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, 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 Hilbert-Schmidt speed can efficiently detect negative permittivity and refractive index, which is of great importance from a practical point of view.

Quantum teleportation and phase quantum estimation in a two-qubit state influenced by dipole and symmetric cross interactions

“…In this paper, ÿ = 1 is considered and all the parameters are nondimensionalized in plotting figures. More precisely similar to what was done in [82][83][84]; In plotting figures for quantities that have energy and time dimensions, respectively, the values of x ˜and x 1 ˜equal to the unit have been chosen, where x ˜is an arbitrary…”