Monitoring variations of refractive index via Hilbert–Schmidt speed and applying this phenomenon to improve quantum metrology

Abstract In this paper, we investigate the role of the nonlinear response of a material to improve quantum metrology. We show that the collective optical behavior of an atomic ensemble can be applied to enhance frequency estimation through one of the atoms. In fact, the collective optical behavior of the atomic ensemble by analyzing the quantum information extracted from one of its elements. Moreover, we introduce Hilbert–Schmidt speed (HSS), an easily computable theoretical tool, to monitor the variations of linear as well as nonlinear refractive indices and evaluate the strength of the nonlinear response of optical materials. Furthermore, we illustrate that quantum Fisher information and HSS can efficiently detect negative permittivity and refractive index, which is of great importance from a practical point of view.