Magnetically Induced Transparency-Absorption and Normal-Anomalous Dispersion Characteristics of ${}^{87}\text{Rb}$ Medium or Any J-Type Configuration Atomic Vapors Subject to a Vector Magnetic Field and a Weak Resonant Pump

TL;DR

This paper presents an analytical model for magnetically induced transparency-absorption and dispersion in ${}^{87}\text{Rb}$ vapor, revealing frequency-dependent effects useful for sensing and photonic applications.

Contribution

It develops a comprehensive analytical framework for MITA and MINAD in J-type atomic systems under a vector magnetic field, including bifurcation analysis and spectral behavior.

Findings

Frequency-dependent transparency and absorption effects identified.

Normal and anomalous dispersion with sign reversals demonstrated.

Potential applications in magnetometry and spectral filtering suggested.

Abstract

We have developed an analytical framework for magnetically induced transparency-absorption (MITA) and normal-anomalous dispersion (MINAD) in a weakly driven ${}^{87}\text{Rb}$ vapor, or any J-type three-level system, under a vector magnetic field. By solving the Bloch equations in the stationary, quasi-stationary, and short-pulse regimes, we obtained closed-form expressions for the atomic populations and coherences and identified a bifurcation in the oscillatory dynamics at zero longitudinal Zeeman splitting. The Fourier-domain analysis reveals alternating transparency/absorption and normal/anomalous dispersion with frequency-dependent sign reversals, enabling spectrally selective filtering and group-delay effects. Slow oscillatory behavior in the radio-frequency range makes the system suitable for weak magnetic-field sensing, while fast oscillations at optical frequencies suggest applications in spectral filtering and frequency-comb-like signal shaping. The results provide a theoretical basis for experimental observation of MITA/MINAD and for optimizing atomic-vapor platforms for precision magnetometry and related photonic functionalities.