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

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We report the first measurement of the quantum phase-difference noise of an ultrastable nondegenerate optical parametric oscillator that emits twin beams classically phase-locked at exact frequency degeneracy. The measurement illustrates the property of a lossless balanced beam-splitter to convert number-difference squeezing into phase-difference squeezing and, thus, provides indirect evidence for Heisenberg-limited interferometry using twin beams. This experiment is a generalization of the Hong-Ou-Mandel interference effect for continuous variables and constitutes a milestone towards continuous-variable entanglement of bright, ultrastable nondegenerate beams. and progress has been made in this direction [9]. Recently, Silberhorn et al. made a beautiful demonstration of continuous-variable entanglement of picosecondpulsed optical beams, by simultaneous squeezing of the number sum and of the phase difference [10]. For highprecision measurements, however, stable CW beams are preferable. One interesting system for this purpose is the ultrastable nondegenerate optical parametric oscillator (OPO), which emits intense twin beams. In a type II OPO, these twin beams are orthogonally polarized. It is thus easy to separate them spatially and to subsequently make their polarizations parallel. Then, the twin beams can be made indistinguishable by locking their frequency difference to zero, which has been an experimental challenge. This Letter reports the first experimental demonstration of nonclassical interference of such macroscopic boson fields.In general, a quantum interference experiment consists in "splitting" a quantum field into two subfields, each experiencing its own phase evolution, and then "recombining" these subfields and performing a measurement. The corresponding probability distribution presents fringes which give information about the phase difference of the two subfields. Examples include the Mach-Zehnder interferometer for light and the Ramsey interferometer for matter, which are isomorphic to each other. "Nonclassical interference" may either mean that waves of a nonclassical nature are involved (e.g. matter waves), or that their behavior itself has no classical optical equivalent. The latter situation is what interests us, and is determined by the role of the vacuum modes of the quantum field, i.e. the physics of the "splitting." The physics of the beam splitter ( Fig. 1) takes center stage here and also determines the phase measurement noise. Take the example of an initial N -photon Fock state |k a ,ǫ, ω; N a , wherek andǫ are the unit wave and polarization vectors and ω the angular frequency. The beam splitter output is given by the interference of this state with the corresponding polarization-and frequency-degenerate vacuum state |k b ,ǫ, ω; 0 b . As was first demonstrated by Caves in 1980 [11], this yields a (classically intuitive) binomial probability distribution of the photon number between modes c and d, with standard deviation ∆N out − = ∆(N c − N d ) ∝ N 1/2 . Using the Heisenberg inequality...

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional 28.4% speedup compared with the traditionally used Asynchronous Multispin Coding (AMSC). Our overall design sustains a performance of 33.5 picoseconds per spin flip attempt for simulating the three-dimensional Edwards-Anderson model with parallel tempering, which significantly improves the performance over existing GPU implementations.

We report the realization of a light source specifically designed for the generation of bright continuousvariable entangled beams and for Heisenberg-limited inteferometry. The source is a nondegenerate, singlemode, continuous-wave optical parametric oscillator in Na:KTP, operated at frequency degeneracy and just above threshold, which is also of interest for the study of critical fluctuations at the transition point. The residual frequency-difference jitter is ± 150 kHz for a 3 MHz cold cavity half-width at half maximum. We observe 4 dB of photon-number-difference squeezing at 200 kHz. The Na:KTP crystal is noncritically phase-matched for a 532 nm pump and polarization crosstalk is therefore practically nonexistent.

We report an experimental demonstration of a heterodyne polarization rotation measurement with a noise floor 4.8 dB below the optical shot noise by use of classically phase-locked quantum twin beams emitted above threshold by an ultrastable type II Na:KTP cw optical parametric oscillator. We believe that this is the largest noise reduction achieved to date in optical phase-difference measurements.