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}

(a), (c) The mean chiral displacements C1,2 varying as functions of the rotation angle θ₁ and the step t with θ₁ = 3π/4, the rotation angle θ₂ is fixed at 3π/2. The solid (dash-dotted) line indicates the mean chiral displacement C1 (C2 ), and the dotted (dashed) line corresponds to the topological invariant ν₁/2 (ν₂/2) governed by U₁ (U₂). (c), (d) The associated mean chiral displacements C1∓C2 varying as functions of the rotation angle θ₁ and the time step t with θ₁ = 3π/4, the rotation angle θ₂ is fixed at 3π/2. The solid (dash-dotted) line indicates the associated mean chiral displacement C1−C2 \ (C1+C2 ), and the dotted (dashed) line corresponds to the topological invariant ν₀ (ν_π) of our DTQWs.