We show theoretically that concurrent interactions in a second-order nonlinear medium placed inside an optical resonator can generate multipartite entanglement between the resonator modes. We show that there is a mathematical connection between this system and van Loock and Braunstein's proposal for entangling N continuous quantum optical variables by interfering with the outputs of N degenerate optical parametric amplifiers (OPA) at a N-port beam splitter. Our configuration, however, requires only one nondegenerate OPA and no interferometer. In a preliminary experimental study, we observe the concurrence of the appropriate interactions in periodically poled RbTiOAsO 4 .

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We observed continuous-variable entanglement between the bright beams emitted above threshold by an ultrastable optical parametric oscillator ͑OPO͒, classically phase locked at a frequency difference of 161.827 324 0͑5͒ MHz. The amplitude-difference squeezing is −3 dB and the phase-sum one is −1.35 dB. Besides proving entanglement in a phase-locked OPO, such outstanding frequency-difference stability paves the way for transferring entanglement between different optical frequencies and densely implementing continuous-variable quantum information in the frequency domain.The nondegenerate optical parametric oscillator ͑OPO͒ is a natural source of continuous-variable-͑CV-͒ entangled electromagnetic fields ͓1͔. Below threshold, it is a phasesensitive amplifier whose quantum evolution can be described by a unitary two-mode squeeze operator ͓2͔, which, in the ideal case yields, for example, a common eigenstate of the amplitude-difference and phase-sum field quadratures. Since the amplitude and phase of a quantized field correspond exactly to the position and momentum of a mechanical quantum oscillator, this two-mode squeezed state is identical to that of the Einstein-Podolsky-Rosen ͑EPR͒ paradox ͓3͔, which has been implemented experimentally with finite squeezing ͓4͔ and used in CV quantum information ͑CVQI͒ ͓5,6͔. Above threshold, the OPO is a true oscillator rather than an amplifier and its dynamics become richer: as is well known, the phase difference of the two OPO signal beams undergoes, above threshold, an undamped diffusion process, driven by vacuum fluctuations and analogous to that of the phase of a laser beam, resulting in the Schawlow-Townes linewidth ͓7͔. There is, therefore, excess quantum noise on the phase difference of the OPO signal beams, compared to that of two independent ideal laser beams of the same power. This is a consequence of the number-phase Heisenberg uncertainty for the photon-number-correlated OPO beams. We made the first experimental measurement of this excess quantum noise, which can also be understood as a macroscopic Hong-Ou-Mandel interference experiment ͓8͔. It is, however, possible to suppress the Schawlow-Townes phasedifference drift by locking the phase difference of the signal beams of the OPO, thereby profoundly altering its natural dynamics and quantum properties. Indeed, perfect locking of the phase difference implies phase-difference squeezing, which means that the expected photon-number correlations in such a two-photon emitter are lost. This is clearly a different physical system from the standard OPO. Recently, CV entanglement was observed above threshold in standard OPO's ͓9,10͔ with unbridled Schawlow-Townes phasedifference drift. An elegant self-phase-locked type-II OPO, Corresponding author. Electronic address: opfister@virginia.edu PHYSICAL REVIEW A 74, 041804͑R͒ ͑2006͒