  Recently, the method of off-resonant modulated driving (ORMD) with a special
category of synthetic analytical pulses has improved the experimental
performance of two- and multi-qubit gates and aroused many interests for
further investigations. It particularly offers a helpful tool to the cold atom
qubit platform and works well with the Rydberg dipole-dipole interaction. In
order to explore more possibilities and wider ranges of options in constructing
fast-speed and high-fidelity quantum logic gates, we design and analyze the
entangling quantum gates via the almost-resonant modulated driving (ARMD)
method. Apart from the apparent distinctions in resonance conditions, the ARMD
gate protocols also have its different mechanisms in quantum physics compared
with ORMD gate protocols. ARMD gates usually have abrupt phase changes and at
certain points during the time evolution. In other words, whilst the modulation
forms the key concept of high-fidelity Rydberg blockade gates, the on-off
resonance condition can lead to nontrivial nuances in the styles of dynamics.
From a more fundamental point of view, the ORMD and the ARMD methods all
together belong to the unitary operation family of fast modulated driving with
respect to precisely characterized inter-qubit interactions, which usually
allows the quantum logic gate to concludes within one continuous pulse.
