Squeezing and photon antibunching in harmonic generation

Quantum fluctuations in second-harmonic light generation

The statistical properties of the second harmonic and subharmonic are investigated on the basis of the generalized Fokker-Planck equation making use of the coherent state technique. An iterative procedure of solving the Fokker-Planck equation is adopted making it possible to obtain some recursion equations, particularly two iterations are explicitly performed providing approximate solutions for the normal and antinormal characteristic functions. Higher-order corrections to the superposition of coherent and chaotic fields are found in the subharmonic mode or if the coupling of modes is taken into account. Earlier results for the anticorrelation effect are rederived, the reservoir effect is obtained and the related problems of the existence of the Glauber-Sudarshan quasidistribution are discussed.

Master equation approach to the second harmonic and subharmonic generation

Second harmonic generation and statistical properties of light

We develop a recursion procedure for solving the generalized Fokker-Planck equation for a system of three interacting one-mode boson fields including the proof of convergence. Approximate formulae for the quantum antinormal characteristic function and the corresponding quasidistribution are obtained for the whole system and as a consequence quantum fluctuations in single fields, correlations among them and various cases of occurrence of the anticorrelation effect are discussed including losses. Initial fields are assumed to be coherent or partly chaotic and it is shown that in some cases the lossy mechanism as well as if some of these fields are chaotic can support the occurrence of the anticorrelation effect. The most important cases are described by the model of the superposition of coherent and chaotic fields although some corrections to this model are also found.

Generalized Fokker-Planck equation approach to optical parametric processes I. Equations of motion and their solutions

We study the statistical properties of parametric processes (parametric amplification, frequency conversion, splitting of frequency, etc.) described by the trilinear Hamiltonian and of the second harmonic generation including the lossy mechanism and rotating terms. In a short-time approximation some conservation laws are derived and the existence of the Glauber-Sudarshan weighting function is discussed. It is shown in the second harmonic generation case that good coherence of the incident radiation is lost proportionally to the intensity in interaction while the second harmonic radiation has tendency to be coherent. The effects of the spontaneous emission of the medium and of the physical vacuum are also discussed. In this approximation the statistics is generally described by the superposition of coherent and chaotic fields with correlated components.

J. Peřina

Papers

Dynamics of non-linear optical processes