  We propose methods to create and observe Laughlin-like states of photons in a
strongly nonlinear optical cavity. Such states of strongly interacting photons
can be prepared by pumping the cavity with a Laguerre-Gauss beam, which has a
well-defined orbital angular momentum per photon. The Laughlin-like states
appear as sharp resonances in the particle-number-resolved transmission
spectrum. Power spectrum and second-order correlation function measurements
yield unambiguous signatures of these few-particle strongly-correlated states.
