  Ultracold atoms in periodical driven optical lattices enable us to
investigate novel band structures and explore the topology of the bands. In
this work, we investigate the impact of the ramping process of the driving
signal and propose a simple but effective method to realize desired asymmetric
population in momentum distribution by controlling the initial phase of the
driving signal. A quasi-momentum oscillation along the shaking direction in the
frame of reference co-moving with the lattice is formed, causing the formation
of the mix of ground energy band and first excited band in laboratory frame,
within the regime that the driving frequency is far less than the coupling
frequency between ground band and higher energy bands. This method avoids the
construction of intricate lattices or complex control sequence. With a
triangular lattice, we experimentally investigate the influence of the initial
phase, frequency, amplitude of the driving signal on the population difference,
and observe good agreement with our theoretical model. This provides guidance
on how to load a driving signal in driven optical lattice experiment and also
potentially supplies a useful tool to form a qubit that can be used in quantum
computation.
