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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 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.
Yurke et al. (Sun,) studied this question.