Correlations and One-quantum Pulse Shapes in Photon Pair Generation

Abstract

We examine the correlation between a pair of photons in the information entropy context. Either in two-photon cascade decay of a three-level system or in parametric down-conversion a pure state of two distinguishable photons is produced, with the states of the individual photons entangled. We obtain state amplitudes in the Weisskopf-Wigner approximation and use them to derive the two-photon density matrix in the ‘arrival time’ basis. It is found that only a finite number of eigenvectors of the appropriate density matrices is required to describe the system. That is, despite the continua of wave-vectors involved in the double spontaneous decay the two-photon entanglement is effectively discrete; furthermore, the eigenvectors in the arrival time basis can be interpreted as the fundamental orthogonal spontaneous emission pulses of the two systems.