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 Vxe/(h) over bar, when the initial energy range of a decaying electron is restricted. The condition for photon antibunching in a narrow frequency interval below eV/(h) over bar reads [Sigma(n)T(n)(1-T-n)](2)<2Sigma(n)[T-n(1-T-n)](2), with T-n an eigenvalue 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.