REVIEW
Sudden Death of Entanglement of Two Jaynes-Cummings Atoms
Quantum Physics · Submitted 24 Feb 2006 · 17 references
Pith's verdict: A clean, correct analytic demonstration that entanglement sudden death can occur in lossless, closed cavity-QED systems once the cavity modes are traced out; the main blemishes are a typo in Eq. (17) and an overbroad priority claim.
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Referee report
The paper
The paper claims
Two atoms in separate lossless cavities can undergo entanglement sudden death and revival.
The reading
What carries the argument
The machinery is the double Jaynes-Cummings Hamiltonian $$H_{\rm tot}=\omega\sigma_z^A+\omega\sigma_z^B+g(a^\dagger\sigma_-^A+a\sigma_+^A)+g(b^\dagger\sigma_-^B+b\sigma_+^B)+\nu a^\dagger a+\nu b^\dagger b,$$ with each atom coupled only to its own cavity mode and no coupling between the two subsystems. The dressed eigenstates of the individual Jaynes-Cummings systems, combined with Wootters concurrence, carry the argument. Tracing out both cavity modes produces a reduced two-atom density matrix in the 'standard form' whose concurrence can be computed in closed form. The factorization of $f(t)$ into an atom-field information-exchange factor and a factor depending on the initial entanglement is what produces both the abrupt zero and the revival.
Extended reading notes
Core claim
The paper's central claim is that for an initial atomic Bell state of the form $\cos\alpha|\uparrow\uparrow\rangle+\sin\alpha|\downarrow\downarrow\rangle$, the concurrence of the two atoms is $$C_{AB}(t)=\max\{0,f(t)\}, \qquad f(t)=\bigl(1-$4N^{2}$\$sin^{2}$(\delta t/2)\bigr)\bigl(|\sin 2\$\alpha$|-$8N^{2}$\$sin^{2}$(\delta t/2)\$cos^{2}$\$\alpha$\bigr).$$ For small enough $\alpha$ the function $f(t)$ is negative over a finite time interval, so the atoms' entanglement vanishes abruptly, stays zero, and then revives periodically with the Rabi frequency of the Jaynes-Cummings interaction. This is presented as the first instance of entanglement sudden death without traditional decoherence, because the cavities are lossless. For the other Bell-type initial state $\cos\alpha|\uparrow\downarrow\rangle+\sin\alpha|\downarrow\uparrow\rangle$ the concurrence is $|\sin 2\alpha|[1-4N^2\sin^2(\delta t/2)]$ and never stays at zero, so sudden death depends on the symmetry of the initial entangled state.
Load-bearing premise
The argument depends on treating the two cavity modes as unobserved and averaging over them; if the cavities were measured instead, the total pure state would remain fully entangled and the unitary dynamics would conserve entanglement.
Editorial extensions
If this is right
- Entanglement sudden death is not tied to a noisy or dissipative environment; a closed lossless system with finite local Hilbert spaces can produce it.
- The dead interval lengthens as the initial entanglement decreases, and entanglement revives periodically because the lossless cavities act as finite memories that return the lost information.
- The effect is state-dependent: initial states of the $|\Psi\rangle$-type never exhibit a finite dead interval, while $|\Phi\rangle$-type states do.
- Since the cavities never exchange photons, the revivals are a local memory effect of each atom's own cavity, not a communication between atoms.
Reading between the lines
- The same 'sudden death by partial trace' mechanism should appear in any bipartite system coupled to finite local ancillas, so the result likely generalizes beyond atom-cavity systems to trapped ions, superconducting qubits, or photon pairs.
- The relation between the zero interval and the initial entanglement suggests a quantitative diagnostic: the dead time could be used to infer the initial entanglement when direct preparation is imperfect.
- One could test the memory interpretation by varying detuning $\Delta$: the revival period is set by $\delta=\sqrt{\Delta^2+G^2}$, so detuning should stretch both the oscillation and the dead interval.
Original abstract
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.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes-Cummings cavity. | contribution 0.91 | 0.70 | 0.04 | asserted 0.72 |
| s1 | We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect. | result 0.95 | 0.94 | 0.80 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
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- relations to other papers
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Figures
Showing 1 of the paper's 3 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:quant-ph/0602206 by the authors.
References
How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
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On the other hand, many efforts have been devoted to the study of the evolution of the joint system formed by two qubits [ref] .
Controlling entanglement sudden death in cavity QED by classical driving fields · INTRODUCTION · 0.99
Discussion
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