  External driving of bath temperatures with a phase difference of a
nonequilibrium quantum engine leads to the emergence of geometric effects on
the thermodynamics. In this work, we modulate the amplitude of the external
driving protocols by introducing envelope functions and study the role of
geometric effects on the flux, noise and efficiency of a four-level driven
quantum heat engine coupled with two thermal baths and a unimodal cavity. We
observe that having a finite width of the modulation envelope introduces an
additional control knob for studying the thermodynamics in the adiabatic limit.
The optimization of the flux as well as the noise with respect to thermally
induced quantum coherences becomes possible in presence of geometric effects,
which is hitherto not possible with sinusoidal driving without an envelope. We
also report the deviation of the slope and generation of an intercept in the
standard expression for efficiency at maximum power as a function of Carnot
efficiency in presence of geometric effects under the amplitude modulation.
Further, a recently developed universal bound on the efficiency obtained from
thermodynamic uncertainty relation is shown not to hold when a small width of
the modulation envelope along with a large value of cavity temperature is
maintained.
