Variations of the degree of angular entanglement in noncollinear regimes of Spontaneous Parametric Down-Conversion (SPDC)

As known, the process of Spontaneous Parametric Down-Conversion in birefringent crystals (SPDC) produces states of photon pairs [1-3] which can be entangled. The variables of the biphoton wave function can be different and characterizing different degrees of freedom of photons: their polarizations, or propagation angles, or frequencies of photons ?1 and ?2. In the last case one can speak about spectral entanglement of sates characterized by the wave function ?(?1, ?2). The phenomenon of spectral entanglement and its degree were rather thoroughly investigated in the work [4], both theoretically and experimentally . On the other hand, the double Fourier transformation of ?(?1, ?2) gives the temporal biphoton wave function ?(t1, t2), in which the time variables t1 and t2 can be interpreted as the arrival times of photons to detectors. In terms of the temporal wave function ?(t1, t2) one can speak about temporal entanglement of biphoton states, which is discussed in this talk.
1. D.N. Klyshko, JETP Lett, 6, 90 (1967).
2. S.E. Harris, M.K. Oshman, and R.L. Byer, PRL, 18, 732 (1967).
3. D. Magde, H. Marr, PRL, 18, 905 (1967).
4. G. Brida, V. Caricato, M.V. Fedorov, M. Genovese, S.P. Kulik, EPL, 87, 64003 (2009).