Scalability and coherence are two essential requirements for the experimental implementation of quantum information and quantum computing. Here, we report a breakthrough toward scalability: the simultaneous generation of a record 15 quadripartite entangled cluster states over 60 consecutive cavity modes (Q modes), in the optical frequency comb of a single optical parametric oscillator. The amount of observed entanglement was constant over the 60 Q modes, thereby proving the intrinsic scalability of this system. The number of observable Q modes was restricted by technical limitations, and we conservatively estimate the actual number of similar clusters to be at least 3 times larger. This result paves the way to the realization of large entangled states for scalable quantum information and quantum computing.

We report on our research effort to generate large-scale multipartite optical-mode entanglement using as few physical resources as possible. We have previously shown that cluster-and GHZ-type N -partite continuous-variable entanglement can be obtained in an optical resonator that contains a suitably designed second-order nonlinear optical medium, pumped by at most O(N 2 ) fields. In this paper, we show that the frequency comb of such a resonator can be entangled into an arbitrary number of independent 2×2 and 2×3 continuous-variable cluster states by a single optical parametric oscillator pumped by just a few optical modes.

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

We generated −2.2 dB of broadband amplitude squeezing at 1064 nm in a periodically poled KTiOPO 4 (PP-KTP) waveguide by coupling of the fundamental and second-harmonic cw fields. This is the largest amount of squeezing obtained to date in a KTP waveguide, limited by propagation losses. This result paves the way for further improvements by use of lower-loss buried ion-exchanged waveguides. © 2009 Optical Society of America OCIS codes: 270.6570, 270.1670 The experimental implementation of continuousvariable (cv) quantum information [1], an ambitious and exciting endeavor requires the creation of strongly squeezed light. Squeezed light has been produced using a number of methods, but the most successful experiments to date (ranging from −9 to −10 dB of squeezing) have used optical parametric oscillators, which feature a second-order nonlinear material placed in a resonant optical cavity [2][3][4]. In such systems, intracavity losses are amplified by the resonator buildup and thus present a serious hindrance to increasing the squeezing level. It would therefore be beneficial to suppress the optical cavity by use of nonlinear optical waveguides in which the transverse field confinement yields an increase of the nonlinear efficiency that can make up for the buildup of a reasonably high finesse cavity [5,6]. If need be, some cavity modes can still be exquisitely well defined by seeding the nonlinear waveguide with an optical frequency comb [7,8]. Waveguides are ideally suited for applications, such as integrated circuits, owing to their small size [9] and could also help alleviate gain-induced diffraction, which has been seen with traveling waves in bulk crystals [10]. Moreover, removing the optical cavity yields an increase of the squeezing bandwidth by several orders of magnitude [11], which is of interest for fast quantum processing. Finally, comb-seeded waveguides are of great interest for a recently proposed method to generate massively scalable cv entanglement [12]. Over a decade ago, several experiments tried to exploit the increase in nonlinear efficiency that waveguides provide in an attempt to obtain large amounts of traveling-wave squeezing with pulsed inputs [13][14][15][16]. However, owing to propagation losses in the waveguide, these works achieved a maximum of −1.5 dB of squeezing. Recently, advances in waveguide fabrication techniques have allowed for better than −4 dB of pulsed traveling-wave squeezing in MgO-doped periodically poled LiNbO 3 (PPLN) waveguides [17]. Undoped PPLN waveguides were used to obtain squeezing and entanglement with a cw input [11]. Other media for nonlinear optical waveguides include quasi-phase-matched KTP [13], quasi-phase-matched LiTaO 3 (LT) [14], and periodically poled stoichiometric LT [18]. Although the first measurement of squeezed light from an optical waveguide was made in KTP [13], squeezing in KTP waveguides has not been explored in recent years. There are, however, a number of reasons to do so. High-squeezing experiments have been carried out in bulk KTP and PPKT...

We present the experimental realization of a theoretical effect discovered by Olivares and Paris [1], in which a pair of entangled optical beams undergoing independent losses can see nonlocal correlations restored by the use of a nonlocal resource correlating the losses. Twin optical beams created in an entangled Einstein-Podolsky-Rosen (EPR) state by an optical parametric oscillator above threshold were subjected to 50% loss from beamsplitters in their paths. The resulting severe degradation of the signature quantum correlations observed between the two beams was then suppressed when another, independent EPR state impinged upon the other input ports of the beamsplitters, effectively entangling the losses inflicted to the initial EPR state. The additional EPR beam pair was classically coherent with the primary one but had no quantum correlations with it. This result may find applications as a "quantum tap" for entanglement.

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Toward the implementation of universal quantum computing in the optical frequency comb, we recently demonstrated the entanglement of 60 cavity modes of a single optical parametric oscillator into 15 independent quadripartite ring cluster states.The experimental implementation of quantum computing, driven by the promise of exponential speedup for tasks such as the simulation of quantum physics and integer factoring [1] is a daunting challenge that requires exquisite levels of control over the quantum mechanical properties of numerous individual physical systems (quantum bits or, in this paper, quantum modes or Qmodes). Here, we demonstrate a breakthrough toward scalability [2]: the ultracompact implementation of 15 quantum registers, each in a quadripartite cluster state [3,4], in the optical frequency comb (OFC) formed by the spectrum of a single optical parametric oscillator (OPO). In the quantum OFC, each (Q)mode is well approximated by a quantum harmonic oscillator whose continuous-variable Hilbert space is defined by its amplitudeor phase-quadrature field observables. There is no known fundamental impossibility to the implementation of quantum computing with Qmodes [4-6], even though the implementation of quantum error correction appears likely to require Hilbert-space discretization [7,8]. It was shown that a square-grid continuous-variable cluster state of arbitrary size, suitable for universal one-way quantum computing, can be generated in the OFC of a single OPO [9,10]. In this work, we achieved the first step toward this goal: the parallel generation of 15 quantum computing registers, each comprising 4 Qmodes in a quadripartite cluster state, in the quantum OFC of a single OPO.The quantum OFC was generated by a bowtie ring OPO containing two x-cut KTiOPO 4 (KTP) nonlinear crystals, of 10 mm length, and rotated by 90 • from each other about the x axis. This ensured the perfect overlap of the respective OFCs of orthogonal linear polarizations y and z. One crystal was not phasematched. The other was periodically poled with two distinct periods: 9 µm over a 3 mm length, and 458 µm over 7 mm. The former quasiphasematched the zzz parametric downconversion, where the first letter denotes the polarization of the pump field at frequency 2ω o and the other letters denote the polarization of the n th signal field pair at ω ±n =ω o ±(n − 1/2)∆, with ∆=945.66 MHz the free spectral (FSR) range of the OPO cavity. The latter period quasiphasematched the yzy and yyz interactions simultaneously (dispersion was negligible for our values of n). The pump polarization was carefully adjusted in the (yz) plane, using OPO characterization by resonant second harmonic generation, to yield the Hamiltonian [11]where a † j,k is the creation operator of the k-polarized Qmode of frequency ω j . This Hamiltonian entangles the OFC as depicted in Fig. 1 and proven by the solutions of the Heisenberg equations for the n th Qmode quartet:(2) P + = [P −n,y + P n,y ] + Φ [P −n,z + P n,z ] e −rΦ (3)P − = Φ [P −n,y − P n,y ] − [P −n,z − P n,z ] ...