Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime

We propose an experimental setup to probe the low-lying excitation modes of a parametrically oscillating planar cavity, in particular the soft Goldstone mode which appears as a consequence of the spontaneously broken U(1) symmetry of signal-idler phase rotations. A strong and narrow peak corresponding to the Goldstone mode is identified in the transmission spectrum of a weak probe beam incident on the cavity. When the U(1) symmetry is explicitly broken by an additional laser beam pinning the signal-idler phase, a gap opens in the dispersion and the Goldstone peak is dramatically suppressed. Quantitative predictions are given for the case of semiconductor planar cavities in the strong exciton-photon coupling regime