Realizing the Haldane Model in Thermal Atoms

Da-Wei Wang; Han Cai; Huizhu Hu; Jianhao Dai; Jiefei Wang; Ruosong Mao; Shi-Yao Zhu; Xiao Liu; Xingqi Xu; Yunzhou Lu

Realizing the Haldane Model in Thermal Atoms

T0 review · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper demonstrates the experimental realization of the Haldane model in a room-temperature atomic vapor, using a momentum-space superradiance lattice and reading out topological phases through the sign of superradiance contrast.

desk verdict First room-temperature Haldane-model realization in a superradiance lattice looks solid for C=±1; the high-Chern C=1→C=−2 claim is honestly labeled as inferred, not measured. read the letter →

arxiv 2509.08411 v1 pith:E7UH3TCK submitted 2025-09-10 quant-ph physics.atom-phphysics.optics

Jiefei Wang , Jianhao Dai , Ruosong Mao , Yunzhou Lu , Xiao Liu , Huizhu Hu , Shi-Yao Zhu , Xingqi Xu

show 2 more authors

Han Cai Da-Wei Wang

This is my paper · ORCID

classification quant-phphysics.atom-phphysics.optics

keywords Haldanemodelsuperradiancelatticeroom-temperaturequantumsimulationtimedDickestatesChernnumberFloquetmodulationelectromagneticallyinducedtransparencythermalatoms

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports the experimental realization of the Haldane model—the paradigmatic Chern insulator with no net magnetic field—in a room-temperature atomic vapor. The platform is a momentum-space superradiance lattice: three laser fields in an electromagnetically induced transparency configuration couple atomic timed Dicke states into a honeycomb tight-binding lattice, and periodic phase modulation breaks time-reversal symmetry through complex next-nearest-neighbor hopping. The topological phase is read out in situ from the sign of the superradiance contrast η between two directional emission channels, after velocity scanning tomography and homodyne detection isolate the zero-velocity atoms. Because the lattice is driven rather than material-bound, the same setup reaches strong modulation where longer-range hopping creates satellite Dirac points and a higher-order transition from Chern number C=1 to C=-2. If correct, this makes topological band physics accessible without cryogenics and opens a reconfigurable, high-Chern-number quantum simulation platform.

What carries the argument

The load-bearing object is the momentum-space superradiance lattice: a tight-binding network of timed Dicke states (collective atomic excitations with fixed phase gradients) in a thermal atomic ensemble. Topological engineering relies on Floquet phase modulation θ_j=f sin(δt+φ_j) of the coupling lasers, which produces complex next-nearest-neighbor hoppings in second order. The observable is η=(|c_k+|^2−|c_k−|^2)/(|c_k+|^2+|c_k−|^2), the normalized contrast of the two directional superradiant channels, whose sign is argued to equal the sign of the Chern number. The supporting instrumental mechanism is velocity scanning tomography with homodyne detection, which isolates the v_x≈0 atoms and sup

What would settle it

Measure the winding of the band geometric phase across the Brillouin zone for the same f=3.2, Ω=25 MHz configuration and compare the Chern number obtained from that winding with the sign of η at every phase point; any mismatch—or any η sign change without a Chern-number change—would falsify the claim that η tracks the topological transition.

Watch

Extended reading notes

Core claim

At room temperature, the authors build a momentum-space honeycomb lattice from timed Dicke states of a rubidium vapor in an EIT configuration driven by three coupling lasers. A weak probe excites |b_kp>; the coupling fields move excitations between Dicke states, forming nearest-neighbor hoppings. Modulating the coupling phases as θ_j=f sin(δt+φ_j) makes the Dirac points orbit and, via Floquet second-order processes, generates the complex next-nearest-neighbor hoppings ±i that break time-reversal symmetry—the Haldane ingredient. The measured sign of the superradiance contrast η between the two directional emissions |b_k+> and |b_k−> matches the Chern-number sign for C=±1 (f=1.0) and for the d

Load-bearing premise

The measurement of η in a warm vapor is trustworthy only if subtracting pump-on minus pump-off signals after homodyne detection isolates the superradiant field amplitudes of zero-velocity atoms, with no residual interference from other velocity classes or from other sidebands of the periodic modulation.

Editorial extensions

If this is right

Topological band structure can be measured in a room-temperature atomic vapor, removing cryogenic constraints from Haldane-model simulation and its applications.
The superradiance contrast η gives a direct, in-situ topological phase probe without requiring chiral edge currents or Hall transport, since momentum-space superradiance lattices have no physical edges.
Strong Floquet driving no longer forbids topological experiments; the same platform reaches deep-modulation regimes where longer-range hopping produces satellite Dirac points and Chern numbers beyond ±1.
Because the phase diagram is controlled by laser phases and powers, topological phases can be reconfigured dynamically in a single setup, including future spin-Hall-like two-copy generalizations.
The absorption spectra and η measurements together map band-flattening regions and phase boundaries over a broad parameter range, connecting band-structure geometry directly to collective emission.

Reading between the lines

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

A quantitative measurement of the geometric-phase winding across the Brillouin zone in this same setup would convert the sign-only η readout into an actual Chern-number value, directly testing the C=-2 assignment rather than just its sign.
The same velocity-selective and homodyne readout should transfer to other laser-dressed lattice geometries, where a two-channel contrast may not exist but other momentum-space observables could reveal topological transitions.
The Bessel-function formula for the Chern number at large f predicts additional sign-changing islands at even larger modulation depths; locating them experimentally would provide a strong quantitative test of the Floquet expansion used here.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper delivers what it says at the core: a room-temperature thermal-atom realization of the Haldane model in a momentum-space superradiance lattice, with the topological phase transition read out through the sign of the superradiance contrast η. That part is convincing. The C=±1 phase diagram in Fig. 3 is supported by sign flips along the predicted boundary, five data sets with error bars, and matching numerical simulations. The velocity scanning tomography plus homodyne detection is a genuinely clever way to isolate zero-velocity atoms in a room-temperature vapor, and it appears to address the Doppler-broadening problem without a fitting procedure. Credit is due for that.

The softer spot is exactly where the reader and stress-test put it: the claimed high-Chern transition from C=1 to C=−2 in Fig. 4 is not directly measured. The only observable is a sign change in η, and the paper itself states that η alone is insufficient to determine the precise topological invariant, leaving a Wilson-loop measurement for future work. That means the 'beyond Haldane' headline is a prediction backed by the same group's Floquet/tight-binding mapping and the computed phase diagram, not an independent measurement. This is an admitted gap, not a manufactured one, and it should temper how the abstract and discussion phrase the achievement. The C=±1 result stands on its own; the C=−2 claim should be presented as a predicted transition with a clear disclaimer.

Minor concerns: the SI is not available for review, so I could not check the full derivations of the effective Hamiltonian or the homodyne subtraction details. The simulation code is 'available upon request,' which is better than nothing but not open. The self-citation of Ref. [21] for the η-to-Chern mapping is not by itself a flaw—the experiment is a genuine test of that theory—but it does mean the high-Chern interpretation is not independent of the authors' prior framework.

Who is this for? People working on topological photonics, quantum simulation with thermal atoms, and Floquet topological phases will want to read it. The central experimental advance deserves a serious referee. The authors should be pushed to either make the SI public, release the data and code, or explicitly label the high-Chern claim as a theory-driven inference rather than a direct measurement. With those revisions, this is a solid paper. Recommending: send it to peer review, but require the high-Chern language to be scaled back or supported by a direct invariant measurement.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the measured superradiance contrast is an independent observable, though high-Chern identification relies on same-group theory and is admittedly not directly measured.

full rationale

The paper's central derivation is not circular. The Haldane lattice is constructed from the EIT/Floquet Hamiltonian, and the measured quantity η is an independently defined contrast of steady-state amplitudes (Eq. 2), not a fitted parameter nor a restatement of the Chern number. The connection between the sign of η and the sign of the Chern number is taken from prior theory [21] with overlapping authors, but the present experiment is an external, falsifiable test of that mapping: the measured sign changes are compared with the theoretically predicted phase diagram rather than used as input to compute the invariant. The deep-modulation phase diagram additionally uses distant-neighbor hopping theory [23], which is not by the present authors. The paper explicitly admits that 'η alone is insufficient to determine the precise value of the topological invariant' and that a Wilson-loop/Zak-phase measurement is left for future work. This means the claimed C=1 → C=-2 transition is not directly measured and is an evidentiary overclaim, but it is not a circular reduction of the prediction to the input. The self-citations here are prior predictions tested by new data, not load-bearing unverified premises that force the conclusion.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new particles, forces, or conserved quantities are introduced. The superradiance lattice, timed Dicke states, and satellite Dirac points are borrowed from prior literature. The free parameters are experimental control settings, not hidden fitting constants.

free parameters (4)

modulation depth f = 1.0, 3.2, 2.6, 5.7 (selected by EOM drive voltage)
Chosen by hand to realize weak and deep modulation regimes; not fitted to the measured contrast.
modulation frequency delta = 80 MHz
Fixed Floquet drive frequency separating Floquet replicas; set by the experiment, not fitted.
coupling Rabi frequency Omega = 10 MHz and 25 MHz
Laser power chosen to set the energy scale of the lattice and the location in the phase diagram.
modulation phases phi1, phi2, phi3 = phi1=0; phi2 and phi3 swept, e.g. 2pi/3, 4pi/3
Control the rotation direction of the Dirac points and hence the Chern number; used as phase diagram axes.

assumptions (5)

domain assumption Timed Dicke states form a momentum-space tight-binding lattice with hopping driven by the coupling fields.
Foundational superradiance lattice mapping from [15,16,21]; not re-derived here.
domain assumption Floquet expansion of the phase-modulated coupling fields yields an effective two-band Hamiltonian with complex NNN hoppings +/-i.
Stated in Results and deferred to SI; central to identifying the system with the Haldane model.
domain assumption Only the x-component of atomic velocity matters and VST/homodyne subtraction isolates the v_x about 0 response.
Required for room-temperature operation; if the subtraction fails the measured eta is contaminated.
domain assumption The sign of the superradiance contrast eta gives the sign of the Chern number.
Takes the topological observable from the authors' prior theory [21]; not independently measured by a Wilson loop in this work.
domain assumption Longer-range hoppings t3,t4 and satellite Dirac points cause a C=1 to C=-2 transition at f about 2.6.
Based on distant-neighbor hopping theory [23]; used to interpret the sign change in eta at deep modulation.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Realizing the Haldane Model in Thermal Atoms." pith.science (2026). https://pith.science/paper/E7UH3TCK

@misc{pith2026250908411,
  author       = {Pith},
  title        = {Pith review of: Realizing the Haldane Model in Thermal Atoms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E7UH3TCK}},
  note         = {Machine review of arXiv:2509.08411}
}

read the original abstract

Topological materials hold great promise for developing next-generation devices with transport properties that remain resilient in the presence of local imperfections. However, their susceptibility to thermal noise has posed a major challenge. In particular, the Haldane model, a cornerstone in topological physics, generally requires cryogenic temperatures for experimental realization, limiting both the investigation of topologically robust quantum phenomena and their practical applications. In this work, we demonstrate a room-temperature realization of the Haldane model using atomic ensembles in momentum-space superradiance lattices, a platform intrinsically resistant to thermal noise. The topological phase transition is revealed through the superradiant emission contrast between two timed Dicke states in the lattice. Crucially, the thermal resilience of this platform allows us to access a deep modulation regime, where topological transitions to high Chern number phases emerge -- going beyond the traditional Haldane model. Our results not only deepen the understanding of exotic topological phases, but also offer a robust, reconfigurable, and room-temperature-compatible platform that connects quantum simulation to real-world quantum technologies.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 33 canonical work pages

[21]

D. W. Wang, H. Cai, L. Yuan, S. Y. Zhu, and R. B. Liu, Topological phase transitions in superradiance lattices, Optica2, 712 (2015)

work page 2015
[1]

parity anomaly

F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett.61, 2015 (1988)

2015
[2]

M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys.82, 3045 (2010)

2010
[3]

X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys.83, 1057 (2011)

work page 2011
[4]

A. B. Khanikaev and G. Shvets, Two-dimensional topological photonics, Nat. Photonics11, 763 (2017)

work page 2017
[5]

Ozawa, H

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys.91, 015006 (2019)

2019
[6]

D. W. Zhang, Y. Q. Zhu, Y. X. Zhao, H. Yan, and S. L. Zhu, Topological quantum matter with cold atoms, Adv. in Phys.67, 253 (2018)

work page 2018
[7]

N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys.91, 015005 (2019)

2019

Show all 45 references

[8]

Nayak, S

C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys.80, 1083 (2008)

2008
[9]

Jotzu, M

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature515, 237 (2014)

2014
[10]

J. M. Mclver, B. Schulte, F.-U. Stein, T. Matsuyama, G. Meier, and A. Cavalleri, Light-induced anomalous Hall effect in graphene, Nat. Phys.16, 38 (2020)

2020
[11]

W. Zhao, K. Kang, Y. Zhang, P. Kn¨ uppel, Z. Tao, L. Li, C. L. Tschirhart, E. Redekop, K. Watanabe, T. Taniguchi, A. F. Young, J. Shan, and K. F. Mak, Realization of the Haldane Chern insulator in a moir´ e lattice, Nat. Phys.20, 275 (2024)

2024
[12]

J. Deng, H. Dong, C. Zhang, Y. Wu, J. Yuan, X. Zhu, F. Jin, H. Li, Z. Wang, H. Cai, C. Song, H. Wang, J. Q. You, and D. W. Wang, Observing the quantum topology of light, Science378, 966 (2022)

2022
[13]

M. S. Rudner and N. H. Lindner, Band structure engineering and non-equilibrium dynamics in Floquet topological insulators, Nat. Rev. Phys.2, 229 (2020)

2020
[14]

Oka and S

T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annu. Rev. Conden. Ma. P.10, 387 (2019)

2019
[15]

D. W. Wang, R. B. Liu, S. Y. Zhu, and M. O. Scully, Superradiance lattice, Phys. Rev. Lett.114, 043602 (2015)

2015
[16]

L. Chen, P. Wang, Z. Meng, L. Huang, H. Cai, D. W. Wang, S. Y. Zhu, and J. Zhang, Experimental observation of one-dimensional superradiance lattices in ultracold atoms, Phys. Rev. Lett.120, 193601 (2018)

2018
[17]

H. Cai, J. Liu, J. Wu, Y. He, S. Y. Zhu, J. X. Zhang, and D. W. Wang, Experimental observation of momentum-space chiral edge currents in room-temperature atoms, Phys. Rev. Lett.122, 023601 (2019)

2019
[18]

Y. He, R. Mao, H. Cai, J.-X. Zhang, Y. Li, L. Yuan, S.-Y. Zhu, and D.-W. Wang, Flat-band localization in Creutz superradiance lattices, Phys. Rev. Lett.126, 103601 (2021)

2021
[19]

R. Mao, X. Xu, J. Wang, C. Xu, G. Qian, H. Cai, S. Y. Zhu, and D. W. Wang, Measuring Zak phase in room-temperature atoms, Light Sci. Appl.11, 291 (2022)

2022
[20]

X. Xu, J. Wang, J. Dai, R. Mao, H. Cai, S. Y. Zhu, and D. W. Wang, Floquet superradiance lattices in thermal atoms, Phys. Rev. Lett.129, 273603 (2022). 7

2022
[22]

J. Wang, R. Mao, X. Xu, Y. Lu, J. Dai, X. Liu, G. Q. Liu, D. Lu, H. Hu, S. Y. Zhu, H. Cai, and D. W. Wang, Velocity scanning tomography for room-temperature quantum simulation, Phys. Rev. Lett.133, 183403 (2024)

2024
[23]

Sticlet and F

D. Sticlet and F. Pi´ echon, Distant-neighbor hopping in graphene and Haldane models, Phys. Rev. B87, 115402 (2013)

2013
[24]

Fleischhauer, A

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev. Mod. Phys.77, 633 (2005)

2005
[25]

M. O. Scully, E. S. Fry, C. H. Ooi, and K. W´ odkiewicz, Directed spontaneous emission from an extended ensemble of N atoms: Timing is everything, Phys. Rev. Lett.96, 010501 (2006)

2006
[26]

M. O. Scully and A. A. Svidzinsky, The super of superradiance, Science325, 1510 (2009)

2009
[27]

M. O. Ara´ ujo, I. Kreˇ si´ c, R. Kaiser, and W. Guerin, Superradiance in a large and dilute cloud of cold atoms in the linear-optics regime, Phys. Rev. Lett.117, 073002 (2016)

2016
[28]

S. J. Roof, K. J. Kemp, and M. D. Havey, Observation of single-photon superradiance and the cooperative Lamb shift in an extended sample of cold atoms, Phys. Rev. Lett.117, 073003 (2016)

2016
[29]

Y. He, L. Ji, Y. Wang, L. Qiu, J. Zhao, Y. Ma, X. Huang, S. Wu, and D. E. Chang, Geometric control of collective spontaneous emission, Phys. Rev. Lett.125, 213602 (2020)

2020
[30]

C. Mi, K. S. Nawaz, L. Chen, P. Wang, H. Cai, D. W. Wang, S. Y. Zhu, and J. Zhang, Time-resolved interplay between superradiant and subradiant states in superradiance lattices of Bose-Einstein condensates, Phys. Rev. A104, 043326 (2021)

2021
[31]

M. O. Scully, Single photon subradiance: Quantum control of spontaneous emission and ultrafast readout, Phys. Rev. Lett.115, 243602 (2015)

2015
[32]

Oka and H

T. Oka and H. Aoki, Photovoltaic Hall effect in graphene, Phys. Rev. B79, 081406 (2009)

2009
[33]

Zak, Berry’s phase for energy bands in solids, Phys

J. Zak, Berry’s phase for energy bands in solids, Phys. Rev. Lett.62, 2747 (1989)

1989
[34]

D. Xiao, M. C Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys.82, 1959 (2010)

1959
[35]

Atala, M

M. Atala, M. Aidelsburger, J. T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, and I. Bloch, Direct measurement of the Zak phase in topological Bloch bands, Nat. Phys.9, 795 (2013)

2013
[36]

G. Li, L. Wang, R. Ye, Y. Zheng, D. W. Wang, X. J. Liu, A. Dutt, L. Yuan, and X. Chen, Direct extraction of topological Zak phase with the synthetic dimension, Light Sci. Appl.12, 81 (2023)

2023
[37]

D. A. Abanin, T. Kitagawa, I. Bloch, and E. Demler, Interferometric approach to measuring band topology in 2D optical lattices, Phys. Rev. Lett.110, 165304 (2013)

2013
[38]

Vanderbilt, Berry phases in electronic structure theory, Cambridge University Press (2018)

D. Vanderbilt, Berry phases in electronic structure theory, Cambridge University Press (2018)

2018
[39]

Mitra, ´A

S. Mitra, ´A. Jim´ enez-Gal´ an, M. Aulich, M. Neuhaus, R. E. F. Silva, V. Pervak, M. F. Kling, and S. Biswas, Light-wave-controlled Haldane model in monolayer hexagonal boron nitride, Nature628, 752 (2024)

2024
[40]

Z. Li, H. Cao, and S. Meng, Light-induced above-room-temperature Chern insulators in group-IV Xenes, npj Compt. Mater.11, 160 (2025)

2025
[41]

X. Xie, K. Sun, and H. Deng, Polariton Chern bands in 2D photonic crystals beyond Dirac cones, Phys. Rev. X15, 021061 (2025)

2025
[42]

C. L. Kane and E. J. Mele,Z 2 Topological order and the quantum spin Hall effect, Phys. Rev. Lett.95, 146802 (2005)

2005
[43]

D. Ding, Z. Bai, Z. Liu, B. Shi, G. Guo, W. Li, and C. S. Adams, Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system, Sci. Adv.10, eadl5893 (2024). 8

2024
[44]

X. Wu, Z. Wang, F. Yang, R. Gao, C. Liang, M. K. Tey, X. Li, T. Pohl, and L. You, Dissipative time crystal in a strongly interacting Rydberg gas, Nat. Phys.20, 1389 (2024)

2024
[45]

Pioneer” and “Leading Goose

D. Yu, W. Song, L. Wang, R. Srikanth, S. K. Sridhar, T. Chen, C. Huang, G. Li, X. Qiao, X. Wu, Z. Dong, Y. He, M. Xiao, X. Chen, A. Dutt, B. Gadway, and L. Yuan, Comprehensive review on developments of synthetic dimensions, Photnics Insights4, R06 (2025). Code availability The...

2025

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [21]

D. W. Wang, H. Cai, L. Yuan, S. Y. Zhu, and R. B. Liu, Topological phase transitions in superradiance lattices, Optica2, 712 (2015)

work page 2015

[2] [1]

parity anomaly

F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett.61, 2015 (1988)

2015

[3] [2]

M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys.82, 3045 (2010)

2010

[4] [3]

X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys.83, 1057 (2011)

work page 2011

[5] [4]

A. B. Khanikaev and G. Shvets, Two-dimensional topological photonics, Nat. Photonics11, 763 (2017)

work page 2017

[6] [5]

Ozawa, H

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys.91, 015006 (2019)

2019

[7] [6]

D. W. Zhang, Y. Q. Zhu, Y. X. Zhao, H. Yan, and S. L. Zhu, Topological quantum matter with cold atoms, Adv. in Phys.67, 253 (2018)

work page 2018

[8] [7]

N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys.91, 015005 (2019)

2019