Theory of feedback-generated squeezed states

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Abstract
Conservation of commutator brackets imposes constraints on the response of linear systems. From these constraints the minimum uncertainties of in-phase and quadrature field components in linearized parametric and oscillator systems can be determined. In this paper, a cavity containing a ‘‘degenerate parametric wall’’ is analyzed and the resulting equations are found to be identical with those of a saturated oscillator. The ideal parametric wall resonator has lower noise than the saturated oscillator. Feedback is put onto an oscillator formed by the parametric wall, and onto the saturated oscillator, by degenerate heterodyne (homodyne) detection of the oscillator output. It is shown in both cases that the field fluctuations incident upon the photodetector in the feedback loop are ‘‘squeezed,’’ i.e., the photodetector current fluctuation level is below shot noise. A semiclassical analysis arrives at the same expression for the detector current fluctuations in the limit of a highly saturated oscillator, thus permitting an alternative interpretation of these results. However, a quantum nondemolition measurement via a nonlinear interferometer ‘‘extracts’’ the squeezed states, predicted by the quantum analysis, from the feedback loop. This result has no semiclassical interpretation.