A Lie-group-theoretical approach to the analysis of interferometers is presented. Conventional interferometers such as the Mach-Zehnder and Fabry-Perot can be characterized by SU(2). We introduce a class of interferometers characterized by SU(1,1). These interferometers employ active elements such as four-wave mixers or degenerate-parametric amplifiers in their construction. Both the SU(2) and SU(1,1) interferometers can in principle achieve a phase sensitivity {Δ}{φ} approaching 1/N, where N is the total number of quanta entering the interferometer, provided that the light entering the input ports is prepared in a suitable quantum state. SU(1,1) interferometers can achieve this sensitivity with fewer optical elements.
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Yurke et al. (1986) studied this question.
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