Effect of photonic band gap on entanglement dynamics of qubits

TL;DR

This paper investigates how photonic band gap environments influence qubit entanglement, showing that PBG can prevent decoherence and enable long-term entanglement preservation, especially when qubit frequencies are within the PBG.

Contribution

It introduces a fractional calculus approach to analyze non-Markovian entanglement dynamics in PBG environments, revealing conditions for entanglement trapping and decoherence prevention.

Findings

PBG environment prevents qubit decoherence with steady non-zero entropy.

Long-time entanglement preservation occurs in two-qubit systems within PBG.

Entanglement trapping does not occur when qubit frequency is outside the PBG.

Abstract

We study how the environment of photonic band gap (PBG) materials affects entanglement dynamics of qubits. Entanglement between the single qubit and the PBG environment is investigated through the von Neumann entropy while that for two initially entangled qubits in this PBG reservoir is through concurrence. Dynamics of these measurements are solved in use of the fractional calculus which has been shown appropriate for the systems with non-Markovian dynamics. Entropy dynamics of the single qubit system reveals that the coupling with the PBG reservoir prevents decoherence of the qubit through the steady entropy with non-zero value. The effect of PBG reservoir on the concurrence of the two-qubit system leads to the long-time entanglement preservation. The concurrence dynamics shows that unphysical entanglement trapping does not exist in the system with the qubit frequency lying outside the PBG region. Long-time memory effect of the PBG reservoir occurs only for the qubit frequency in the PBG region. Entanglement mechanisms resulting from this long-time memory effect are discussed.