Asymmetric population of momentum distribution by quasi-periodically driving a triangular optical lattice

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.