Geometry in the entanglement dynamics of the double Jaynes-Cummings model

TL;DR

This paper explores the geometric structure of entanglement dynamics in the double Jaynes-Cummings model, revealing how entanglement evolves on 3D surfaces and relating conic projections to measurable predictability.

Contribution

It introduces a geometric perspective on entanglement evolution, characterizes the surfaces in concurrence space, and links conic projections to predictability, advancing understanding of entanglement behavior.

Findings

Entanglement dynamics form 3D surfaces in concurrence space.

Projections of these surfaces are conics related to predictability.

Sudden death of entanglement is connected to the radius of a hyper-sphere.

Abstract

We report on the geometric character of the entanglement dynamics of to pairs of qubits evolving according to the double Jaynes-Cummings model. We show that the entanglement dynamics for the initial states |{\psi}_0> = Cos{\alpha} |1 0> + Sin{\alpha} |0 1> and |{\phi}_0> = Cos{\alpha} |1 1> + Sin{\alpha} |0 0> cover 3-dimensional surfaces in the diagram C_ij\timesC_ik\timesC_il, where C_mn stands for the concurrence between the qubits m and n, varying 0\leq{\alpha}\leq{\pi}/2. In the first case projections of the surfaces on a diagram C_ij\timesC_kl are conics. In the second case the curves can be more complex. We relate those conics with a measurable quantity, the {\it predictability}.We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the radius of a hyper-sphere.