Fig. 5: Measured beam refractions by a dc-driving, moving gauge-potential barrier.

a Schematic waveform of dc-driving phase modulation. Tdc = 2π/α is dc-driving period, α is dc-driving force and ϕv2(0) is the initial phase in the long loop. b–d Measured field evolutions for k1+ = −0.5π, 0.5π, and 0, corresponding to rightward dmax = W/2 (b), leftward dmin = −W/2 (c), and d = 0 (d) under v = 1, (Δφ, ΔA) = (−π/2, −π/2), A2(0) = −0.5π, β = π/3 and Tdc = W = 40. e, f Measured field evolutions for k1+ = −0.5π, 0, corresponding to rightward dmax = 3W/2 (e) and d = 0 (f) under v = 1/3, (Δφ, ΔA) = (−π/2, −3π/2), A2(0) = −0.25π, β = π/3, and Tdc = W/v = 90 for W = 30. In (b–f), the green dashed lines denote the two moving boundaries of the moving potential. The blue solid lines denote the incident and transmitted packets’ trajectories in the (n, m) plane.