Abstract
In conclusion we have solved the QFPE for the Q- as well as for the P-function with a non positive definite diffusion matrix describing optical bistability with the matrix continued fraction method. Expectation values, the squeezing parameter and the eigenvalues for both functions agree very accurately. The lowest nonzero real eigenvalue has a minimum approximately in the middle of the bistable region. An appreciable oscillating variation of the location of this minimum with the ratio of the detuning to the parameter of the nonlinear susceptibility was found for small cavity damping. Furthermore, the stationary Q-function as well as its eigenfunction belonging to the lowest nonzero eigenvalue have been obtained. The calculation of timedependent correlation functions by the MCF method seems also to be possible.
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© 1987 Springer-Verlag
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Risken, H., Vogel, K. (1987). Expectation values, Q-functions and eigenvalues for dispersive optical bistatbility. In: Ehlotzky, F. (eds) Fundamentals of Quantum Optics II. Lecture Notes in Physics, vol 282. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18035-4_71
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DOI: https://doi.org/10.1007/3-540-18035-4_71
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