Quantum Interference in Atomic Systems: Mathematical Formalism

Thi-Thuy Nguyen, Chin‐Chun Tsai

We study the light-atom interaction in a four-level atomic system in a ladder-vee type configuration employing the density matrix formalism with exact numerical solutions. By varying the third driving strength, we achieve continuous control over the quantum interference of the system, shifting it from destructive to constructive interference. Our analysis reveals a narrow existence window for the EIT signal when the driving field is active, suggesting effective control ability. Finally, we propose the required driving Rabi frequency as a function of the given coupling Rabi frequency to achieve a 90% reduction in EIT magnitude, effectively altering the quantum interference by a π /2 phase shift.

Urbasi Sinha, Debadrita Ghosh

Y. Kim

Sitotaw Eshete

According to our work, we assert that the dynamics of electromagnetically induced transparency in lambda type atomic system by taking the basics in line with the quantum mechanical aspects. We wonder that incorporating the condition for electromagnetically induced transparency to happen is a meaningful arm to generating a conclusion for a considerable quantum optical system; lambda type atomic system. In this work, mainly quantum interference of light generated from an atomic system has been studied significantly. Accordingly, the mathematical result shows that the quantum interference is due to spontaneous decay rate of the atom from the upper energy state to two ground energy states and sufficiently affects the transparency of the medium. To have such transparency we must have initially the atom in the upper physical state. Keywords: Electromagnetically induced transparency, Orthogonal states, Interference, Light, Lambda system.

James, Kazadi

Abstract: This work develops a unified and gauge-invariant framework in which quantum interference is described as a measurement of relative holonomy between two coherent evolutions in a combined configuration space X = M × Λ. Both the Aharonov–Bohm (Abelian) and Wilczek–Zee (non-Abelian) effects appear as limits of a single Wilson-loop observable. A block connection is introduced on the direct-sum bundle E = H ⊕ (T X ⊗ ℂ), with structure group U(n) × O(p,q), thereby unifying Berry parallel transport and Levi-Civita geometry within one connection. The formalism ensures gauge and diffeomorphism covariance, analytic well-posedness under back-reaction, and establishes conditions for reconstructing the spacetime metric from holonomy data. The resulting theory provides a mathematically consistent and experimentally testable synthesis of geometric phase, interference, and spacetime connection. Potential physical implementations include mesoscopic rings, cold-atom systems, and superconducting circuits. Keywords: geometric phase; holonomy; Aharonov–Bohm effect; Berry phase; Wilczek–Zee connection; differential geometry; quantum interference; gauge theory.

Evgeny B. Alexandrov, М. П. Чайка, Gennadij I. Khvostenko