Simultaneous generation of multiple quadripartite continuous-variable cluster states in the optical frequency comb of a single optical parametric oscillator

We report the experimental generation of multiple, four-mode, continuous-variable cluster states from a single optical parametric oscillator (OPO) operating below threshold. We use a PPKTP crystal phasematching two concurrent nonlinear interactions to entangle the optical frequency comb formed by the OPO cavity. Four independent entanglement witnesses (a.k.a. infinitesimal operators of stabilizers, or ``nullifiers'') display squeezing in each cluster state, and we utilize the large phase-matching bandwidth of the nonlinear interactions to display the simultaneous creation of several such cluster states using only a single pump frequency. A slightly more sophisticated version of this experimental method, using a crystal with three nonlinear interactions and 15 pump frequencies, has theoretically shown the ability to produce arbitrarily large square-grid cluster states suitable for universal one-way quantum computing.