Superradiant Mpemba Relaxation in a Dicke Ladder

Abstract

The Mpemba effect occurs when a state initially farther from stationarity overtakes a closer one during relaxation. We show that this anomalous ordering can coexist with superradiant emission in a collectively damped ensemble of two-level systems. In the symmetric Dicke manifold, zero-temperature decay is a population cascade with rates Γn(N−n+1). We construct the sparse family ρ_A=|⌈2N/3⌉⟩⟨⌈2N/3⌉| and ρ_B=(|0⟩⟨0|+|N⟩⟨ N|)/2. Although A is initially more energetic and more distant from the stationary ground state, it crosses B in both energy and trace distance because it starts in a more radiative region of the Dicke ladder. Both states develop emission peaks larger than their independent-emitter references. The crossing persists for all examined sizes from N=6 to $60$, while the peak intensities show an effective scaling close to N². The same pair has no crossing under independent decay, identifying collective radiative kinetics as the origin of the effect.

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BibTeX RIS

BibTeX

@misc{santos2026superradiant,
  title = {{Superradiant Mpemba Relaxation in a Dicke Ladder}},
  author = {Matheus G. H. Santos and Hugo Sanchez and Italo M. de Araújo and Luis Felipe A. da Silva and Miled H. Y. Moussa and Norton G. de Almeida},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25359},
  eprint = {2609.25359},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25359},
}

RIS

TY  - UNPB
TI  - Superradiant Mpemba Relaxation in a Dicke Ladder
AU  - Matheus G. H. Santos
AU  - Hugo Sanchez
AU  - Italo M. de Araújo
AU  - Luis Felipe A. da Silva
AU  - Miled H. Y. Moussa
AU  - Norton G. de Almeida
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25359
UR  - https://arxiv.org/abs/2609.25359
AB  - The Mpemba effect occurs when a state initially farther from stationarity overtakes a closer one during relaxation. We show that this anomalous ordering can coexist with superradiant emission in a collectively damped ensemble of two-level systems. In the symmetric Dicke manifold, zero-temperature decay is a population cascade with rates Γn(N−n+1). We construct the sparse family ρ_A=|⌈2N/3⌉⟩⟨⌈2N/3⌉| and ρ_B=(|0⟩⟨0|+|N⟩⟨ N|)/2. Although A is initially more energetic and more distant from the stationary ground state, it crosses B in both energy and trace distance because it starts in a more radiative region of the Dicke ladder. Both states develop emission peaks larger than their independent-emitter references. The crossing persists for all examined sizes from N=6 to $60$, while the peak intensities show an effective scaling close to N^2. The same pair has no crossing under independent decay, identifying collective radiative kinetics as the origin of the effect.
ER  -

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