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arXiv:1206.1171 · AIP conference proceedings

Entanglement dynamics of double Jaynes-Cummings interaction model based on geometric invariants

Hoshang Heydari

Published Jan 1, 2012• 1 citation
arXivHTMLPDF

Abstract

We investigate entanglement dynamics and properties of double Jaynes-Cummings model. In particular we study the dynamics of double Jaynes-Cummings model based on geometric invariants for four qubits. We show that these geometric invariants provide us with useful information about different types of entanglement during the quantum evolution of the system.

DOI
10.1063/1.4773154

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We investigate entanglement dynamics and properties of double Jaynes-Cummings model. In particular we study the dynamics of double Jaynes-Cummings model based on geometric invariants for four qubits. We show that these geometric invariants provide us with useful information about different types of entanglement during the quantum evolution of the system.
We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings Hamiltonians, via an entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as ``entanglement sudden death.'' We find a natural entanglement invariant under evolution, demonstrating that entanglement spreads out over all of the system's degrees of freedom that become entangled through the interaction. We also provide an analysis of why certain initial states lose all their entanglement in a finite time, although their excitation and coherence vanish only asymptotically with time.
Abstract In this paper, we investigate the dynamics and transfer of multipartite entanglement via concurrence and three-tangle in a double and a triple Tavis–Cummings model (TCM). The results are compared with those of the double and triple Jaynes–Cummings model (JCM). We find that the dynamics and transfer of multipartite entanglement are dependent only on the initial entanglement type itself and not on model type for the double and triple TCM. For the triple TCM and the triple JCM we find that entanglement of a different type from the initial entanglement is created. Our work will further enrich the previous results for the JCM and the TCM.
"We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ 0 ?= cos α | 10 ?+ sin α | 01 and | φ 0 ?= cos α | 11 ?+ sin α | 00 cover three-dimensional surfaces in the diagram C ij × C ik × C il , where C mn stands for the concurrence between qubits m and n , varying 0 ≤ α ≤ π/ 2. In the first case, projections of the surfaces on a diagram C ij × C kl are conics. In the second case, curves can be more complex. We relate those con- ics with a measurable quantity, the predictability .Wealso 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 average radius of a hypersphere."