Quantum Statistics of Dissipative Nonlinear Oscillators

Marco Patriarca

Jacques J. van der Klink, F. Reuse, K. Maschke +2 more

V. Peinová, A. Luk

The statistical properties of the third-order nonlinear dissipative oscillator, which evolves from any state, are derived on the basis of the exact solution to the master equation. Some important features of the nonlinear oscillator model, such as the recurrences of the initial state, are related to the properties of quasidistributions connected with the phase of the complex field amplitude.

Brad R. Trees, Elizabeth Segelken

Vlasta Peřinová, A. Lukš

Recently the statistical properties of the third-order nonlinear dissipative oscillator have been determined exactly to an approximation respecting non-zero reservoir temperatures for a most general input state.1 Later the assumption of zero-'temperature heat bath has been removed, but the initial coherent state has been considered. In this coinmunication we present the statistical characteristics of the third-order non linear dissipative oscillator responsive to the requirements of quantum optics and established without any restrictions on the initial state.

V. Peinová, M. Kárská

The statistical properties of nonlinear oscillators modeling dissipative forward four-wave mixing are investigated, adopting the Fokker-Planck equation approach. The photon statistics are shown to be insensitive to the nonlinearities and are formulated in terms of the superposition of coherent and chaotic fields. The only approximation in describing the squeezing properties consists in the way of including thermal noise. The effect of the initial coherent amplitudes, that of the interplay of the coupling constants, and that of the reservoir on the squeezing properties are studied. An interesting connection between the revivals of coherent amplitudes and squeezing is pointed out.