Antibunched photons emitted by a quantum point contact out of equilibrium

Motivated by the experimental search for "GHz nonclassical light", we identify the conditions under which current fluctuations in a narrow constriction generate sub-Poissonian radiation. Antibunched electrons generically produce bunched photons, because the same photon mode can be populated by electrons decaying independently from a range of initial energies. Photon antibunching becomes possible at frequencies close to the applied voltage V, when the initial energy range of a decaying electron is restricted. The condition for photon antibunching in a narrow frequency interval below V is derived in terms of the eigenvalues T_n of the transmission matrix. This condition is satisfied in a quantum point contact, where only a single T_n differs from 0 or 1. The photon statistics is then a superposition of binomial distributions.