Spin Pumping and Entanglement Spectrum of Quantum Spin Hall States in a π-flux Model

We propose a new way of realizing quantum spin Hall effect in cold atoms by shaking an optical lattice, which produces an effective π-flux per plaquette on the square lattice. We demonstrate a spin pumping process during flux insertion in this quantum spin hall state. We also study the evolution of entanglement spectrum under the flux insertion, which provides a sharp signature for the quantum spin Hall effects.