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We propose a one-dimensional Floquet ladder that possesses two distincttopological transport channels with opposite directionality. The transportchannels occur due to a $\mathbb Z_2$ non-Hermitian Floquet topological phasethat is protected by time-reversal symmetry. The signatures of this phase aretwo pairs of Kramers degenerate Floquet quasienergy bands that are separated byan imaginary gap. We discuss how the Floquet ladder can be implemented in aphotonic waveguide lattice and show that the direction of transport in theresulting waveguide structure can be externally controlled by focusing twolight beams into adjacent waveguides. The relative phase between the two lightbeams selects which of the two transport channels is predominantly populated,while the angles of incidence of the two light beams determine which of thetransport channels is suppressed by non-Hermitian losses. We identify theoptimal lattice parameters for the external control of transport anddemonstrate the robustness of this mechanism against disorder.

Controlling the direction of topological transport in a non-Hermitian time-reversal symmetric Floquet ladder