Fig. 2: Reconstruction of the photon number distribution with a phase-randomized pump-probe experiment.

a Experimental scheme. The signal and idler outputs of an optical parametric amplifier (OPA), such that ωSIG = 2ωIDL, are used in combination with a second harmonic generation process to set up a phase-averaged pump-probe heterodyne detection sensitive to the random laser CEP (details in text). b Wigner distribution of the phase-averaged coherent state resulting from the randomization of the CEP-dependent LO-probe phase. c The detection output is the distribution of the phase-averaged quadrature. d Applying the tomography procedure to the quadrature data we obtain the probe photon number distribution