Quantum Theory of High-resolution Length Measurement with a Fabry-Perot Interferometer

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Abstract
The quantum limits on measurements of small changes in the length of a Fabry-Perot cavity are calculated. The cavity is modelled by a pair of dissimilar mirrors oriented perpendicular to a one-dimensional axis of infinite extent. The continuous spectrum of spatial modes of the system is derived, and the electromagnetic field is quantized in terms of a continuous set of mode creation and destruction operators. Coherent state and squeezed vacuum-state excitations of the field are characterized by energy flow, or intensity, variables. The determination of small changes in the cavity length by observations of fringe intensity is considered for schemes in which the cavity is simultaneously excited by coherent and squeezed vacuum-state inputs. The contributions to the limiting resolution from photocount and radiation-pressure length uncertainties are evaluated. These properties of the Fabry-Perot cavity are compared with the corresponding results for the Michelson interferometer.