Entanglement of Two Distinguishable Atoms in a Rectangular Waveguide: Linear Approximation with Single Excitation

TL;DR

This paper models the entanglement dynamics of two distinguishable two-level atoms in a rectangular waveguide, deriving delay-differential equations to analyze how their energy differences and separation affect quantum entanglement over time.

Contribution

It introduces a linear approximation approach with single excitation to describe entanglement in two TLSs within a waveguide, including the derivation of coupled delay-differential equations.

Findings

Entanglement dynamics depend on inter-atom distance and energy differences.

Delay-differential equations effectively model the system's evolution.

Energy separation far from cutoff frequencies simplifies the analysis.

Abstract

We consider two two-level systems (TLSs) coupled to the vacuum of guided modes confined in a rectangular waveguide. Two TLSs are fixed at different points in the waveguide and initially share an excitation. For the energy separation of the TLSs far away from the cutoff frequencies of transverse modes, two coupled delay-differential equations are obtained for the probability amplitudes of the TLSs. The effects of the difference of TLSs' energy separations and the inter-TLS distance on the time evolution of the concurrence of the TLSs are examined.