arXiv:0706.3813 · Physical Review A

Entanglement invariant for the double Jaynes-Cummings model

Isabel Sainz, Gunnar G. Bjork

Published Oct 8, 2007• 110 citations

Abstract

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.

DOI: 10.1103/physreva.76.042313

Related papers

Time evolution and transfer of entanglement between an isolated atom and a Jaynes–Cummings atom

Zhi-Jian Li, Jun‐Qi Li, Yan-Hong Jin +1 more

We investigate the entanglement dynamics of two space-separated atoms, one of them in Jaynes–Cummings cavity and the other isolated completely. We show analytically that initial entanglement has an interesting subsequent time evolution and transfer, including the so-called sudden death effect. A little inconsistency of concurrence and negativity is indicated qualitatively to measure the two-qubit states.

Journal of Physics B Atomic Molecular and Optical PhysicsAug 21, 200744 citations

A NEW FEATURE ON THE SUDDEN DEATH OF ENTANGLEMENT

Xue‐Qun Yan

Based on the exactly analytic solution obtained of the intensity-dependent Jaynes–Cummings model for a certain class of initial entangled mixed states, we explore the time evolution of the entanglement between two atoms, initially non-locally correlated and separately interacting with two distinct cavities. The results show that entanglement sudden death is dependent on the different initial states of atoms, and the length of the time interval for the zero entanglement is invariant for a certain class of initial mixed states.

Modern Physics Letters BOct 10, 20081 citation

Entanglement evolution of two remote and non-identical Jaynes–Cummings atoms

Stanley Chan, M. D. Reid, Z. Ficek

A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.

arXiv:0810.3050Journal of Physics B Atomic Molecular and Optical PhysicsMar 9, 200962 citations

Sudden death of entanglement of two Jaynes–Cummings atoms

Muhammed Yönaç, Ting Yu, Joseph H. Eberly

We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes–Cummings cavity. We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect.

arXiv:quant-ph/0602206Journal of Physics B Atomic Molecular and Optical PhysicsJul 24, 2006320 citations

On entanglement invariant for a double Jaynes–Cummings model

Man Zhong-Xiao, Yun‐Jie Xia

In a recent paper [ Phys. Rev. A 76 042313 (2007)], Sainz and Bjork introduced an entanglement invariant E under evolution for a system of four qubits interacting through two isolated Jaynes–Cummings Hamiltonians. This paper proves that this entanglement invariant E is closely connected with the linear entropy between two independent subsystems.

Chinese Physics BDec 1, 20082 citations

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. +1 more

"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."

Jan 1, 201410 citations