pith. sign in

arxiv: 2510.26351 · v4 · submitted 2025-10-30 · 🪐 quant-ph · cond-mat.quant-gas

Quantum dynamics of spin-J particles in static and rotating magnetic fields: Entanglement resonances and kinks

Nargis Sultana , Siddharth Seetharaman , Rejish Nath This is my paper

Pith reviewed 2026-05-18 03:20 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gas
keywords quantum spin dynamicsresonance conditionsentanglementkinksmagnetic fieldsdipole-dipole interactionspin-J particlesqudit technologies
0
0 comments X

The pith

Resonant periodic oscillations between two maximally stretched states occur for any spin J in static and rotating magnetic fields.

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

This paper examines the quantum dynamics of single spin-J particles and pairs of them under static and rotating magnetic fields. It establishes resonant conditions that produce periodic oscillations between the two maximally stretched states regardless of the value of J. The work also identifies periodic transitions between magnetic sublevels of opposite signs and a periodic transfer of population from the initial ground state to the stretched state. For two spins the dipole-dipole interaction generates entanglement whose time evolution displays resonances and kinks; the locations of these features follow directly from the energy spectrum, so that the kink itself becomes a controllable handle for shaping the entanglement.

Core claim

Resonant, periodic oscillations between two maximally stretched states occur irrespective of the value of J. Periodic transitions between sublevels with magnetic quantum numbers of opposite signs are observed, together with periodic transfer of the spin to the maximally stretched state starting from the ground state of the initial Hamiltonian. For a pair of spins various resonance conditions are derived, and for two spin-1/2 particles the entanglement dynamics reveal resonances and kinks in the maximum entanglement whose criteria are obtained from the energy spectrum, allowing the kink to be exploited to engineer the entanglement dynamics.

What carries the argument

Resonance conditions extracted from the energy spectrum of the Hamiltonian that contains Zeeman terms for the static and rotating fields plus the dipole-dipole interaction.

If this is right

  • Resonant oscillations between maximally stretched states hold for arbitrary J.
  • Periodic transfer of population to the stretched state occurs from the initial ground state.
  • Entanglement resonances and kinks appear in the dynamics of two spin-1/2 particles, with locations fixed by the energy spectrum.
  • The kink provides a direct means to engineer the time evolution of entanglement.
  • The same framework applies in the weak dipolar-interaction regime relevant to dipolar Bose-Einstein condensates.

Where Pith is reading between the lines

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

  • The J-independent resonance may support robust control protocols for qudit-based quantum technologies.
  • The energy-spectrum criterion for kinks could be tested in systems with more than two spins or with additional field gradients.
  • Atomic-physics experiments with controllable rotating fields could directly observe the predicted kink-based entanglement engineering.
  • In the weak-interaction limit the resonance structure may connect to collective spin dynamics in spinor condensates.

Load-bearing premise

The system evolves coherently under a Hamiltonian limited to Zeeman and dipole-dipole terms, with no decoherence or additional interactions present.

What would settle it

Time-resolved measurement of the m = J and m = -J populations for a spin-1 particle in a rotating field at the predicted resonance frequencies that fails to show periodic oscillations between those two states would falsify the central resonance result.

Figures

Figures reproduced from arXiv: 2510.26351 by Nargis Sultana, Rejish Nath, Siddharth Seetharaman.

Figure 1
Figure 1. Figure 1: (a) (Smin) 1/2J as a function of Ω/ωz and B⊥/Bz. (b) shows maximum population attained in |mj = +J⟩ as a function of Ω/ωz for an initial state, |ψ0⟩ = |mj = −J⟩ and B⊥/Bz = 0.1. As J increases it gets narrow and tails decay rapidly. which increases with the value of J. Away from the resonance, and as the rotation frequency increases, a larger B⊥ is required to induce transitions. Hence, in the high￾frequen… view at source ↗
Figure 2
Figure 2. Figure 2: (a) (Smin) 1/2J , (b) (P2J,max) 1/2J and (c) (PGS,min) 1/2J as a function of Ω/ωz and B⊥/Bz. The dashed line in (b) shows the criteria Ω/ωz = B/Bz, where B = p B2 ⊥ + B2 z and that in (c) corresponds to Ω/ωz = (B/Bz) 2 where the overlap vanishes and the population is periodically transferred to the highest stretched state along the instantaneous magnetic field. (P2J,max) 1/2J and (PGS,min) 1/2J . For suffi… view at source ↗
Figure 3
Figure 3. Figure 3: Variation of S(t) 1/2J with time for B⊥/Bz = 1 for different rotation frequencies. B⊥/Bz → ∞. In contrast, when Ω/ωz > 1, where the system does not adiabatically follow the rotating field, as B⊥/Bz is increased, Smin approaches zero at finite values of B⊥/Bz, because of the resonance condition, Ω = ω. As shown in figure 2(c), the minimum population in the instantaneous ground state becomes zero when Ω/ωz =… view at source ↗
Figure 4
Figure 4. Figure 4: Ground state properties of a spin pair. (a)-(c) show [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The maximum entanglement entropy of the ground state for fixed [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Resonant dynamics of two J = 1/2 spins at βz = 3 and β⊥ = 0.5. (a) and (b) show population dynamics corresponding to the two resonances discussed in the main text. The corresponding dynamics of entanglement entropy SA are shown in (c) and (d). (a) and (c) are for Ω = 3gd (first resonance), and (b) and (d) are for Ω = 4.5gd (second resonance). each of the energy eigenstates. The horizontal gray line (E2) in… view at source ↗
Figure 7
Figure 7. Figure 7: Maximum of entanglement entropy as a function of Ω for different [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Population and entanglement dynamics for [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Fig (a) shows the energy spectrum and (b) shows the energy difference between [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Maximum of entanglement entropy as a function of Ω for different [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Maximum of entanglement entropy as a function of Ω for different [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
read the original abstract

We examine the quantum dynamics of both a single spin-J particle and a pair of spin-J particles in the presence of static and rotating magnetic fields, which can be important for qudit-based quantum technologies. Notably, we find resonant, periodic oscillations between two maximally stretched states, irrespective of the value of J. Additionally, we observe periodic transitions between sublevels with magnetic quantum numbers of opposite signs. The dynamics also exhibit a periodic transfer of the spin to the maximally stretched state, starting from the ground state of the initial Hamiltonian. For a pair of spins, we derive various resonance conditions and further analyze the entanglement generated by dipole-dipole interactions. In the case of two spin-1/2 particles, the entanglement dynamics reveal resonances and kinks in the maximum entanglement, and their criteria can be obtained from the energy spectrum. Strikingly, we show that the kink can be exploited to engineer the entanglement dynamics. Finally, we briefly discuss the regime of weak dipolar interactions, which are relevant for dipolar Bose-Einstein condensates.

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 paper examines the quantum dynamics of a single spin-J particle and pairs of spin-J particles in static and rotating magnetic fields. It reports resonant periodic oscillations between the maximally stretched states |J, J⟩ and |J, −J⟩ that hold irrespective of J, along with periodic sign-flip transitions between sublevels of opposite magnetic quantum number and spin transfer from the initial ground state. For two spins, resonance conditions are derived from the driven Hamiltonian spectrum; dipole-dipole interactions generate entanglement whose dynamics for spin-1/2 exhibit resonances and kinks whose locations follow from avoided crossings in the instantaneous eigenenergies. The kink is proposed as a tool to engineer entanglement, and the weak-dipolar regime relevant to dipolar BECs is briefly discussed.

Significance. If the central claims hold, the J-independent resonances and the spectral criteria for entanglement kinks constitute a useful addition to the literature on driven qudit systems and controllable entanglement. The work supplies exact or semi-analytic results for a unitary Zeeman-plus-dipole model that could inform quantum-control protocols and studies of dipolar quantum gases.

major comments (2)
  1. [Single-particle dynamics section] The central claim that resonant oscillations between |J, J⟩ and |J, −J⟩ occur irrespective of J rests on the spectrum of the interaction-picture Hamiltonian being independent of J. The manuscript should explicitly display the rotating-frame Hamiltonian (likely in the section deriving the single-particle dynamics) and show the cancellation of J-dependent terms that produces this independence.
  2. [Entanglement dynamics for two spin-1/2 particles] For the two-spin-1/2 case, the kink in the maximum entanglement (concurrence) is located at parameter values where instantaneous eigenenergies exhibit avoided crossings. The paper should provide the explicit condition on the field parameters or rotation frequency that produces the reported non-analyticity, together with a short derivation linking the avoided-crossing gap to the kink in concurrence.
minor comments (2)
  1. [Discussion or conclusions] A few sentences clarifying the regime of validity of the coherent unitary evolution (e.g., comparison of dipolar strength to decoherence rates) would help readers assess applicability to qudit technologies.
  2. [Figures] Figure captions for the entanglement plots should explicitly mark the resonance frequencies and the kink locations identified in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We appreciate the positive assessment of the work and have addressed the major comments by planning explicit additions to improve clarity, as detailed below.

read point-by-point responses

  1. Referee: [Single-particle dynamics section] The central claim that resonant oscillations between |J, J⟩ and |J, −J⟩ occur irrespective of J rests on the spectrum of the interaction-picture Hamiltonian being independent of J. The manuscript should explicitly display the rotating-frame Hamiltonian (likely in the section deriving the single-particle dynamics) and show the cancellation of J-dependent terms that produces this independence.

    Authors: We agree that an explicit display of the rotating-frame Hamiltonian and a demonstration of the J-term cancellation will strengthen the presentation. In the revised manuscript we will insert the full expression for the interaction-picture (rotating-frame) Hamiltonian in the single-particle dynamics section and provide a step-by-step derivation showing how all J-dependent contributions cancel, leaving a J-independent spectrum that underlies the resonant oscillations between the maximally stretched states. revision: yes

  2. Referee: [Entanglement dynamics for two spin-1/2 particles] For the two-spin-1/2 case, the kink in the maximum entanglement (concurrence) is located at parameter values where instantaneous eigenenergies exhibit avoided crossings. The paper should provide the explicit condition on the field parameters or rotation frequency that produces the reported non-analyticity, together with a short derivation linking the avoided-crossing gap to the kink in concurrence.

    Authors: We thank the referee for this suggestion. In the revised manuscript we will state the explicit condition on the static-field strength, rotating-field amplitude, and rotation frequency that produces the avoided crossings responsible for the kink. We will also add a short derivation that relates the magnitude of the avoided-crossing gap directly to the non-analytic feature observed in the time-dependent concurrence, thereby clarifying the spectral origin of the entanglement kink. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper solves the time-dependent Schrödinger equation for the Zeeman-plus-dipole Hamiltonian in rotating frames, deriving resonance conditions directly from the J-independent energy spectrum in the chosen interaction picture. Entanglement kinks for spin-1/2 pairs are located at parameter values where instantaneous eigenenergies show avoided crossings, producing non-analyticity in concurrence. All steps are internal to the unitary model with no fitted parameters renamed as predictions, no self-citation load-bearing the central claims, and no ansatz smuggled via prior work. Resonance conditions and periodic oscillations between |J, J⟩ and |J, −J⟩ follow from the spectrum without reducing to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claims rest on the standard time-dependent Schrödinger equation for spins in magnetic fields plus dipole-dipole coupling; no additional free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math Unitary evolution under a Hamiltonian consisting of Zeeman and dipole-dipole terms
    The dynamics and resonance conditions are obtained from this Hamiltonian as stated in the abstract.

pith-pipeline@v0.9.0 · 5722 in / 1262 out tokens · 37137 ms · 2026-05-18T03:20:06.686915+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    Levitt M H 2008Spin dynamics: basics of nuclear magnetic resonance(John Wiley & Sons)

    work page

  2. [2]

    Kalatsky V A and Pokrovsky V L 1999Phys. Rev. A60(3) 1824–1844

    work page

  3. [3]

    Rastelli E and Tassi A 2001Phys. Rev. B64(6) 064410

    work page

  4. [4]

    Rev.51(8) 652–654

    Rabi I I 1937Phys. Rev.51(8) 652–654

    work page

  5. [5]

    1) (Wiley) ISBN 9782705658335

    Cohen-Tannoudji C, Diu B and Lalo¨ e F 1977Quantum Mechanics(A Wiley - Interscience publicationno v. 1) (Wiley) ISBN 9782705658335

    work page

  6. [6]

    Suzuki S, Inoue J i and Chakrabarti B K 2012Quantum Ising phases and transitions in transverse Ising modelsvol 862 (Springer)

    work page

  7. [7]

    Cohen-Tannoudji C 2012Annual review of cold atoms and molecules(World Scientific)

    work page

  8. [8]

    Geier S, Thaicharoen N, Hainaut C, Franz T, Salzinger A, Tebben A, Grimshandl D, Z¨ urn G and Weidem¨ uller M 2021Science3741149–1152

    work page

  9. [9]

    Wang Y, Hu Z, Sanders B C and Kais S 2020Frontiers in Physics8ISSN 2296- 424X

    work page

  10. [10]

    Barra A L, Debrunner P, Gatteschi D, Schulz C E and Sessoli R 1996Europhysics Letters35133

    work page

  11. [11]

    Friedman J R, Sarachik M P, Tejada J and Ziolo R 1996Phys. Rev. Lett.76(20) 3830–3833

    work page

  12. [12]

    Ahmed H, Litvinov A, Guesdon P, Mar´ echal E, Huckans J H, Pasquiou B, Labupdfrthe-Tolra B and de Saint-Vincent M R 2025 Coherent control over the high-dimensional space of the nuclear spin of alkaline-earth atoms (Preprint)

    work page 2025

  13. [13]

    White B, Bulstrode N C M, Forest D H, Honeyball C, Evans B and Butt L 2025 Journal of Physics B: Atomic, Molecular and Optical Physics58035001 REFERENCES34

    work page 2025

  14. [14]

    Budker D, DeMille D, Commins E D and Zolotorev M S 1993Phys. Rev. Lett. 70(20) 3019–3022

    work page

  15. [15]

    Budker D, DeMille D, Commins E D and Zolotorev M S 1994Phys. Rev. A50(1) 132–143

    work page

  16. [16]

    Lepers M, Li H, Wyart J F, Qu´ em´ ener G and Dulieu O 2018Physical Review Letters121063201

    work page

  17. [17]

    Mishra C, Santos L and Nath R 2020Phys. Rev. Lett.124(7) 073402

    work page

  18. [18]

    Ghosh R, Mishra C, Santos L and Nath R 2022Phys. Rev. A106(6) 063318

    work page

  19. [19]

    Anich G, H¨ ollrigl N, Kreyer M, Grimm R and Kirilov E 2024Phys. Rev. A110(2) 023311

    work page

  20. [20]

    Maguire L P, van Bijnen R M W, Mese E and Scholten R E 2006Journal of Physics B: Atomic, Molecular and Optical Physics392709

    work page

  21. [21]

    ˇSkolnik G, Vujiˇ ci´ c N and Ban T 2009Optics Communications2821326–1334 ISSN 0030-4018

    work page

  22. [22]

    Chalopin T, Bouazza C, Evrard A, Makhalov V, Dreon D, Dalibard J, Sidorenkov L A and Nascimbene S 2018Nature Communications94955

    work page

  23. [23]

    Bender J, Mischke P, Klas T, Binoth F, Naim H, Ott H and Niederpr¨ um T 2024 New Journal of Physics26073012

    work page 2024

  24. [24]

    Li K, Deng L and Payne M G 2009Applied Physics Letters95221103 ISSN 0003- 6951

    work page

  25. [25]

    Mishina O S, Scherman M, Lombardi P, Ortalo J, Felinto D, Sheremet A S, Bramati A, Kupriyanov D V, Laurat J and Giacobino E 2011Phys. Rev. A83(5) 053809

    work page

  26. [26]

    Kawaguchi Y and Ueda M 2012Physics Reports520253–381 ISSN 0370-1573 spinor Bose–Einstein condensates

    work page

  27. [27]

    Munro E, Asenjo-Garcia A, Lin Y, Kwek L C, Regal C A and Chang D E 2018 Phys. Rev. A98(3) 033815

    work page 2018

  28. [28]

    Cidrim A, Pi˜ neiro Orioli A, Sanner C, Hutson R B, Ye J, Bachelard R and Rey A M 2021Phys. Rev. Lett.127(1) 013401

    work page

  29. [29]

    Asenjo-Garcia A, Kimble H J and Chang D E 2019Proceedings of the National Academy of Sciences11625503–25511 (Preprint)

    work page

  30. [30]

    Hebenstreit M, Kraus B, Ostermann L and Ritsch H 2017Phys. Rev. Lett.118(14) 143602

    work page

  31. [31]

    Pi˜ neiro Orioli A and Rey A M 2019Phys. Rev. Lett.123(22) 223601

    work page

  32. [32]

    Pi˜ neiro Orioli A and Rey A M 2020Phys. Rev. A101(4) 043816

    work page

  33. [33]

    Pi˜ neiro Orioli A, Thompson J K and Rey A M 2022Phys. Rev. X12(1) 011054

    work page

  34. [34]

    Hensler S, Werner J, Griesmaier A, Schmidt P O, G¨ orlitz A, Pfau T, Giovanazzi S and Rza˙ zewski K 2003Applied Physics B77765–772

    work page

  35. [35]

    Pasquiou B, Mar´ echal E, Bismut G, Pedri P, Vernac L, Gorceix O and Laburthe- Tolra B 2011Phys. Rev. Lett.106(25) 255303 REFERENCES35

    work page

  36. [36]

    Giovanazzi S, G¨ orlitz A and Pfau T 2002Phys. Rev. Lett.89(13) 130401

    work page

  37. [37]

    Tang Y, Kao W, Li K Y and Lev B L 2018Phys. Rev. Lett.120(23) 230401

    work page

  38. [38]

    Pedri P and Santos L 2005Phys. Rev. Lett.95(20) 200404

    work page

  39. [39]

    Nath R, Pedri P and Santos L 2007Phys. Rev. A76(1) 013606

    work page

  40. [40]

    Nath R, Pedri P and Santos L 2009Phys. Rev. Lett.102(5) 050401

    work page

  41. [41]

    Klawunn M, Nath R, Pedri P and Santos L 2008Phys. Rev. Lett.100(24) 240403

    work page

  42. [42]

    Nath R, Pedri P and Santos L 2008Phys. Rev. Lett.101(21) 210402

    work page

  43. [43]

    Bland T, Edmonds M J, Proukakis N P, Martin A M, O’Dell D H J and Parker N G 2015Phys. Rev. A92(6) 063601

    work page

  44. [44]

    Prasad S B, Bland T, Mulkerin B C, Parker N G and Martin A M 2019Phys. Rev. Lett.122(5) 050401

    work page

  45. [45]

    Baillie D and Blakie P B 2020Phys. Rev. A101(4) 043606

    work page

  46. [46]

    Prasad S B, Bland T, Mulkerin B C, Parker N G and Martin A M 2019Phys. Rev. A100(2) 023625

    work page

  47. [47]

    Klaus L, Bland T, Poli E, Politi C, Lamporesi G, Casotti E, Bisset R N, Mark M J and Ferlaino F 2022Nature Physics181453–1458

    work page

  48. [48]

    Landau L and Lifshitz E 1981Quantum Mechanics: Non-Relativistic Theory Course of theoretical physics (Butterworth-Heinemann) ISBN 9780080503486

    work page

  49. [49]

    Griesmaier A, Werner J, Hensler S, Stuhler J and Pfau T 2005Phys. Rev. Lett. 94(16) 160401

    work page

  50. [50]

    Beaufils Q, Chicireanu R, Zanon T, Laburthe-Tolra B, Mar´ echal E, Vernac L, Keller J C and Gorceix O 2008Phys. Rev. A77(6) 061601

    work page

  51. [51]

    Aikawa K, Frisch A, Mark M, Baier S, Rietzler A, Grimm R and Ferlaino F 2012 Phys. Rev. Lett.108(21) 210401

    work page 2012

  52. [52]

    Lahaye T, Menotti C, Santos L, Lewenstein M and Pfau T 2009Reports on Progress in Physics72126401

    work page

  53. [53]

    Baranov M A 2008Physics Reports46471–111 ISSN 0370-1573

    work page

  54. [54]

    Varghese D, W¨ uster S, Li W and Nath R 2023Phys. Rev. A107(4) 043311

    work page

  55. [55]

    Seetharaman S, Singh C and Nath R 2025Phys. Rev. D111(7) 076014

    work page