periodically driven spin–orbit coupled BECs with effective two‐body interactions are analytically calculated by using variational method. The phase diagrams of periodically driven87   Rb    and23   Na    systems present distinguished features from undriven systems, respectively. For the87   Rb    BECs, the critical density    n  c    (density at quantum tricritical point) will be dramatically reduced in some parameter regions, and the prospect of observing this intriguing quantum tricritical point is greatly enlarged. Moreover, a series of quantum tricritical points emerge quasi‐periodically when increasing the Raman coupling strength with fixed87   Rb    density. In the23   Na    BECs, two hyperfine states of23   Na    atoms can be miscible within the suitable regions of driving parameter space. As a result,23   Na    systems will stay in the stripe phase with small Raman frequency at typical density, which expands the region of stripe phase in the phase diagram. In addition, an absence of quantum tricritical point in such23   Na    system is observed, which is very unlike87   Rb    systems.

Phase Diagrams of Periodically Driven Spin–Orbit Coupled 87 Rb and 23 Na Bose–Einstein Condensates