Fig. 1. Ground state quantum phase diagrams of Floquet spinor BEC when modulation intensity takes different values. Black dash-dotted and white solid lines represent first-order and second-order phase transition boundaries, respectively. Green circle represents tricritical point of S1, S2, and plane wave phases, and red stars represent tricritical points between S2, plane wave, and zero momentum phases. Black solid lines represent dispersion spectrum of each phase, where purple dots represent wave function occupation. S1, S2, PW, and ZM stand for two stripe phases, plane wave phase, and zero momentum phase, respectively. (a) α/ω=0; (b) α/ω=1

Fig. 2. Ground state quantum phase diagrams of Floquet spinor BEC when constant Rabi frequency takes different values. Black dash-dotted and white solid lines represent first-order and second-order phase transition boundaries, respectively, and phase transition can be achieved by tuning modulation intensity. Dashed lines imply corresponding phase transitions when ε=-1ER. (a) Ω0=0.2ER; (b) Ω0=1ER

Fig. 3. Collective excitation of stripe phase S1 with Ω0=0.2ER and ε=0.5ER at different modulation intensities, where arrows indicate roton excitation in first and second excitation bands

Fig. 4. Excitation spectrum ς, static response function χ, and structure factor S of Floquet spinor BEC with Ω0=1ER and ε=-1ER. Solid and dashed lines in each subset represent first and second excitation bands, respectively. Dash-dot lines in response function and structure factor diagrams represent the summation of χ or S generated by all excitation bands. (a)‒(c) Stripe phase; (d)‒(f) plane wave phase; (g)‒(i) zero momentum phase

Fig. 5. Sound velocity c as a function of modulation intensity α/ω when constant Rabi frequency takes different values. Solid lines represent sound velocity when Ω0=0.2ER, while corresponding PW phase boundary is also solid line; dashed lines represent sound velocity when Ω0=1ER, while corresponding PW phase boundary is also dashed line. ε=-1ER, which is consistent with dashed lines in Fig. 2