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Effects of cavity-field statistics on atomic entanglement in the Jaynes-Cummings model

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Biplab Ghosh, A. S. Majumdar, N. Nayak

Quantum Physics · Submitted 6 Mar 2006 · 17 references

Pith's verdict: Clean, modest calculation of two-atom entanglement in sequential Jaynes-Cummings dynamics; derivations hold up, but the high-mean-photon thermal claim is asserted, not shown.

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arXiv IDquant-ph/0603039 (version 2)
Pith IDCP6H6YIJ, Pith's permanent record of this paper and its review
CitationA. S. Majumdar, Biplab Ghosh, N. Nayak. "Effects of cavity-field statistics on atomic entanglement in the Jaynes-Cummings model." arXiv:quant-ph/0603039 (2006). https://pith.science/paper/CP6H6YIJ
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The paper

The paper claims

Fewer cavity photons yield stronger atomic entanglement in a sequential Jaynes-Cummings setup

The reading

This paper claims that when two two-level atoms pass through a cavity one after the other, interacting with the same photon field through the Jaynes-Cummings interaction, the statistics of the cavity field determine how much the two atoms become entangled. Concretely, for both a Fock-state field and a thermal field, the entanglement of formation of the final two-atom state falls as the average photon number rises in the low-photon regime. The paper also establishes a sharp contrast with the Tavis-Cummings model: while simultaneous interaction of two excited atoms with a Fock-state cavity field produces no two-atom entanglement, the sequential Jaynes-Cummings dynamics always produces some entanglement, even for the vacuum. These results show how a realistic micromaser-type device can entangle distant atomic qubits without direct atom-atom interaction.

What carries the argument

The central object is the Jaynes-Cummings interaction Hamiltonian $H_I = g(\sigma_+ a + \sigma_- a^\dagger)$ in the rotating-wave approximation, which generates Rabi oscillations with frequency $\sqrt{n+1}gt$ for each photon number $n$. After both atoms pass through the cavity, the joint atom-atom-field state is a superposition of four terms (Eq. 11) whose coefficients $\alpha_i$ depend on these Rabi frequencies. Tracing out the field yields the reduced two-atom density matrix, and the entanglement of formation is computed from its concurrence (Eqs. 7 and 8). This machinery turns the photon statistics of the cavity field into a concrete number for the two-atom entanglement.

Extended reading notes

Core claim

For a lossless cavity (Q = ∞), the reduced two-atom state after their sequential passages is a mixed entangled state. For a Fock-state cavity field in state $|n\rangle$, the joint atom-field state evolves by Jaynes-Cummings dynamics, and the atom-atom entanglement of formation $E_F$ plotted against the Rabi angle $gt$ shows peaks that decrease sharply as $n$ grows from 0 to 100. For a thermal field, the entanglement is computed by averaging over the Bose-Einstein photon distribution; it also decreases with increasing mean photon number, so that a high-mean-photon thermal field loses its ability to entangle atomic qubits. The qualitative difference between field statistics is most pronounced at low $n$: a Fock state with small $n$ yields larger entanglement, reflecting its non-classical character.

Load-bearing premise

The calculation assumes a perfectly lossless cavity (Q = ∞), so that the field modification created by the first atom survives unchanged until the second atom passes through, and any photon decay between the two passages would reduce the predicted entanglement.

Editorial extensions

If this is right

  • The sequential micromaser scheme can entangle two atomic qubits that never interact directly, starting from a completely unentangled initial state, even if the cavity initially contains a Fock state with zero photons.
  • The amount of entanglement is tunable in practice by choosing the interaction time (the Rabi angle $gt$), so the protocol can produce a desired level of mixed-state entanglement.
  • The contrast with the Tavis-Cummings case shows that the order of many-atom passages matters: for Fock fields, sequential interaction creates entanglement where simultaneous interaction creates none.
  • For thermal fields, the entanglement decreases with the mean photon number, meaning that low-temperature cavities are needed to preserve atomic entanglement in this scheme.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same analysis would apply to a coherent-state cavity field (Poisson statistics), and the framework suggests its entanglement would lie between the Fock and thermal curves; this is a testable extension the paper does not calculate.
  • A real cavity with finite Q adds photon loss between the two passages, so the paper's predictions function as upper bounds on the attainable entanglement and on the useful interaction time before the field decoheres.
  • Because the reduced two-atom state in the Fock case contains a single off-diagonal coherence, the entanglement of formation is essentially set by the product $\alpha_2\alpha_3$, so two population measurements could be enough to infer the entanglement experimentally.
Original abstract

We study the entanglement properties of a pair of two-level atoms going through a cavity one after another. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity photon field result in the final two-atom state being of a mixed entangled type. We consider the field statistics of the Fock state field, and the thermal field, respectively, inside the cavity. The entanglement of formation of the joint two-atom state is calculated for both these cases as a function of the Rabi-angle $gt$. We present a comparitive study of two-atom entanglement for low and high mean photon number cases corresponding to the different fields statistics.

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.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,827 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.30 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.34 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the entanglement properties of a pair of two-level atoms going through a cavity one after another. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity photon field result in the final two-atom state being of a mixed entangled type. We consider the field statistics of the Fock state field, and the thermal field, respectively, inside the cavity. The entanglement of formation of the joint two-atom state is calculated for both these cases as a function of the Rabi-angle $gt$. We present a comparitive study of two-atom entanglement for low and high mean photon number cases corresponding to the different fields statistics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the entanglement properties of a pair of two-level atoms going through a cavity one after another. contribution 0.95 0.87 0.03 asserted 0.89
s1 The initial joint state of two successive atoms that enter the cavity is unentangled. method 0.71 0.35 0.03 asserted 1.00
s2 Interactions mediated by the cavity photon field result in the final two-atom state being of a mixed entangled type. result 1.00 0.78 0.57 asserted 1.00
s3 We consider the field statistics of the Fock state field, and the thermal field, respectively, inside the cavity. method 0.81 0.74 0.03 asserted 0.73
s4 The entanglement of formation of the joint two-atom state is calculated for both these cases as a function of the Rabi-angle $gt$. method 0.83 0.95 0.09 asserted 0.99
s5 We present a comparitive study of two-atom entanglement for low and high mean photon number cases corresponding to the different fields statistics. contribution 0.95 0.90 0.17 asserted 0.86

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from simulation or computation 0.55.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Two atoms prepared in excited states are pass through a
Figure 2. Atom-atom entanglement versus gt. Solid line, dotted line, and dashed line indicate EF between two atoms when the cavity fock states are n = 0, n = 10, and n = 100 respectively. The peaks of the entanglement of formation are reflective of the photon statistics that are typical in micromaser dynamics[14]. We see that EF falls off sharply as n increases. The non-classical character of the field for small values of the average photon number n, is reflected in larger entanglement between the two atoms. An interesting comparison can be made with the 6
Figure 3. Atom-atom entanglement of formation mediated by the th

Figures reproduced from arXiv:quant-ph/0603039 by the authors.

References

Discussion

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