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

TLDR

Conventional interferometers such as the Mach‑Zehnder and Fabry‑Perot are characterized by SU(2). The paper presents a Lie‑group theoretical framework for interferometers and introduces a new class characterized by SU(1,1). The SU(1,1) interferometers employ active elements such as four‑wave mixers or degenerate‑parametric amplifiers. Both SU(2) and SU(1,1) interferometers can, in principle, achieve a phase sensitivity of 1/N with suitably prepared input states, and SU(1,1) does so with fewer optical elements.

Abstract

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 \ensuremath{\Delta}\ensuremath{\varphi} 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.