https://doi.org/10.1007/s100530070074
Dependence on crystal parameters of the correlation time between signal and idler beams in parametric down conversion calculated in the Wigner representation
1
Departamento de Física Aplicada, Universidad de Sevilla,
41092 Sevilla, Spain
2
Department of Mathematics, University of
Manchester, Manchester M13 9PL, UK
3
Departamento
de Física Moderna, Universidad de
Cantabria, 39005 Santander, Spain
Received:
24
January
2000
Revised:
24
March
2000
Published online: 15 September 2000
The theory of parametric down conversion within the framework of the Wigner representation has been treated recently in a series of papers using the standard model Hamiltonian. Here we take a more fundamental point of view studying the mechanism, inside the crystal, for the production of the signal and idler beams. We begin from the evolution equations for the quantum field operators, pass to the Wigner function and solve the resulting (Maxwell) equations with the use of the Green's function method. We derive the time dependence of the coincidence detection probability as a function of the parameters of the nonlinear crystal (in particular the length) the radius of the pumping beam, and the bandwidth of the filters in front of the detectors.
PACS: 42.50.Ar – Photon statistics and coherence theory / 03.65.Sq – Semiclassical theories and applications / 42.50.Lc – Quantum fluctuations, quantum noise, and quantum jumps
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
