Multi-parameter Estimation with Multi-mode Ramsey Interferometry

Simultaneous estimation of multiple parameters near classical precision limit is of fundamental importance to measurement sciences and applications. The associated tasks constitute mainly of two aspects: finding an input quantum state capable of realizing the optimal precision limited by the laws of quantum mechanics, and finding a corresponding measurement scheme that saturates this precision. The latter aspect is typically challenging and usually requires optimization on a case by case basis. Focusing on achieving the precision of the classical limit, or the standard quantum limit, with uncorrelated particles and mutually commuting phase measurements, we present a generic and experimentally feasible Ramsey-like multi-mode interferometer that fulfils the aforementioned tasks. The proposed interferometer features a beam splitting process by a unitary transformation $U$ (with all matrix elements real), and a recombining process by $ U^†$. How such transformations $U$ can be constructed experimentally for both optical and atomic based measurements are discussed, opening up practically useful implementations for multi-mode optical and atomic sensing.