Probe of topological invariants using quantum walks of a trapped ion in coherent state space

Meng Ya^{1, 2}, Mei Feng^{1, 2, †}, Chen Gang^{1, 2, 3, ‡}, Jia Suo-Tang^{1, 2}

The diagram of the spin-dependent flipping translation T↑↓α=U†RπU in the system of a trapped ion. The interaction of the displacement Raman beams and the trapped ion allow the coherent displacements in coherent state space. Between two displacement Raman beams, a π pulse, which exchanges the spin, is required. In this diagram, the Rabi frequencies satisfy Ω↑=−32Ω↓ as an example.