Two-color continuous-variable quantum entanglement in a singly resonant optical parametric oscillator

Abstract

We apply the input-output theory of optical cavities to formulate a quantum treatment of a continuous-wave singly resonant optical parametric oscillator. This case is mainly relevant to highly nondegenerate signal and idler modes. We show that both intensity and quadrature squeezing are present and that the maximum noise reduction below the standard quantum limit is the same at the signal and idler frequencies as in the doubly resonant case. As the threshold of oscillation is approached, however, the intensity-difference and quadrature spectra display a progressive line narrowing which is absent in the balanced doubly resonant case. By use of the separability criterion for continuous variables, the signal-idler state is found to be entangled over wide ranges of the parameters. We show that attainable levels of squeezing and entanglement make singly resonant configurations ideal candidates for two-color quantum information processes, because of their ease of tuning in experimental realizations.