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Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model

A. R. Vieira, de Oliveira Junior, J. G. G., Peixoto de Faria, J. G., Maria Carolina Nemes

Published Jan 1, 2014• 10 citations

Abstract

"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."

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"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."

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.

A double Tavis-Cummings model (DTCM) is developed to simulate the entanglement dynamics of realistic quantum information processing where two entangled atom-pairs AB and CD are distributed in such a way that atoms AC are embedded in a cavity a while BD are located in another remote cavity b .T he evolutions of different types of initially shared entanglement of atoms are studied under various initial states of cavity fields. The results obtained in the DTCM are compared with that obtained in the double Jaynes- Cummings model (DJCM) (M. Yonac, T. Yu, J.H. Eberly, J. Phys. B40, S45 (2007)) and an interaction strength theory is proposed to explain the parameter domain in which the so-called entanglement sudden death occurs for both the DTCM and DJCM.