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 phase diagram governed by U_1,2. The DTQWs have effective Hamiltonians with gaps around both ε = 0 and ε = π, except at the gapless points where gaps close at ε = 0 (dashed) or ε = π (dotted). For each gapped phase, the corresponding pair of winding numbers {ν₁,ν₂} as well as the pair of topological invariants (ν₀,ν_π) are shown. The dash-dotted line and the two symbols indicate the rotating parameters for detecting the topological invariants.