Fig. 4

Farey tree locking bandwidth. a Lower panel (bottom-x and left-y): Modulation power versus locking bandwidth for different Farey fractions outlined by the Farey tree structure in the inset. Upper panel (top-x and right-y): Plots of Arnold tongues corresponding to the results shown in the lower panel. The blue-shaded area represents the Farey tree locking region. In the measurement, the step size for the modulation power is 1 dBm. For the case of 1/1 Farey fraction, as the modulation power is increased, the locking state cannot be confirmed by the intermode beatnote spectra due to the large phase noise introduced by the RF synthesizer (see details in the main text). In view of this, the measured locking bandwidths under high modulation power (>10 dBm) are represented by grey squares and these data are not included in the plot of Arnold tongue. b–d are recorded locked intermode beatnote spectra (left and right edges in the locking bandwidth) at Farey fractions of 1/1 (−5 dBm), 1/2 (10 dBm), and 2/3 (25 dBm), respectively