pith. sign in

arxiv: 2604.21320 · v1 · submitted 2026-04-23 · 🪐 quant-ph

Observation of quantum multi-Mpemba effect in a trapped-ion system

Gang Xia , Yu-Jie Zheng , Jing Huang , Chun-Wang Wu , Yi Xie , Ting Chen , Wei Wu , Weibin Li
show 4 more authors
Hui Jing Jie Zhang Yan-Li Zhou Ping-Xing Chen
This is my paper

Pith reviewed 2026-05-09 22:13 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum Mpemba effecttrapped ionsrelaxation dynamicsdecay modestrajectory crossingsopen quantum systemsMarkovian evolution
0
0 comments X

The pith

Trapped ions exhibit multiple relaxation trajectory crossings even when the initial state overlaps more with the slowest decay mode.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that relaxation trajectories in a Markovian open quantum system can cross more than once in an unexpected case where the starting state has a larger overlap with the slowest decay mode. This multi-Mpemba effect arises because the earliest part of the relaxation is set by the fastest decaying components rather than the long-term behavior. By measuring the full time evolution in a trapped-ion experiment, the authors build a phase diagram from the initial speed and the slow-mode overlap to predict when crossings occur and what type they are. A sympathetic reader would care because this shows that quantum states can approach equilibrium through richer transient paths than the conventional long-time picture allows.

Core claim

We experimentally observe multiple trajectory crossings in the relaxation dynamics of a trapped ion even when the initial state instead has a larger overlap with the slowest decay mode. We develop a theoretical framework based on relaxation speed to understand this. The initial relaxation speed is governed by the fastest decay mode, which together with the slowest decay mode overlap gives a phase diagram that reveals both the occurrence and the types of the effect. This framework tracks the continuous quantum relaxation dynamics beyond the long-time limit.

What carries the argument

A phase diagram whose axes are the initial relaxation speed set by the fastest decay mode and the overlap with the slowest decay mode; it classifies when and how multiple trajectory crossings appear.

If this is right

  • Relaxation trajectories can cross repeatedly when the early fast changes outrun the slow final approach to the steady state.
  • Different kinds of the effect can be predicted and distinguished using only the initial speed and the slow-mode overlap.
  • The full time-dependent path, not merely the long-time limit, determines the observed crossings in Markovian systems.
  • Trapped-ion experiments can test the phase diagram by preparing states with chosen projections onto the decay modes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same two-parameter description could be used to engineer desired relaxation orders in other open quantum platforms with separated decay timescales.
  • Classical non-equilibrium systems with multiple relaxation rates might display analogous multiple crossings if prepared with comparable initial conditions.
  • Including additional decay modes in the diagram could forecast more intricate crossing sequences in higher-dimensional systems.
  • This view of transient speed might help estimate effective thermalization times in quantum devices where fast components dominate early dynamics.

Load-bearing premise

The system's time evolution is completely described by adding up independent exponential decays at fixed rates, without memory of past states or other interactions.

What would settle it

Direct measurements of the time-dependent distance to steady state in the trapped-ion system that show no multiple crossings for prepared initial states with large overlap to the slowest decay mode but high projection onto the fast mode would disprove the account.

Figures

Figures reproduced from arXiv: 2604.21320 by Chun-Wang Wu, Gang Xia, Hui Jing, Jie Zhang, Jing Huang, Ping-Xing Chen, Ting Chen, Weibin Li, Wei Wu, Yan-Li Zhou, Yi Xie, Yu-Jie Zheng.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Initial state dependent relaxation process. (b) The overlaps [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Eigenspectra of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a)-(d) Quantum ME. The distance [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase diagram of the ME and Multi ME. The distri [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The quantum Mpemba effect (ME) in Markovian systems is conventionally explained by a smaller overlap between the initial state and the slowest decay mode (SDM). Such state, initially farther away from equilibrium or steady state, relaxes faster than closer ones, resulting to a crossing of their trajectories. This picture, by neglecting the transient dynamics, holds in the long-time limit. Here we experimentally observe multiple trajectory crossings (multi-ME) in the relaxation dynamics of a trapped ion. Such novel dynamics takes place in a unusual scenario where the initial state instead has a larger overlap with the SDM. We develop a theoretical framework based on relaxation speed to understand the multi-ME. We show that the initial relaxation speed is governed by the fastest decay mode, which together with the SDM overlap gives a phase diagram that reveals both the occurrence and the types of quantum ME observed in our experiment. Our study goes beyond the simple picture based on the long-time limit, tracks continuously the quantum ME dynamics, and establishes a comprehensive framework to describe the transient quantum relaxation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an experimental observation of the quantum multi-Mpemba effect (multi-ME) in a trapped-ion system, featuring multiple trajectory crossings during relaxation. This occurs in the regime where the initial state has larger overlap with the slowest decay mode (SDM), contrary to the standard long-time picture. The authors introduce a framework in which initial relaxation speed is set by the fastest decay mode; combined with SDM overlap this yields a phase diagram that classifies the occurrence and type of ME.

Significance. If the observations and phase diagram are confirmed, the work is significant for extending Mpemba-effect analysis from the asymptotic regime to full transient dynamics in open quantum systems. The decay-mode decomposition with explicit initial-speed criterion supplies a predictive, falsifiable classification tool that is directly tested in a controllable trapped-ion platform.

major comments (2)
  1. [Experimental results] Experimental results section: the abstract and main text claim quantitative observation of multiple trajectory crossings and agreement with the derived phase diagram, yet no description of data processing, error analysis, or quantitative fitting procedures is supplied. This information is load-bearing for the central experimental claim.
  2. [Theoretical framework] Theoretical framework (phase-diagram construction): the statement that initial speed is governed exclusively by the fastest decay mode is used to delineate the multi-ME region, but the manuscript does not show an explicit check that higher-order transients do not alter the ordering of initial slopes for the prepared states.
minor comments (2)
  1. [Abstract] Abstract: 'resulting to a crossing' should read 'resulting in a crossing'.
  2. [Abstract] Abstract: 'a unusual scenario' should read 'an unusual scenario'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the positive assessment of its significance. The comments highlight important points that will improve the clarity and rigor of the presentation. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: Experimental results section: the abstract and main text claim quantitative observation of multiple trajectory crossings and agreement with the derived phase diagram, yet no description of data processing, error analysis, or quantitative fitting procedures is supplied. This information is load-bearing for the central experimental claim.

    Authors: We agree that explicit details on data processing, error analysis, and quantitative fitting are necessary to substantiate the experimental claims. In the revised manuscript we will insert a new subsection (or expanded paragraph) in the Experimental Results section that describes the raw data acquisition from ion fluorescence, the post-processing steps to obtain the relaxation trajectories, the statistical error estimation from repeated experimental runs, systematic uncertainties, and the quantitative procedures used to identify trajectory crossings and compare them with the theoretical phase diagram. revision: yes

  2. Referee: Theoretical framework (phase-diagram construction): the statement that initial speed is governed exclusively by the fastest decay mode is used to delineate the multi-ME region, but the manuscript does not show an explicit check that higher-order transients do not alter the ordering of initial slopes for the prepared states.

    Authors: We acknowledge the value of an explicit verification. In the revised manuscript we will add a short analytical argument together with a supplementary numerical check showing that, for the specific initial states realized in the trapped-ion experiment, the ordering of the initial relaxation speeds (i.e., the sign of the time derivative of the distance to the steady state at t = 0+) remains unchanged when higher-order decay modes are included. This will be presented either as an additional panel in the main text or as a supplementary figure. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central framework decomposes the Markovian dynamics into a linear combination of exponential modes from the Liouvillian spectrum, a standard result in open quantum systems. The statement that initial relaxation speed is governed by the fastest mode follows from the short-time Taylor expansion of the observable expectation value without redefining any quantity in terms of the multi-ME crossings themselves. The phase diagram is then assembled from independently computed overlaps and rates; it does not reduce to a fit or self-citation by construction. Experimental observation of multiple trajectory crossings supplies independent evidence outside the theoretical construction. No load-bearing step collapses to its own input.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard open-quantum-system assumptions; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The system obeys Markovian dynamics described by a Lindblad master equation
    Explicitly stated as applying to Markovian systems.
  • standard math Relaxation trajectories are linear combinations of exponential decay modes with distinct rates
    Implicit in the use of slowest and fastest decay modes.

pith-pipeline@v0.9.0 · 5512 in / 1316 out tokens · 54369 ms · 2026-05-09T22:13:13.513620+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages

  1. [1]

    G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja, Speedups in nonequilibrium thermal relax- ation: Mpemba and related effects, Physics Reports 1164, 1 (2026)

    work page 2026

  2. [2]

    F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba effects, Nature Reviews Physics7, 451 (2025)

    work page 2025

  3. [3]

    I. G.-A. Pemart´ ın, E. Momp´ o, A. Lasanta, V. Mart´ ın- Mayor, and J. Salas, Shortcuts of freely relaxing systems using equilibrium physical observables, Phys. Rev. Lett. 132, 117102 (2024)

    work page 2024

  4. [4]

    Seifert, Stochastic thermodynamics, fluctuation the- orems and molecular machines, Reports on Progress in Physics75, 126001 (2012)

    U. Seifert, Stochastic thermodynamics, fluctuation the- orems and molecular machines, Reports on Progress in Physics75, 126001 (2012)

    work page 2012

  5. [5]

    Gong and R

    Z. Gong and R. Hamazaki, Bounds in nonequilibrium quantum dynamics, International Journal of Modern Physics B36, 2230007 (2022)

    work page 2022

  6. [6]

    Beato and G

    N. Beato and G. Teza, Relaxation control of open quan- tum systems, Phys. Rev. Lett.136, 070401 (2026)

    work page 2026

  7. [7]

    Bao and Z

    R. Bao and Z. Hou, Accelerating quantum relaxation via temporary reset: A Mpemba-inspired approach, Phys. Rev. Lett.135, 150403 (2025)

    work page 2025

  8. [8]

    J.-Y. Sun, K. Xu, and Z.-D. Li, Quantum speedup dy- namics process in multiqubit-interacting system, Phys. Rev. Research6, 013317 (2024)

    work page 2024

  9. [9]

    E. B. Mpemba and D. G. Osborne, Cool?, Physics Edu- cation4, 172 (1969)

    work page 1969

  10. [10]

    Bechhoefer, A

    J. Bechhoefer, A. Kumar, and R. Ch´ etrite, A fresh un- derstanding of the Mpemba effect, Nat. Rev. Phys.3, 534 (2021)

    work page 2021

  11. [11]

    Lasanta, F

    A. Lasanta, F. Vega Reyes, A. Prados, and A. Santos, When the hotter cools more quickly: Mpemba effect in granular fluids, Phys. Rev. Lett.119, 148001 (2017)

    work page 2017

  12. [12]

    Lu and O

    Z. Lu and O. Raz, Nonequilibrium thermodynamics of the markovian Mpemba effect and its inverse, Proc. Natl. Acad. Sci.114, 5083 (2017)

    work page 2017

  13. [13]

    Klich, O

    I. Klich, O. Raz, O. Hirschberg, and M. Vucelja, Mpemba index and anomalous relaxation, Phys. Rev. X9, 021060 (2019)

    work page 2019

  14. [14]

    Kumar, H

    S. Kumar, H. Fan, H. K¨ ubler, A. J. Jahangiri, and J. P. Shaffer, Rydberg-atom based radio-frequency electrom- etry using frequency modulation spectroscopy in room temperature vapor cells, Optics Express25, 8625–8637 (2017)

    work page 2017

  15. [15]

    Yang and J.-X

    Z.-Y. Yang and J.-X. Hou, Non-markovian Mpemba ef- fect in mean-field systems, Phys. Rev. E101, 052106 (2020)

    work page 2020

  16. [16]

    Zhang and J.-X

    S. Zhang and J.-X. Hou, Theoretical model for the Mpemba effect through the canonical first-order phase transition, Phys. Rev. E106, 034131 (2022)

    work page 2022

  17. [17]

    Biswas, V

    A. Biswas, V. V. Prasad, and R. Rajesh, Mpemba ef- fect in driven granular gases: Role of distance measures, Phys. Rev. E108, 024902 (2023)

    work page 2023

  18. [18]

    G. Teza, R. Yaacoby, and O. Raz, Relaxation short- cuts through boundary coupling, Phys. Rev. Lett.131, 017101 (2023)

    work page 2023

  19. [19]

    Nava and R

    A. Nava and R. Egger, Pontus-Mpemba effects, Physical Review Letters135, 140404 (2025)

    work page 2025

  20. [20]

    Van Vu and H

    T. Van Vu and H. Hayakawa, Thermomajorization Mpemba effect, Phys. Rev. Lett.134, 107101 (2025)

    work page 2025

  21. [21]

    Macieszczak, M

    K. Macieszczak, M. Gut ¸˘ a, I. Lesanovsky, and J. P. Garra- han, Towards a theory of metastability in open quantum dynamics, Phys. Rev. Lett.116, 240404 (2016)

    work page 2016

  22. [22]

    D. C. Rose, K. Macieszczak, I. Lesanovsky, and J. P. Gar- 6 rahan, Metastability in an open quantum ising model, Phys. Rev. E94, 052132 (2016)

    work page 2016

  23. [23]

    Ivander, N

    F. Ivander, N. Anto-Sztrikacs, and D. Segal, Hyperaccel- eration of quantum thermalization dynamics by bypass- ing long-lived coherences: An analytical treatment, Phys. Rev. E108, 014130 (2023)

    work page 2023

  24. [24]

    Minganti, A

    F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of Liouvillians for dissipative phase transitions, Phys. Rev. A98, 042118 (2018)

    work page 2018

  25. [25]

    Macieszczak, Y.-L

    K. Macieszczak, Y.-L. Zhou, S. Hofferberth, J. P. Garra- han, W. Li, and I. Lesanovsky, Metastable decoherence- free subspaces and electromagnetically induced trans- parency in interacting many-body systems, Phys. Rev. A96, 043860 (2017)

    work page 2017

  26. [26]

    Carollo, A

    F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially accelerated approach to stationarity in markovian open quantum systems through the Mpemba effect, Phys. Rev. Lett.127, 060401 (2021)

    work page 2021

  27. [27]

    Kochsiek, F

    S. Kochsiek, F. Carollo, and I. Lesanovsky, Accelerat- ing the approach of dissipative quantum spin systems towards stationarity through global spin rotations, Phys. Rev. A106, 012207 (2022)

    work page 2022

  28. [28]

    A. K. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba effect in a quantum dot with reservoirs, Phys. Rev. Lett.131, 080402 (2023)

    work page 2023

  29. [29]

    Nava and R

    A. Nava and R. Egger, Mpemba effects in open nonequi- librium quantum systems, Phys. Rev. Lett.133, 136302 (2024)

    work page 2024

  30. [30]

    Longhi, Quantum Pontus-Mpemba effect enabled by the liouvillian skin effect (2026), arXiv:2601.14083 [quant-ph]

    S. Longhi, Quantum Pontus-Mpemba effect enabled by the liouvillian skin effect (2026), arXiv:2601.14083 [quant-ph]

    work page arXiv 2026

  31. [31]

    Zhang, G

    J. Zhang, G. Xia, C.-W. Wu, T. Chen, Q. Zhang, Y. Xie, W.-B. Su, W. Wu, C.-W. Qiu, P.-X. Chen, W. Li, H. Jing, and Y.-L. Zhou, Observation of quantum strong Mpemba effect, Nature Communications16, 301 (2025)

    work page 2025

  32. [32]

    Kumar, K

    P. Kumar, K. Snizhko, Y. Gefen, and B. Rosenow, Op- timized steering: Quantum state engineering and excep- tional points, Phys. Rev. A105, L010203 (2022)

    work page 2022

  33. [33]

    F. Ares, S. Murciano, and P. Calabrese, Entanglement asymmetry as a probe of symmetry breaking, Nat. Com- mun.14, 2036 (2023)

    work page 2036

  34. [34]

    Rylands, K

    C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Mur- ciano, and B. Bertini, Microscopic origin of the quantum Mpemba effect in integrable systems, Phys. Rev. Lett. 133, 010401 (2024)

    work page 2024

  35. [35]

    Kumar and J

    A. Kumar and J. Bechhoefer, Exponentially faster cool- ing in a colloidal system, Nature584, 64 (2020)

    work page 2020

  36. [36]

    Ib´ a˜ nez, C

    M. Ib´ a˜ nez, C. Dieball, A. Lasanta, A. Godec, and R. A. Rica, Heating and cooling are fundamentally asymmetric and evolve along distinct pathways, Nature Physics20, 135–141 (2024)

    work page 2024

  37. [37]

    Y. Tian, Y. Zheng, L.-H. Liu, L. Wang, G.-C. Guo, and F.-W. Sun, Experimental study of Mpemba effect in an energy langevin system, Phys. Rev. Res.7, L042020 (2025)

    work page 2025

  38. [38]

    Aharony Shapira, Y

    S. Aharony Shapira, Y. Shapira, J. Markov, G. Teza, N. Akerman, O. Raz, and R. Ozeri, Inverse Mpemba ef- fect demonstrated on a single trapped ion qubit, Phys. Rev. Lett.133, 010403 (2024)

    work page 2024

  39. [39]

    L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Cal- abrese, C. F. Roos, and M. K. Joshi, Observing the quan- tum Mpemba effect in quantum simulations, Phys. Rev. Lett.133, 010402 (2024)

    work page 2024

  40. [40]

    B. P. Schnepper, J. L. D. de Oliveira, C. H. S. Vieira, K. Zawadzki, and R. M. Serra, Experimental observation and application of the genuine quantum Mpemba effect (2025), arXiv:2511.14552 [quant-ph]

    work page arXiv 2025

  41. [41]

    Chalas, F

    K. Chalas, F. Ares, C. Rylands, and P. Calabrese, Multi- ple crossings during dynamical symmetry restoration and implications for the quantum Mpemba effect, Journal of Statistical Mechanics: Theory and Experiment2024, 103101 (2024)

    work page 2024

  42. [42]

    Zhang, C

    X. Zhang, C. Sun, and F. Li, Engineering quan- tum Mpemba effect by liouvillian skin effect, (2026), arXiv:2601.16002 [quant-ph]

    work page arXiv 2026

  43. [43]

    Deffner, Geometric quantum speed limits: a case for wigner phase space, New J

    S. Deffner, Geometric quantum speed limits: a case for wigner phase space, New J. Phys.19, 103018 (2017)

    work page 2017

  44. [44]

    Deffner and S

    S. Deffner and S. Campbell, Quantum speed limits: from heisenberg’s uncertainty principle to optimal quantum control, Journal of Physics A: Mathematical and The- oretical50, 453001 (2017)

    work page 2017

  45. [45]

    Minganti, A

    F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians : The effects of quantum jumps, Phys. Rev. A100, 062131 (2019)

    work page 2019

  46. [46]

    Gaidash, A

    A. Gaidash, A. D. Kiselev, A. Kozubov, and G. Mirosh- nichenko, Lindblad dynamics of open multimode bosonic systems: Algebra of quadratic superoperators, excep- tional points, and speed of evolution, Phys. Rev. A111, 062211 (2025)

    work page 2025

  47. [47]

    D. P. Pires, M. Cianciaruso, L. C. C´ eleri, G. Adesso, and D. O. Soares-Pinto, Generalized geometric quantum speed limits, Phys. Rev. X6, 021031 (2016)

    work page 2016

  48. [48]

    Deffner and E

    S. Deffner and E. Lutz, Quantum speed limit for non- markovian dynamics, Phys. Rev. Lett.111, 010402 (2013)

    work page 2013

  49. [49]

    del Campo, I

    A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, Quantum speed limits in open system dynamics, Phys. Rev. Lett.110, 050403 (2013)

    work page 2013

  50. [50]

    Z. Sun, J. Liu, J. Ma, and X. Wang, Quantum speed lim- its in open systems: Non-markovian dynamics without rotating-wave approximation, Sci. Rep.5, 8444 (2015)

    work page 2015

  51. [51]

    M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho, Quantum speed limit for physical pro- cesses, Phys. Rev. Lett.110, 050402 (2013)

    work page 2013

  52. [52]

    A. K. Chatterjee, S. Takada, and H. Hayakawa, Multiple quantum Mpemba effect: Exceptional points and oscilla- tions, Phys. Rev. A110, 022213 (2024)

    work page 2024

  53. [53]

    M. A. Nielsen and I. L. Chuang, Quantum computa- tion and quantum information (10th anniversary edition) (Oxford University Press, 2011)

    work page 2011

  54. [54]

    Ringbauer, M

    M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, A universal qudit quantum processor with trapped ions, Nat. Phys.18, 1053–1057 (2022)

    work page 2022

  55. [55]

    D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta, Efficient Z gates for quantum comput- ing, Phys. Rev. A96, 022330 (2017)

    work page 2017

  56. [56]

    R. T. Thew, K. Nemoto, A. G. White, and W. J. Munro, Qudit quantum-state tomography, Phys. Rev. A66, 012303 (2002)

    work page 2002

  57. [57]

    M. Qin, Z. Li, Y. Wang, Y. Chen, Z. Wang, G. Chen, X. Zhou, P. Wang, Z. Bian, J. Zhang, K. Xu, and T. Li, Self-testing of a single quantum system from theory to experiment, npj Quantum Information9, 103 (2023). 7 Supplemental Material for ”Observation of quantum multi-Mpemba effect in a trapped-ion system” I. Distance and the derivation of bound We define...

    work page 2023