Figure 1: Parametric phase-locked oscillator (PPLO).
(a) Schematic of the device. The application of a pump microwave field at 
with a power Pp above the threshold generates an output signal at ωp/2 with a power Pout. Here, 
is the static resonant frequency of the PPLO resonator, and ωs, 
and θs represent the frequency, power and phase of the LS, respectively. 
represents the coupling capacitance between the resonator and the feedline, and Φsq represents the magnetic flux penetrating the SQUID loop. (b) Cross-section of the Hamiltonian g(qx, 0) in the rotating frame for various powers and a fixed phase (θs=π/2) of the LS. Here the LS power is represented by the mean photon number in the PPLO resonator, 
. Here the internal (
) and external (
) quality factors of the PPLO resonator are measured to be 5,200 and 340, respectively at 
, which give a loaded quality factor 
of 320. The pump power Pp/Pp0 is fixed at 2.0. Two minima correspond to 0π and 1π states of the phase-locked oscillations. (c) Same as b, but for NPO=1 and various values of θs.
