Highly entangled quantum networks cluster states lie at the heart of recent approaches to quantum computing [1,2]. Yet, the current approach for constructing optical quantum networks does so one node at a time [3][4][5], which lacks scalability. Here we demonstrate the singlestep fabrication of a multimode quantum network from the parametric downconversion of femtosecond frequency combs. Ultrafast pulse shaping [6] is employed to characterize the comb's spectral entanglement [7]. Each of the 511 possible bipartitions among ten spectral regions is shown to be entangled; furthermore, an eigenmode decomposition reveals that eight independent quantum channels [8] (qumodes) are subsumed within the comb. This multicolor entanglement imports the classical concept of wavelength-division multiplexing (WDM) to the quantum domain by playing upon frequency entanglement as a means to elevate quantum channel capacity. The quantum frequency comb is easily addressable, robust with respect to decoherence, and scalable, which renders it a unique tool for quantum information.Theoretical Description The use of photonic architectures to realize quantum networks is appealing since photons are immune from environmental disturbances, readily manipulated with classical tools, and subject to high efficiency detection [10,11]. We consider here the creation of nonclassical, continuous variable states with an optical parametric oscillator (OPO), in which a pump photon of frequency 2ω 0 splits into a pair of lower energy photons subject to energy conservation and the cavity resonance condition. The generation of a photon pair initiates a nonclassical correlation between the cavity modes ω −p and ω p , where ω p = ω 0 + p · ω FSR and ω FSR is the cavity free spectral range. Given a sufficiently large phase-matching bandwidth, a frequency comb emerges from the cavity with all of the resonant photon pairs independently entangled [12]. The inclusion of additional pump photons of frequencies 2ω 0 + p · ω FSR opens the possibility for richer frequency correlations beyond purely symmetric pair creation. Femtosecond pulse trains contain upwards of ∼ 10 5 individual frequency modes, and the simultaneous injection of all these modes into a nonlinear optical element induces an intricate network of both symmetric and asymmetric frequency correlations [13]. To access such states, a synchronously pumped optical parametric oscillator (SPOPO), which consists of an OPO driven by a femtosecond pulse train with a repetition rate matching the cavity free spectral range, is exploited and creates correlations governed by the Hamil-where g regulates the overall interaction strength and a † m is the photon creation operator associated with a mode of frequency ω m . The coupling strength between modes at frequencies ω m and ω n is dictated by the matrix L m,n = f m,n · p m+n , where f m,n is the phase-matching function [14,15] and p m,n is the pump spectral amplitude at frequency ω m + ω n [16]. Frequency Entanglement We experimentally demonstrate that the photonic s...

Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example in cluster state computation. We report in this paper the first experimental evidence of a multimode non-classical frequency comb in a femtosecond synchronously pumped optical parametric oscillator. In addition to a global reduction of its quantum intensity fluctuations, the system features quantum correlations between different parts of its frequency spectrum. This allows us to show that the frequency comb is composed of several uncorrelated eigenmodes having specific spectral shapes, two of them at least being squeezed, and to characterize their spectral shapes.PACS numbers: 42.50. Dv, 42.50.Lc, 42.65.Yj Optical frequency combs are perfect tools for high precision metrological applications [1,2]. The extension of their extraordinary properties to the quantum domain may lead to significant progress in different areas of quantum physics, in particular in quantum metrology and parameter estimation [3,4], but also in quantum computation with continuous variables [5,6]. Indeed, one of the main challenges of experimentally implementing quantum computers in the continuous variable regime, for example in cluster state computation [6,7], is the generation of highly multimode non-classical states of light, and the scalability of this generation. As the difficulty of linearly mixing distinct squeezed light sources [8,9] increases as the number of modes increases, it can be more interesting to use instead a single highly multimode source which directly produces non-classical resources shared between many modes within a same beam. In this perspective, optical frequency combs, which span over thousands of different frequency modes, are a very promising system for scalable generation of spectral/temporal multimode quantum states. We report in this paper the first experimental evidence of multimode non-classical frequency comb generated by an Optical Parametric Oscillator (OPO) in the femtosecond regime, which opens the way to the generation of these highly multimode states.Multimode non-classical light has been already experimentally generated with spatial multimode beams produced by OPOs [10,11], and very recently, with the longitudinal modes of an OPO [12,13]. In the domain of temporal modes, single mode squeezing of short pulses has been observed in various experiments starting from [14] in the nanosecond regime. Non-classical states of single femtosecond pulses are the subject of many recent studies (for example [15]). Multimode squeezed solitons have been generated in an optical fiber [16]. Single mode quantum noise reduction in picosecond frequency combs has already been achieved with a Synchronously Pumped Optical Parametric Oscillator (SPOPO) [17], which is an OPO pumped by a train of ultrashort pulses that are synchronized with the pulses making round trips inside the optical cavity.It has recently been shown [18,19] that such SPOPOs generate squeezed frequency combs which are multimode. ...