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arXiv:quant-ph/9902070

Statistics of the single mode light in the transparent medium with cubic nonlinearity

В. Н. Горбачев, A. I. Zhiliba

Published Feb 23, 1999• 0 citations
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Abstract

The quantum statistics of the light in the transparent medium with cubic nonlinearity is considered. Two types of transparent media are treated, namely, the cold transparent medium with a ground working level and the inversion-free medium with the lasing levels of the same population. The spectra of light fluctuation are found on the basis of both Scully-Lamb and Haken theories. The conditions for the use of effective Hamiltonian are determined. Basing on the exact solution of the Fokker-Plank equation for the Glauber-Sudarshan P-function the inversion-free medium with cubic nonlinearity is shown to be the source of spontaneous radiation with non-Gaussian statistics.

DOI
10.48550/arxiv.quant-ph/9902070

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The quantum statistics of the light in the transparent medium with cubic nonlinearity is considered. Two types of transparent media are treated, namely, the cold transparent medium with a ground working level and the inversion-free medium with the lasing levels of the same population. The spectra of light fluctuation are found on the basis of both Scully-Lamb and Haken theories. The conditions for the use of effective Hamiltonian are determined. Basing on the exact solution of the Fokker-Plank equation for the Glauber-Sudarshan P-function the inversion-free medium with cubic nonlinearity is shown to be the source of spontaneous radiation with non-Gaussian statistics.
The quantum statistics of light in a transparent medium with cubic nonlinearity is considered. Two types of transparent medium are treated, namely, a cold transparent medium with a ground working level and an inversion-free medium with upper and lower levels of the lasing transition having the same population. The spectra of light fluctuations are derived on the basis of both the Scully-Lamb and the Haken theories. The conditions for the use of an effective Hamiltonian of interaction are determined. Based on the exact solution of the Fokker-Planck equation for the Glauber-Sudarshan P -function, the inversion-free medium is shown to be a source of spontaneous radiation with non-Gaussian statistics.
The quantum statistical properties of a single mode of the radiation field, prepared in the coherent state, interacting with a nonlinear medium of inversion symmetry are studied with the help of the usual two photon correlation function for zero time delay. We report the photon antibunching and sub-Poissonian photon statistics in addition to the usual photon bunching and the super-Poissonian photon statistics for an input vacuum field. The manipulation of the phase of input coherent light gives rise to the well known self induced transparency. The possible physical explanations for these events are presented.
A scheme for deriving a field kinetic equation for the problems of macroscopic quantum optics has been formulated. The general master equation obtained for the s-ordered quasi-probability, and Glauber-Sudarshan P-function in particular, has been concretized for the case of three-photon parametric processes in a multi-level medium. Thus the three-photon parametric phenomena have been examined without exploiting the traditional effective Hamiltonian. Discussed here is the problem of formation of field statistics depending on the type of excitation medium with two-level lasing levels that reduce to the Lamb-Scully or Haken models. The form of the kinetic equation obtained is shown to depend on the types of atomic transitions.
A quantum treatment of a coherently driven dispersive cavity is given based on a cubic nonlinearity in the polarisability of the internal medium. This system displays bistability and hysteresis in the semiclassical solutions. Quantum fluctuations are included via a Fokker-Planck equation in a generalised P representation. The transmitted light shows a transition from a single-peaked spectrum to a double-peaked spectrum above the threshold of the lower branch. Fluctuations in the field are reduced on the upper branch and both photon bunching and photon antibunching are predicted, for different operating points. An exact solution obtained for the steady-state generalised P function shows decidedly non-equilibrium behaviour, e.g. the lack of a Maxwell construction.
A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized PPP representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.