Coherent Splitting of Single Photons by an Ideal Beam Splitter
To a first approximation, a single photon incident upon an ideal beam splitter will either be transmitted or reflected. The author has recently shown, however, that an ideal beam splitter has a small probability of coherently splitting a single photon into a pair of secondary photons, conserving energy in the process. This process is analogous to parametric down-conversionl,2, except that the necessary nonlinearity does not come from any inherent nonlinearity of the medium but comes, instead, from the A 2 term in the Hamiltonian. The necessary inversion asymmetry is also not a property of the medium and is dependent upon the direction of the wave vectors of the incident and secondary photons. The secondary photons have little or no first-order coherence but they do possess second-order coherence, which allows their use in two-photon interferometry3.