SU(2) and SU(1,1) interferometers.

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 delta phi approaching 1/N, where N is the total number of quanta entering the interferometer, provided 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.