Noisy Stark probes as quantum-enhanced sensors

Wannier-Stark localization has been proven to be a resource for quantum-enhanced sensitivity for precise estimation of a gradient field. An extremely promising feature of such probes is their ability to showcase such enhanced scaling even dynamically with system size, on top of the quadratic scaling in time. In this paper, we address the issue of decoherence that occurs during time evolution and characterize how that affects the sensing performance. We determine the parameter domains in which the enhancement is sustained under dephasing dynamics. In addition, we consider an effective non-Hermitian description of the open quantum system dynamics for describing the effect of decoherence on the sensing performance of the probe. By investigating the static and dynamic properties of the non-Hermitian Hamiltonians, we show that quantum-enhanced sensitivity can indeed be sustained over certain range of decoherence strength for Wannier-Stark probes. This is demonstrated with two examples of non-Hermitian systems with non-reciprocal couplings.