  In the rapid development of cold atom qubit platform, the two-qubit
Controlled-PHASE Rydberg blockade gate via off-resonant modulated driving has
been making significant progress recently. In pursuit of higher fidelity,
faster operation and better robustness, a major upgrade about suppression of
high-frequency components in the modulation is called for, and a systematic
method has been established here for this purpose. The quintessence of this
newly constructed method can be interpreted as filtering out the relatively
high frequency ingredients embedded in basis functions to generate the
modulation waveforms and then analyzing whether they fulfill the requirement of
gate condition. It turns out that appropriate waveforms of two-qubit entangling
gate protocols can be successfully established via these frequency-adjusted
basis functions, with the help of numerical optimization procedures. Moreover,
this timely upgrade version can be further enhanced with adaptions to specific
finite Rydberg blockade strength values and dual-pulse technique to overcome
residual thermal motion of qubit atoms. Besides theoretical derivations, we
also thoroughly investigate the representative modulation patterns,
demonstrating the versatility of off-resonant modulated driving method in the
design of two-qubit entangling Rydberg blockade gate.
