  We propose to synchronize Bloch oscillations in a double phase-slip junction
by modulating the gate voltage rather than the bias voltage. We show this is
advantageous and the relatively small a.c. modulation of the gate voltage gives
rise to the pronounced plateaux of quantized current of the width of the order
of Coulomb blockade threshold.
  We theoretically investigate the setup distinguishing three regimes of the
strong, weak, and intermediate coupling defined by the ratio of the gate
capacitance $C$ and the effective capacitance of the phase-slip junctions. An
important feature of the intermediate coupling regime is the occurrence of the
fractional plateaux of the quantized current. We investigate the finite
temperature effects finding an empirical scaling for the smoothing of integer
plateaux.
