  We perform the noise spectroscopy of a Josephson parametric oscillator (JPO)
by implementing a microwave homodyne interferometric measurement scheme. We
observe the fluctuations in the self-oscillating output field of the JPO for a
long 10 s time interval in a single shot measurement and characterize the phase
and amplitude noise. Furthermore, we investigate the effects of the pump
strength on the output noise power spectra of the JPO. We found strong
fluctuations in the phase with a $1/f^2$ characteristics in the phase noise
power spectrum, which is suppressed by increasing the pump strength.
