  In this article we propose a novel method to accelerate adiabatic passage in
a two-level system with only longitudinal field (detuning) control, while the
transverse field is kept constant. The suggested method is a modification of
the Roland-Cerf protocol, during which the parameter quantifying local
adiabaticity is held constant. Here, we show that with a simple ``on-off"
modulation of this local adiabaticity parameter, a perfect adiabatic passage
can be obtained for every duration larger than the lower bound $\pi/\Omega$,
where $\Omega$ is the constant transverse field. For a fixed maximum amplitude
of the local adiabaticity parameter, the timings of the ``on-off"
pulse-sequence which achieves perfect fidelity in minimum time are obtained
using optimal control theory. The corresponding detuning control is continuous
and monotonic, a significant advantage compared to the detuning variation at
the quantum speed limit which includes non-monotonic jumps. The proposed
methodology can be applied in several important core tasks in quantum
computing, for example to the design of a high fidelity controlled-phase gate,
which can be mapped to the adiabatic quantum control of such a qubit.
Additionally, it is expected to find applications across all Physics
disciplines which exploit the adiabatic control of such a two-level system.
