Entangling the optical frequency comb: simultaneous generation of multiple 2x2 and 2x3 continuous-variable cluster states in a single optical parametric oscillator

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 2x2 and 2x3 continuous-variable cluster states by a single optical parametric oscillator pumped by just a few optical modes.