Figure 1

(a) Schematic representation of the measurement setup. Four continuous wave (cw) tones are injected in the three ports of the superconducting Josephson parametric amplifier (gray box). Incoming signal, idler, and pump photon fluxes are designated by ${\dot{n}}_S$, ${\dot{n}}_I$, and ${\dot{n}}_P$, respectively. The output power from the signal port is measured with a spectrum analyzer. (b) Upper: Applied cw tones in frequency space. The horizontal axis is the frequency axis, the colored arrows represent coherent tones, and the Lorentzian shapes represent the gain response function. Lower: enlargement of the signal band. The dashed arrow represents the up-converted idler tone, offset by $\delta f=0.1\mathrm{Hz}$ from the signal tone, producing a slow variation of the relative phase $\varphi =2\pi \delta ft$ between signal and idler tones.Reuse & Permissions

Figure 2

(a) Normalized output power as a function of $\varphi$ (light blue) and fit to Eq. (3) (white), for balanced signal and idler incoming photon fluxes (${\dot{n}}_S={\dot{n}}_I$) and $G_0=11\mathrm{dB}$. Calibration traces are as follows: idler turned off (pink); idler and pump off (purple); signal and idler off (i.e., noise floor, black). Arrows indicate how various quantities [gain ($G_0$), coherent attenuation, distance of zero cancellation to noise floor (dist. to NF)] are measured. Inset: shown traces correspond to gains varying from 1 (red) to 11 dB (green). (b) Magnitude of CA versus gain at maximum interference point (blue). Red solid trace represents the theory, and the black triangles the resolution limitations due to the finite distance to the noise floor.Reuse & Permissions

Figure 3

(a) Phase-dependent depletion of signal port gain ($G_0=11\mathrm{dB}$). Amplified probe power is measured in a 51 Hz RBW (signal tone is offset by 100 kHz). Traces correspond to signal and idler photon fluxes increasing by 2 dB (from blue to red). Dashed lines are least square fits of gain modulation theory. (b) Enlargement of the region around $\varphi =2\pi$. Gain enhancement above $G_0=11\mathrm{dB}$ (0 dB line) is clearly visible for experimental data.Reuse & Permissions