We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

In this work we investigate the quantum noise properties of polarization vortices in connection with an intensity based Clauser-Horne-Shimony-Holt inequality for their spin-orbit separability. We evaluate the inequality for different input quantum states and the corresponding intensity fluctuations. The roles played by coherence and photon number squeezing provide a suitable framework for characterizing pure state spin-orbit entanglement. Structural inseparability of the spin-orbit mode requires coherence, an issue concerning either classical or quantum descriptions. In both cases, it can be witnessed by violation of this intensity based CHSH inequality. However, in the quantum domain, entanglement requires both coherence and reduced photon number fluctuations.Comment: 7 pages, 3 figure

We investigate entanglement in the above-threshold Optical Parametric Oscillator, both theoretically and experimentally, and discuss its potential applications to quantum information. The fluctuations measured in the subtraction of signal and idler amplitude quadratures are ∆ 2p − = 0.50(1), or −3.01(9) dB, and in the sum of phase quadratures are ∆ 2q + = 0.73(1), or −1.37(6) dB. A detailed experimental study of the noise behavior as a function of pump power is presented, and discrepancies with theory are discussed.