Photon-Number Distributions for Number-State Homodyne Photomixing at a Lossless Beam Splitter

Abstract

We have recently determined the homodyne photon-number distribution at the output ports of a lossless beam splitter given any two input states of the field.1 Photomixing with the number states are the basic building blocks of the theory. For pure input number states, the photon-number distribution at the output ports of the device is proportional to the square of Jacobi polynomials in the beam-splitter transmittance τ . When either input state is the vacuum, the output photon number obeys the binomial law, and interference effects in the photon-number domain are not observed. However, when identical number states are incident on the two input ports of a 50/50 beam splitter (τ = 1/2), interference in the photon-number domain is maximized as the output photons cluster in pairs. Odd photon numbers are thus never observed. The output photon number then obeys the discrete arcsine law, which, unlike the binomial, gives greatest weight to the endpoints of the distribution. This is shown in the figure below.