Waveguide Mach-Zehnder interferometer to enhance the sensitivity of quantum parameter estimation

The waveguide Fabry-Perot interferometer (FPI) (see, e.g., in Phys. Rev. Lett.113, 243601 (2015)10.1103/PhysRevLett.115.243601 and Nature569, 692 (2019)10.1038/s41586-019-1196-1), instead of the free space's one, have been demonstrated for the sensitive quantum parameter estimations. Here, we propose a waveguide Mach-Zehnder interferometer (MZI) to further enhance the sensitivity of the relevant parameter estimations. The configuration is formed by two one-dimensional waveguides coupled sequentially to two atomic mirrors, which are served as the beam splitters of the waveguide photons to control the probabilities of the photons being transferred from one waveguide to another. Due to the quantum interference of the waveguide photons, the acquired phase of the photons when they pass through a phase shifter can be sensitively estimated by measuring either the transmitted or reflected probabilities of the transporting photons. Interestingly, we show that, with the proposed waveguide MZI the sensitivity of the quantum parameter estimation could be further optimized, compared with the waveguide FPI, in the same condition. The feasibility of the proposal, with the current atom-waveguide integrated technique, is also discussed.