Dynamics of relaxation, decoherence and entropy of a qubit in anisotropic photonic crystals

TL;DR

This paper analyzes the quantum dynamics of a qubit in anisotropic photonic crystals using fractional calculus, revealing energy and coherence preservation within the photonic band gap, unlike in Markovian systems.

Contribution

It introduces a fractional calculus approach to analytically study qubit dynamics in anisotropic photonic crystals, highlighting non-Markovian effects within the band gap.

Findings

Energy, coherence, and information are preserved inside the PBG.

Preservation does not occur outside the PBG in Markovian systems.

Fractional Langevin equation effectively models non-Markovian quantum dynamics.

Abstract

We study the quantum dynamics of relaxation, decoherence and entropy of a qubit embedded in an anisotropic photonic crystal (PhC) through fractional calculus. These quantum measurements are investigated by analytically solving the fractional Langevin equation. The qubit with frequency lying inside the photonic band gap (PBG) exhibits the preserving behavior of energy, coherence and information amount through the steady values of excited-state probability, polarization oscillation and von Neumann entropy. This preservation does not exist in the Markovian system with qubit frequency lying outside the PBG region. These accurate results are based on the appropriate mathematical method of fractional calculus and reasonable inference of physical phenomena.