Symmetry Imbalance in a Shaking Triangular Optical Lattice

Lots of interesting phenomena can be investigated under symmetry imbalance condition, such as symmetry protected topological orders, simulation of frustrated quantum anti-ferromagnetism and so on. In this work, we demonstrated a simple but effective method to realize desired symmetry imbalance of momentum distribution of the atoms in an optical triangular lattice, by shaking the lattice and controlling the driven signal. A quasi-momentum oscillation along the shaking direction in lattice frame of reference causes the formation of the mix of ground energy band and first excited band in laboratory frame of reference and thus the symmetry imbalance, within the regime that the shaking frequency is far less than the coupling frequency between ground band and higher energy bands. We experimentally investigate the influence of the initial phase, frequency, amplitude of the shaking signal on the symmetry imbalance, and observe good agreement with our theoretical model. This supplies a useful tool to study atomic behavior in the non-zero quasi-momentum.