Quantum correlated pulses from a synchronously pumped optical parametric oscillator operating above threshold

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We perform the quantum analysis of the light emitted by a synchronously pumped optical parametric oscillator operating in the above threshold regime, i.e. when the peak power of pulsed pumping exceeds the threshold of continuous generation. We show that both regimes (below and above threshold) are realized at different times within each pulse of the signal field. We show that the quantum fluctuations of signal and pump pulses are correlated between nearby pulses at times that are placed in the same position relative to the center of the pulses, whereas fluctuations are totally not correlated at different times within the same pulse. The model also predicts the existence of cross-correlations between pump and signal pulses. It is shown theoretically that there is suppression of quantum noise at the frequencies multiple of the pulse repetition frequency in the spectra of phase quadratures of pump and signal fields measured by a balanced homodyne detection with a pulsed local oscillator.