An ideal rapid-cycle Thouless pump

Thouless pumping is a fundamental instance of quantized transport, which topologically protected. Although its theoretical importance, the adiabaticity condition an obstacle for further practical applications. Here, focusing on Rice-Mele model, we provide family finite-frequency examples that ensure both absence excitations and perfect quantization pumped charge at end each cycle. This family, contains adiabatic protocol as limiting case, obtained through mapping onto zero curvature representation Euclidean sinh-Gordon equation.