Pith. sign in

REVIEW 2 major objections 4 minor 47 references

Topological quantum walk in synthetic non-Abelian gauge fields

T0 review · 2 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Non-Abelian SU(2) gauge fields in a four-dimensional photonic quantum walk shift the Floquet bands in both momentum and quasienergy, and the gauge angles control the walk's winding numbers, Chern numbers, and RLBL invariants.

desk verdict A solid non-Abelian quantum-walk proposal whose 1D Peierls substitution holds up cleanly, but the 2D optical implementation is asserted rather than derived. read the letter →

arxiv 2412.03043 v1 pith:SLEJZUZQ submitted 2024-12-04 physics.optics quant-ph

Zehai Pang , Omar Abdelghani , Marin Soljačić , Yi Yang This is my paper · ORCID
classification physics.opticsquant-ph
keywords quantumwalktopologicalFloquetphasesnon-AbeliangaugefieldsphotonicmeshlatticepolarizationmultiplexingRLBLinvariantPeierlssubstitutionentanglementsimulation
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 claims that synthetic non-Abelian SU(2) gauge fields can be inserted into discrete-time quantum walks on a photonic mesh lattice by using polarization multiplexing to enlarge the coin from two to four dimensions. It shows that the gauge fields produce a Peierls substitution in both momentum and quasienergy, so the Floquet bands shift as $\cos(\epsilon\pm\delta\epsilon)=\cos(k\pm\delta k)\cos\alpha$. In one and two dimensions, it constructs topological quantum walks whose Floquet winding numbers, Chern numbers, and Rudner\textendash Lindner\textendash Berg\textendash Levin invariants are controlled by the gauge-field angles, with domain-wall spectra exhibiting the predicted edge modes. A photonic implementation with polarization-maintaining fiber loops is proposed for each walk. If correct, this turns non-Abelian gauge fields into practical knobs for Floquet topological phases and for entangling the coin and pseudospin degrees of freedom.

What carries the argument

The central object is the polarization-multiplexed photonic mesh lattice, which realizes a four-dimensional Hilbert space $\tau\otimes\sigma$ where $\tau$ is the coin space of two coupled fiber loops and $\sigma$ is the polarization pseudospin. The walk operator is the product of a coin rotation $R(\alpha)=e^{i\alpha\tau_y\otimes\sigma_0}$, a conditional translation $S(k)=e^{-ik\tau_z\otimes\sigma_0}$, and a gauge-field factor $G$ that applies SU(2) rotations such as $e^{i\theta\sigma_y}$ or $e^{i\phi\sigma_z}$ to the pseudospin depending on the loop direction. Block diagonalization of the commutative case yields the dispersion identity $\cos(\epsilon\pm\delta\epsilon)=\cos(k\pm\delta k)\cos\alpha$, and for topological walks the winding numbers are computed from the Asb\'oth\textendash Obuse time-symmetric frame while the 2D invariants are computed via the RLBL winding of a time-dependent pulse sequence and cross-checked by spectral flow.

What would settle it

Measure the Floquet band structure of the walker in Eq. (2) with fixed coin angle $\alpha$ and nonzero gauge angles $\theta$ and $\phi$: the dispersion must satisfy $\cos(\epsilon\pm\delta\epsilon)=\cos(k\pm\delta k)\cos\alpha$, meaning the band center shifts in quasienergy by $(\theta+\phi)/2$. A spectrum showing only momentum shifts, or no shift at all, would rule out the claimed quasienergy Peierls substitution.

Watch

Extended reading notes

Core claim

The authors show that in a four-dimensional Hilbert space formed by two loop states (the coin) and two polarization states (the pseudospin), inserting SU(2) rotations on the pseudospin into the translation step of a quantum walk yields a Floquet operator whose dispersion is $\cos(\epsilon\pm\delta\epsilon)=\cos(k\pm\delta k)\cos\alpha$, i.e., non-Abelian gauge fields cause Peierls substitution in the quasienergy as well as the momentum. For non-commuting gauge fields, the bands exhibit level repulsion and spin-texture exchange. They then design 1D and 2D split-step quantum walks in which the gauge-field angles $\theta$ and $\phi$ act as control knobs for the topological invariants: the Floquet winding numbers $(\nu_0,\nu_\pi)$ in 1D and the Chern numbers and RLBL invariants $(W_0,W_\pi)$ in 2D, with domain-wall configurations producing boundary modes exactly where the invariants differ. Finally, they show that making the gauge field block diagonal turns it into a conditional gate that entangles the loop and pseudospin subspaces, enabling the simulation of entangled walkers.

Load-bearing premise

The photonic implementation with polarization-maintaining fibers and components preserves the pseudospin coherence and keeps losses low enough over the many round trips needed to observe the predicted edge modes.

Editorial extensions

If this is right

  • The same photonic platform can realize 1D and 2D topological quantum walks whose Floquet winding numbers, Chern numbers, and RLBL invariants are set by the gauge angles $(\theta,\phi)$, enabling optical control of topological phase transitions.
  • The Peierls substitution in quasienergy means synthetic gauge fields can engineer the Floquet band structure itself, not just the spatial dynamics, which is a new tool for Floquet engineering in time-multiplexed systems.
  • The proposed building blocks (PM couplers, phase delays, and polarization rotators) can be assembled to implement non-Abelian gauge fields and conditional gates, providing a route to entanglement generation between different degrees of freedom in time-multiplexed photonic quantum walks.
  • Bulk-boundary correspondence holds for the 1D and 2D Floquet walks with non-Abelian gauge fields: domain walls between regions with different $(\nu_0,\nu_\pi)$ or RLBL invariants host edge modes, as confirmed numerically.

Reading between the lines

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

  • If the quasienergy Peierls substitution is confirmed experimentally, it suggests non-Abelian gauge fields could serve as a resource for Floquet band-structure engineering in other driven platforms, such as cold atoms or superconducting circuits, where both momentum and quasienergy are separately measurable.
  • The conditional-gate interpretation of the block-diagonal gauge fields implies that the same two-loop architecture could double as a programmable entangling gate for polarization-encoded qubits, with the gauge angles serving as gate parameters.
  • The spectral-flow cross-check hints that the RLBL invariant could be extracted from transport measurements, such as boundary-mode spectral flow, in the proposed photonic setup, connecting the phase diagram to a directly observable response.
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.

Referee Report

2 major / 4 minor

Summary. This theoretical paper introduces a polarization-multiplexed photonic mesh lattice as a platform for quantum walks in synthetic non-Abelian SU(2) gauge fields. The central results are: (i) a 1D walk with commuting SU(2) fields that exhibits a Peierls-like substitution in both momentum and quasienergy, cos(ε±δε)=cos(k±δk)cosα; (ii) 1D and 2D topological quantum walks whose Floquet winding numbers, Chern numbers, and Rudner–Lindner–Berg–Levin invariants are controlled by the gauge-field angles θ and φ; and (iii) a scheme for simulating entangled walkers by making the gauge fields conditional on the coin state. The paper is theoretical and includes proposed optical implementations in Figs. 1–3 and in the Supplementary Information.

Significance. If the proposed setups faithfully realize the target unitaries, the paper provides a concrete and versatile experimental route to Floquet topological phases with non-Abelian gauge fields. The analytical dispersion relation in Eq. (3) is a clean, independently checkable result, and the block-diagonalization presented in Sec. S1 is explicit. The topological invariants are computed with standard algorithms and are cross-checked against domain-wall spectra and a spectral-flow method. The entanglement simulation section is a useful extension. The main weakness is that the mapping from the proposed optical circuits to the split-step topological walkers, especially in 2D, is asserted rather than demonstrated; this currently limits the claim that the Chern/RLBL phase diagrams are predictions for the experimentally described setups.

major comments (2)
  1. [S4A, S4B] The supplementary provides a full port-by-port transfer-matrix derivation only for the minimal 2D walker Eq. (S30). For the split-step walker Eq. (S54), which is the one whose Chern and RLBL phase diagrams are the central 2D result, the equivalence to the optical circuit in Fig. S3b is asserted with the single sentence 'By similar derivation, Eq. (S54) can be realized in Fig. S3b' without showing the mapping. Moreover, the RLBL invariants in Fig. 3e-f are computed from the 15-pulse Hamiltonian in Eqs. (S58)-(S60), but the paper never verifies that the time-ordered product of these pulses reproduces U2D of Eq. (7). The placement of the gauge-field pulses Ux at G[7] and G[15] and Uy at G[6] and G[11] relative to the Sx and Sy pulses is not obviously the same as the operator ordering inside Sx and Sy in Eq. (7), and the coin pulses u(t) in Eq. (S60) are along τx, whereas the walker coins in Eq. (7) are e^{-iατy}. An explicit operator-product calculation, or at least a numerical check that the 15-pulse sequence equals U2D for arbitrary parameters, is required. Without this, the Chern and RLBL phase diagrams in Fig. 3c and Fig. 3e-f, and the domain-wall spectra in Fig. 3g, are not yet demonstrated to be predictions of the proposed photonic setup in Fig. 3a.
  2. [S3] The same completeness issue affects the 1D topological walk. The setup in Fig. 2a is described as realizing the walker in Eq. (4), but no port-by-port transfer-matrix derivation is provided for this four-beam-splitter, four-loop circuit. Given that the paper's stated contribution is 'detailed photonic setups' for topological quantum walks in non-Abelian gauge fields, an explicit check—parallel to the one provided for Eq. (S30)—should be included for Eq. (4) as well. This is needed to support the claim that the winding-number phase diagrams in Fig. 2c-d and the edge-mode spectrum in Fig. 2b describe the proposed experiment.
minor comments (4)
  1. [Abstract and main text] The quasienergy shift is denoted δε in the abstract and δϵ in the main text (Eq. (3) and surrounding text); please unify the notation.
  2. [Fig. 3c] The caption states 'Chern number summed over the top two energy bands,' while the text later refers to 'half of the Floquet bands'; clarify whether the sum is over exactly the two upper bands and why this sum is the appropriate quantity.
  3. [Main text, entanglement section] The claim that θ=0, φ=π/2 realizes the 'controlled-Z gate with an additional phase' should be phrased more precisely, since e^{-i(π/2)σz} = -iσz is a controlled-phase gate only up to single-qubit rotations.
  4. [Eq. (S56)] In the definition of Uε, the expression Vε(kx,ky,2T-2t) has argument 2T-2t which lies in [0,T] for t∈[T/2,T], but this is not stated; adding a sentence would help readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: dispersion, winding, and RLBL phase diagrams are derived from explicitly defined unitaries; the unverified optical mapping is a completeness issue, not a circular reduction.

full rationale

The paper's central results are derived analytically from unitaries that it explicitly defines. Equation (3) follows from the block-diagonalization in Sec. S1 of the walker U(k) = S(k)G(θ,φ)R(α); no parameter is fitted to any target quantity, and the 'Peierls substitution' is a direct algebraic consequence of the defined model rather than an input. The 1D winding numbers are computed from the standard Asbóth–Obuse chiral-frame construction applied to the defined U(k) of Eq. (4), and the RLBL invariants are computed from the explicitly constructed 15-pulse time-dependent Hamiltonian in Eqs. (S58)–(S60), with an independent spectral-flow cross-check in Sec. S5. The 2D Chern and RLBL phase diagrams are evaluations of these invariants on the defined walker, not fits to data. The authors' earlier non-Abelian photonics papers are cited as background and are not load-bearing in the derivation; no uniqueness theorem from the authors' prior work is invoked to forbid alternatives. The notable gap—Sec. S4A asserts 'By similar derivation, Eq. (S54) can be realized in Fig. S3b' without giving the full transfer-matrix proof, and the supplementary does not explicitly verify that one period of the 15-pulse sequence reproduces U2D—is a completeness or correctness issue in the proposed experimental mapping, not a circular reduction of a prediction to its input. No self-definitional, fitted-input-called-prediction, self-citation-load-bearing, or ansatz-smuggled-via-citation step was found.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical particles or forces. Its free parameters are tunable experimental or numerical knobs. The main assumptions are the fidelity of the polarization-multiplexed optical platform and the exactness of the pulse-sequence mapping behind the RLBL invariant calculation.

free parameters (3)
  • Coin angles α1, α2 = π/4, π/4 (1D); π/6, π/6 (2D)
    Chosen for the example phase diagrams and domain-wall calculations; tunable knobs in the proposed platform, not fitted to data.
  • Gauge field strengths θ, φ = varied continuously over [-π, π]
    Axes of the phase diagrams; they are the control parameters whose influence on topology is the paper's subject, not fitted constants.
  • Fictitious magnetic flux p/q and supercell size s = p/q = 1/100, s = 15
    Computational parameters in the spectral-flow check of the RLBL invariant (S5); chosen small enough to approximate the flux-free system.
assumptions (5)
  • domain assumption Time-multiplexed pulse propagation in two coupled fiber loops maps exactly to a discrete-time quantum walk on a 1D chain.
    Used throughout; stated in the platform description and Fig. 1, standard for mesh lattices.
  • domain assumption Polarization-maintaining components preserve the two-by-two pseudospin Hilbert space so the 4D coin space τ⊗σ is well defined.
    Central to the polarization-multiplexing scheme; assumed in Fig. 1 and the platform description.
  • domain assumption The non-overlapping pulse sequence in S4.B exactly reproduces the 2D Floquet operator U2D.
    Needed for the RLBL invariant calculation; the amplitudes are listed but no explicit product identity is shown.
  • standard math Standard Floquet topological invariant machinery (chiral winding numbers, Chern numbers, RLBL invariant) applies to these unitary walkers.
    Used in Eqs. (5)-(6) and S4.B; background from Refs. [28,32,35,45,46].
  • domain assumption The optical elements described (PM couplers, phase delays, polarization rotators, PBS/Cs) implement the corresponding ideal unitary operations with negligible loss.
    Assumed throughout the experimental proposals; not demonstrated experimentally.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Topological quantum walk in synthetic non-Abelian gauge fields." pith.science (2026). https://pith.science/paper/SLEJZUZQ

@misc{pith2026241203043,
  author       = {Pith},
  title        = {Pith review of: Topological quantum walk in synthetic non-Abelian gauge fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SLEJZUZQ}},
  note         = {Machine review of arXiv:2412.03043}
}
read the original abstract

We theoretically introduce synthetic non-Abelian gauge fields for topological quantum walks. The photonic mesh lattice configuration is generalized with polarization multiplexing to achieve a four-dimensional Hilbert space, based on which we provide photonic building blocks for realizing various quantum walks in non-Abelian gauge fields. It is found that SU(2) gauge fields can lead to Peierls substitution in both momenta and quasienergy. In one and two dimensions, we describe detailed photonic setups to realize topological quantum walk protocols whose Floquet winding numbers and Rudner-Lindner-Berg-Levin invariants can be effectively controlled by the gauge fields. Finally, we show how non-Abelian gauge fields facilitate convenient simulation of entanglement in conjunction with polarization-dependent and spatial-mode-dependent coin operations. Our results shed light on the study of synthetic non-Abelian gauge fields in photonic Floquet systems.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references · 33 canonical work pages

  1. [7]

    Brosco , author L

    author author V. Brosco , author L. Pilozzi , author R. Fazio ,\ and\ author C. Conti ,\ 10.1103/PhysRevA.103.063518 journal journal Physical Review A \ volume 103 ,\ pages 063518 ( year 2021 ) NoStop

    work page doi:10.1103/physreva.103.063518 2021

  2. [15]

    Yang , author H

    author author Y. Yang , author H. C. \ Po , author V. Liu , author J. D. \ Joannopoulos , author L. Fu ,\ and\ author M. Solja c i \'c ,\ 10.1103/PhysRevB.106.L161108 journal journal Physical Review B \ volume 106 ,\ pages L161108 ( year 2022 ) NoStop

    work page doi:10.1103/physrevb.106.l161108

  3. [6]

    Jiang , author A

    author author B. Jiang , author A. Bouhon , author Z.-K. \ Lin , author X. Zhou , author B. Hou , author F. Li , author R.-J. \ Slager ,\ and\ author J.-H. \ Jiang ,\ 10.1038/s41567-021-01340-x journal journal Nature Physics \ volume 17 ,\ pages 1239 ( year 2021 ) NoStop

    doi:10.1038/s41567-021-01340-x

  4. [11]

    Noh , author T

    author author J. Noh , author T. Schuster , author T. Iadecola , author S. Huang , author M. Wang , author K. P. \ Chen , author C. Chamon ,\ and\ author M. C. \ Rechtsman ,\ 10.1038/s41567-020-1007-5 journal journal Nature Physics \ volume 16 ,\ pages 989 ( year 2020 ) NoStop

    work page doi:10.1038/s41567-020-1007-5

  5. [1]

    Yang , author B

    author author Y. Yang , author B. Yang , author G. Ma , author J. Li , author S. Zhang ,\ and\ author C. Chan ,\ 10.1126/science.adf9621 journal journal Science \ volume 383 ,\ pages eadf9621 ( year 2024 ) NoStop

    doi:10.1126/science.adf9621 2024

  6. [2]

    Chen , author R.-Y

    author author Y. Chen , author R.-Y. \ Zhang , author Z. Xiong , author Z. H. \ Hang , author J. Li , author J. Q. \ Shen ,\ and\ author C. T. \ Chan ,\ 10.1038/s41467-019-10974-8 journal journal Nature communications \ volume 10 ,\ pages 1 ( year 2019 ) NoStop

    work page doi:10.1038/s41467-019-10974-8

  7. [3]

    Yang , author C

    author author Y. Yang , author C. Peng , author D. Zhu , author H. Buljan , author J. D. \ Joannopoulos , author B. Zhen ,\ and\ author M. Solja c i \'c ,\ 10.1126/science.aay3183 journal journal Science \ volume 365 ,\ pages 1021 ( year 2019 ) NoStop

    doi:10.1126/science.aay3183

  8. [4]

    Yang , author B

    author author E. Yang , author B. Yang , author O. You , author H.-C. \ Chan , author P. Mao , author Q. Guo , author S. Ma , author L. Xia , author D. Fan , author Y. Xiang , et al. ,\ 10.1103/PhysRevLett.125.033901 journal journal Physical Review Letters \ volume 125 ,\ pages 033901 ( year 2020 a ) NoStop

    work page doi:10.1103/physrevlett.125.033901

Show all 47 references
  1. [5]

    Guo , author T

    author author Q. Guo , author T. Jiang , author R.-Y. \ Zhang , author L. Zhang , author Z.-Q. \ Zhang , author B. Yang , author S. Zhang ,\ and\ author C. T. \ Chan ,\ 10.1038/s41586-021-03521-3 journal journal Nature \ volume 594 ,\ pages 195 ( year 2021 ) NoStop

    doi

  2. [8]

    \ Chen , author R.-Y

    author author Z.-G. \ Chen , author R.-Y. \ Zhang , author C. T. \ Chan ,\ and\ author G. Ma ,\ 10.1038/s41567-021-01431-9 journal journal Nature Physics \ volume 18 ,\ pages 179 ( year 2022 ) NoStop

    2022 doi

  3. [9]

    \ Sun , author X.-L

    author author Y.-K. \ Sun , author X.-L. \ Zhang , author F. Yu , author Z.-N. \ Tian , author Q.-D. \ Chen ,\ and\ author H.-B. \ Sun ,\ 10.1038/s41567-022-01669-x journal journal Nature Physics \ volume 18 ,\ pages 1080 ( year 2022 ) NoStop

    doi

  4. [10]

    You , author S

    author author O. You , author S. Liang , author B. Xie , author W. Gao , author W. Ye , author J. Zhu ,\ and\ author S. Zhang ,\ 10.1103/PhysRevLett.128.244302 journal journal Physical Review Letters \ volume 128 ,\ pages 244302 ( year 2022 ) NoStop

    doi

  5. [12]

    \ Zhang , author F

    author author X.-L. \ Zhang , author F. Yu , author Z.-G. \ Chen , author Z.-N. \ Tian , author Q.-D. \ Chen , author H.-B. \ Sun ,\ and\ author G. Ma ,\ 10.1038/s41566-022-00976-2 journal journal Nature Photonics \ volume 16 ,\ pages 390 ( year 2022 ) NoStop

    doi

  6. [13]

    \ Xu , author K

    author author J.-S. \ Xu , author K. Sun , author Y.-J. \ Han , author C.-F. \ Li , author J. K. \ Pachos ,\ and\ author G.-C. \ Guo ,\ 10.1038/ncomms13194 journal journal Nature communications \ volume 7 ,\ pages 1 ( year 2016 ) NoStop

    doi

  7. [14]

    Yang , author B

    author author Y. Yang , author B. Zhen , author J. D. \ Joannopoulos ,\ and\ author M. Solja c i \' c ,\ 10.1038/s41377-020-00384-7 journal journal Light: Science & Applications \ volume 9 ,\ pages 177 ( year 2020 b ) NoStop

    2020 doi

  8. [16]

    Gianfrate , author O

    author author A. Gianfrate , author O. Bleu , author L. Dominici , author V. Ardizzone , author M. De Giorgi , author D. Ballarini , author G. Lerario , author K. W. \ West , author L. N. \ Pfeiffer , author D. D. \ Solnyshkov , author D. Sanvitto ,\ and\ author G. Malpuech ,\...

    doi

  9. [17]

    Whittaker , author T

    author author C. Whittaker , author T. Dowling , author A. Nalitov , author A. Yulin , author B. Royall , author E. Clarke , author M. Skolnick , author I. Shelykh ,\ and\ author D. Krizhanovskii ,\ 10.1038/s41566-020-00729-z journal journal Nature Photonics \ volume 15 ,\ pag...

    doi

  10. [18]

    Iadecola , author T

    author author T. Iadecola , author T. Schuster ,\ and\ author C. Chamon ,\ 10.1103/PhysRevLett.117.073901 journal journal Phys. Rev. Lett. \ volume 117 ,\ pages 073901 ( year 2016 ) NoStop

    2016 doi

  11. [19]

    Polimeno , author A

    author author L. Polimeno , author A. Fieramosca , author G. Lerario , author L. De Marco , author M. De Giorgi , author D. Ballarini , author L. Dominici , author V. Ardizzone , author M. Pugliese , author C. Prontera , et al. ,\ 10.1364/OPTICA.427088 journal journal Optica \...

    doi

  12. [20]

    Cheng , author K

    author author D. Cheng , author K. Wang ,\ and\ author S. Fan ,\ 10.1103/PhysRevLett.130.083601 journal journal Physical Review Letters \ volume 130 ,\ pages 083601 ( year 2023 ) NoStop

    2023 doi

  13. [21]

    Bouhon , author Q

    author author A. Bouhon , author Q. Wu , author R.-J. \ Slager , author H. Weng , author O. V. \ Yazyev ,\ and\ author T. Bzdu s ek ,\ 10.1038/s41567-020-0967-9 journal journal Nature Physics \ volume 16 ,\ pages 1137 ( year 2020 ) NoStop

    doi

  14. [22]

    Jiang , author A

    author author B. Jiang , author A. Bouhon , author S.-Q. \ Wu , author Z.-L. \ Kong , author Z.-K. \ Lin , author R.-J. \ Slager ,\ and\ author J.-H. \ Jiang ,\ 10.1016/j.scib.2024.04.009 journal journal Science Bulletin \ ( year 2024 ),\ 10.1016/j.scib.2024.04.009 NoStop

    2024 doi

  15. [23]

    Yang , author B

    author author Y. Yang , author B. Zhen , author J. D. \ Joannopoulos ,\ and\ author M. Solja c i \'c ,\ 10.1038/s41377-021-00519-4 journal journal Light: Science & Applications \ volume 9 ,\ pages 177 ( year 2020 c ) NoStop

    2020 doi

  16. [24]

    Lovett , author P

    author author S. Lovett , author P. M. \ Walker , author A. Osipov , author A. Yulin , author P. U. \ Naik , author C. E. \ Whittaker , author I. A. \ Shelykh , author M. S. \ Skolnick ,\ and\ author D. N. \ Krizhanovskii ,\ 10.1038/s41377-023-01162-x journal journal Light: Sc...

    doi

  17. [25]

    Nalitov , author G

    author author A. Nalitov , author G. Malpuech , author H. Ter c as ,\ and\ author D. Solnyshkov ,\ 10.1103/PhysRevLett.114.026803 journal journal Physical review letters \ volume 114 ,\ pages 026803 ( year 2015 ) NoStop

    2015 doi

  18. [26]

    Kitagawa ,\ 10.1007/s11128-012-0425-4 journal journal Quantum Information Processing \ volume 11 ,\ pages 1107 ( year 2012 ) NoStop

    author author T. Kitagawa ,\ 10.1007/s11128-012-0425-4 journal journal Quantum Information Processing \ volume 11 ,\ pages 1107 ( year 2012 ) NoStop

    2012 doi

  19. [27]

    Harper , author R

    author author F. Harper , author R. Roy , author M. S. \ Rudner ,\ and\ author S. Sondhi ,\ 10.1146/annurev-conmatphys-031218-013721 journal journal Annual Review of Condensed Matter Physics \ volume 11 ,\ pages 345 ( year 2020 ) NoStop

    doi

  20. [28]

    author author M. S. \ Rudner , author N. H. \ Lindner , author E. Berg ,\ and\ author M. Levin ,\ 10.1103/PhysRevX.3.031005 journal journal Physical Review X \ volume 3 ,\ pages 031005 ( year 2013 ) NoStop

    2013 doi

  21. [29]

    author author J. K. \ Asb \'o th ,\ 10.1103/PhysRevB.86.195414 journal journal Physical Review B \ volume 86 ,\ pages 195414 ( year 2012 ) NoStop

    2012 doi

  22. [30]

    Kitagawa , author M

    author author T. Kitagawa , author M. S. \ Rudner , author E. Berg ,\ and\ author E. Demler ,\ 10.1103/PhysRevA.82.033429 journal journal Physical Review A \ volume 82 ,\ pages 033429 ( year 2010 ) NoStop

    2010 doi

  23. [31]

    Chen , author X

    author author C. Chen , author X. Ding , author J. Qin , author Y. He , author Y.-H. \ Luo , author M.-C. \ Chen , author C. Liu , author X.-L. \ Wang , author W.-J. \ Zhang , author H. Li , et al. ,\ 10.1103/PhysRevLett.121.100502 journal journal Physical review letters \ vol...

    doi

  24. [32]

    author author J. K. \ Asboth \ and\ author J. M. \ Edge ,\ 10.1103/PhysRevA.91.022324 journal journal Physical Review A \ volume 91 ,\ pages 022324 ( year 2015 ) NoStop

    2015 doi

  25. [33]

    Groh , author S

    author author T. Groh , author S. Brakhane , author W. Alt , author D. Meschede , author J. K. \ Asb \'o th ,\ and\ author A. Alberti ,\ 10.1103/PhysRevA.94.013620 journal journal Physical Review A \ volume 94 ,\ pages 013620 ( year 2016 ) NoStop

    doi

  26. [34]

    Chalabi , author S

    author author H. Chalabi , author S. Barik , author S. Mittal , author T. E. \ Murphy , author M. Hafezi ,\ and\ author E. Waks ,\ 10.1103/PhysRevLett.123.150503 journal journal Physical Review Letters \ volume 123 ,\ pages 150503 ( year 2019 ) NoStop

    doi

  27. [35]

    Sajid , author J

    author author M. Sajid , author J. K. \ Asb \'o th , author D. Meschede , author R. F. \ Werner ,\ and\ author A. Alberti ,\ 10.1103/PhysRevB.99.214303 journal journal Physical Review B \ volume 99 ,\ pages 214303 ( year 2019 ) NoStop

    doi

  28. [36]

    Boada , author L

    author author O. Boada , author L. Novo , author F. Sciarrino ,\ and\ author Y. Omar ,\ 10.1103/PhysRevA.95.013830 journal journal Physical Review A \ volume 95 ,\ pages 013830 ( year 2017 ) NoStop

    2017 doi

  29. [37]

    Regensburger , author C

    author author A. Regensburger , author C. Bersch , author B. Hinrichs , author G. Onishchukov , author A. Schreiber , author C. Silberhorn ,\ and\ author U. Peschel ,\ 10.1103/PhysRevLett.107.233902 journal journal Physical review letters \ volume 107 ,\ pages 233902 ( year 20...

    doi

  30. [38]

    Regensburger , author C

    author author A. Regensburger , author C. Bersch , author M.-A. \ Miri , author G. Onishchukov , author D. N. \ Christodoulides ,\ and\ author U. Peschel ,\ 10.1038/nature11298 journal journal Nature \ volume 488 ,\ pages 167 ( year 2012 ) NoStop

    doi

  31. [39]

    Wimmer , author A

    author author M. Wimmer , author A. Regensburger , author M.-A. \ Miri , author C. Bersch , author D. N. \ Christodoulides ,\ and\ author U. Peschel ,\ 10.1038/ncomms8782 journal journal Nature communications \ volume 6 ,\ pages 7782 ( year 2015 ) NoStop

    doi

  32. [40]

    Xiao , author X

    author author L. Xiao , author X. Zhan , author Z. Bian , author K. Wang , author X. Zhang , author X. Wang , author J. Li , author K. Mochizuki , author D. Kim , author N. Kawakami , et al. ,\ 10.1038/nphys4204 journal journal Nature Physics \ volume 13 ,\ pages 1117 ( year 2...

    doi

  33. [41]

    Schreiber , author A

    author author A. Schreiber , author A. G \'a bris , author P. P. \ Rohde , author K. Laiho , author M. S tefa n \'a k , author V. Poto c ek , author C. Hamilton , author I. Jex ,\ and\ author C. Silberhorn ,\ 10.1126/science.1218448 journal journal Science \ volume 336 ,\ page...

    doi

  34. [42]

    Weidemann , author M

    author author S. Weidemann , author M. Kremer , author T. Helbig , author T. Hofmann , author A. Stegmaier , author M. Greiter , author R. Thomale ,\ and\ author A. Szameit ,\ 10.1126/science.aaz8727 journal journal Science \ volume 368 ,\ pages 311 ( year 2020 ) NoStop

    doi

  35. [43]

    Bisio , author G

    author author A. Bisio , author G. M. \ D'Ariano , author M. Erba , author P. Perinotti ,\ and\ author A. Tosini ,\ 10.1103/PhysRevA.93.062334 journal journal Physical Review A \ volume 93 ,\ pages 062334 ( year 2016 ) NoStop

    2016 doi

  36. [44]

    Lorz , author E

    author author L. Lorz , author E. Meyer-Scott , author T. Nitsche , author V. Poto c ek , author A. G \'a bris , author S. Barkhofen , author I. Jex ,\ and\ author C. Silberhorn ,\ 10.1103/PhysRevResearch.1.033036 journal journal Physical Review Research \ volume 1 ,\ pages 03...

    doi

  37. [45]

    author author J. K. \ Asb \'o th \ and\ author H. Obuse ,\ 10.1103/PhysRevB.88.121406 journal journal Physical Review B—Condensed Matter and Materials Physics \ volume 88 ,\ pages 121406 ( year 2013 ) NoStop

    2013 doi

  38. [46]

    author author J. K. \ Asb \'o th \ and\ author A. Alberti ,\ 10.1103/PhysRevLett.118.216801 journal journal Physical Review Letters \ volume 118 ,\ pages 216801 ( year 2017 ) NoStop

    2017 doi

  39. [47]

    Lin , author W

    author author Q. Lin , author W. Yi ,\ and\ author P. Xue ,\ 10.1038/s41467-023-42045-4 journal journal Nature Communications \ volume 14 ,\ pages 6283 ( year 2023 ) NoStop

    2023 doi

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.