Parametric oscillation with squeezed vacuum reservoirs

Abstract

Employing the quantum Hamiltonian describing the interaction of a two-mode light (signal–idler modes) generated by a non-degenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master and the Fokker–Planck equations. The corresponding Fokker–Planck equation for the Q-function is then solved employing a propagator method developed by K. Fesseha [J. Math. Phys. 33 2179 (1992)]. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal–idler modes are in squeezed states. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in one of the quadratures can be achieved.

Acknowledgments

I would like to thank K. Fesseha, M. Lewenstein and A. Sanpera for fruitful discussions. I acknowledge financial support by the Deutscher Akademischer Austausch Dienst (DAAD).

Notes

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A. Mebrahtu *

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