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Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion

T0 review · 2 major / 7 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A single trapped ion can simulate non-Abelian Aharonov-Bohm cages

desk verdict A workable trapped-ion blueprint for non-Abelian AB caging, built on the authors' own prior theory, with no load-bearing flaw in the numerics; worth refereeing but needs cleanup. read the letter →

arxiv 2505.00899 v1 pith:FFDIVR5Z submitted 2025-05-01 quant-ph

Zhiyuan Liu , Wanchao Yao , Sai Li , Yi Li , Yue Li , Zheng-Yuan Xue , Yiheng Lin This is my paper · ORCID
classification quant-ph
keywords non-AbeliangaugefieldAharonov-BohmcagingtrappedionsyntheticdimensionsquditFockstatelatticeinterferencematrixnilpotencyquantumsimulation
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 proposes a concrete experimental route to observe non-Abelian Aharonov-Bohm (AB) caging in a single trapped calcium ion. The key idea is to encode a one-dimensional rhombic lattice by pairing the ion's six internal Zeeman levels with its phonon Fock states, then shape the hoppings with laser carrier and red-sideband transitions so each link carries a unitary U(2) matrix. The paper's central claim is that, for a rightward interference matrix I = (U2 U1 + U4 U3)/2, particles localize when I is nilpotent, and that the non-Abelian nature gives three observable signatures: caging size larger than one, left/right asymmetry that flips with the initial state, and caging induced purely by the initial state even when I is not nilpotent. Numerical simulations including decoherence show these signatures survive in time-domain qudit-phonon detection.

What carries the argument

The load-bearing object is the rightward interference matrix $I = \frac{1}{2}(U_2 U_1 + U_4 U_3)$, built from the four $U(2)$ link variables on the rhombic lattice. A particle moving from site A to the next A has two paths, and $I$ records the average unitary accumulated along those paths; destructive interference localizes the wave function exactly when $I$ is nilpotent, and the nilpotency index bounds the caging size. The companion loop operator $W = U_3^\dagger U_4^\dagger U_2 U_1$ separates the Abelian from the non-Abelian regime: $W \propto \mathbb{1}$ collapses the problem into two identical Abelian cages, while $W \not\propto \mathbb{1}$ permits the exotic features. Experimentally, carrier and red-sideband laser transitions are tuned so that the four link matrices become $2\times 2$ blocks of Rabi frequencies and phases, realizing an arbitrary U(2) gauge field on a single ion.

What would settle it

Run the experiment, or exact numerics with the full laser-ion Hamiltonian, starting from a high Fock state such as $n=5$, and measure the fraction of population leaking beyond the predicted cage size $s=2$. If leakage grows with $n$ in a way the nilpotent-path calculation cannot reproduce, the $\sqrt{n}$ modulation is load-bearing and the claim that it only speeds up the evolution is false.

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Extended reading notes

Core claim

The paper's central claim is that non-Abelian AB caging occurs under two conditions with no Abelian analogue: either the interference matrix $I = \frac{1}{2}(U_2 U_1 + U_4 U_3)$ is nilpotent, or the initial state lies in the kernel of some power $I^m$. It argues in the appendix that if the loop operator $W = U_3^\dagger U_4^\dagger U_2 U_1$ is proportional to the identity, the problem reduces to two identical Abelian cages, forcing nilpotency index one, left-right symmetry, and no initial-state-induced caging. The simulations then demonstrate caging size $s=2$ for a nilpotent $I$, asymmetric cages with $s_r=2, s_l=1$ versus $s_r=1, s_l=2$ for two superposition initial states, and a revival of caging with a specific initial state in a non-nilpotent configuration, all under experimentally realistic parameters and Lindblad decoherence.

Load-bearing premise

The scheme's strongest unproven step is the claim that the $\sqrt{n}$ hopping amplitude in the phonon-implemented Hamiltonian leaves the caging signatures unaffected; if that bosonic modulation destroys the destructive interference at larger $n$, the sharp caged-versus-uncaged contrast in the simulations would break down.

Editorial extensions

If this is right

  • A single trapped ion can stand in for a one-dimensional synthetic lattice with U(2) gauge fields, making non-Abelian caging accessible without building a physical lattice.
  • Caging size larger than one gives a direct time-domain readout of the nilpotency index of the interference matrix.
  • Initial-state-controlled left/right asymmetry offers a switchable directional cage, potentially useful for routing or holding a single quantum excitation.
  • The scheme claims the bosonic $\sqrt{n}$ hopping modulation preserves caging signatures, so the same ion could test how bosonic statistics affect interference-based localization.
  • The electron-shelving plus blue-sideband measurement yields full qudit-phonon joint probabilities, extending single-ion readout to synthetic-lattice physics.

Reading between the lines

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

  • The same encoding could be extended to multiple ions or motional modes to realize higher-dimensional or U(N) non-Abelian cages, since the construction is not tied to one dimension.
  • The initial-state-induced caging suggests a protocol for coherent population storage: preparing the special state would hold an excitation in place even when the unitary links alone do not cage.
  • Because the $\sqrt{n}$ factor is not compensated, an experiment scanning initial Fock state $n$ would isolate how strongly the bosonic modulation distorts the ideal nilpotent condition, quantifying the paper's unproved assumption.
  • The loop-operator criterion could be turned into an interferometric witness: measure $W$ by loop traversal and correlate its non-triviality with the appearance of caging asymmetry.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. The paper proposes a trapped-ion implementation of non-Abelian Aharonov-Bohm caging on a synthetic rhombic lattice. Using the internal Zeeman sublevels of a single 40Ca+ ion and its motional Fock states, the authors show that carrier and red-sideband laser transitions can realize a U(2) gauge field on the lattice. Numerical simulations with realistic parameters demonstrate three non-Abelian signatures: caging size two, initial-state-dependent left-right asymmetry, and caging induced by a specific initial state even when the interference matrix is not nilpotent. Full Lindblad simulations with heating and dephasing show that the signatures survive realistic imperfections, and a readout protocol based on electron shelving and blue-sideband spectroscopy is provided.

Significance. If realized, this scheme would provide the first quantum-simulator demonstration of non-Abelian AB caging in a highly tunable platform with well-developed readout capabilities. The paper gives a concrete, parameterized experimental proposal, including a phonon-number-resolved detection protocol and realistic noise modeling. The predicted time-domain signatures (caging size, asymmetry, and initial-state revival) are falsifiable and directly measurable. The theoretical framework is largely taken from Ref. [18], but the contribution here is the detailed ion implementation and the numerical demonstration of its feasibility, which is a useful and timely step for the field.

major comments (2)
  1. [Experimental Scheme for a Trapped Ion, after Eq. (7)] The statement that the sqrt(n) amplitude modulation "does not affect essential signatures of non-Abelian AB caging" is asserted without proof. This is load-bearing, since all subsequent simulations use Eq. (7) rather than Eq. (1). The assertion is correct for single-particle dynamics (all paths from A_n to A_{n+1} pass through either B_n or C_n and pick up the same scalar factor, so the interference matrix is unchanged), but this argument should be given explicitly in the manuscript rather than left as a heuristic statement.
  2. [Numerical Simulation of Non-Abelian AB Caging Effect, phonon truncation paragraph] The truncation of the phonon Hilbert space at n=7 is not verified for the delocalized control cases. With J/h=2.5 kHz and simulation times up to 1 ms, a wavepacket initially at n=2 can reach the upper boundary n=7 within the displayed time window, so the "no caging" panels of Figs. 2(b), 4(a), and 5(b) may be contaminated by reflections from the truncated boundary. Please provide a convergence check (e.g., increasing n_max to 10 or 12) or restrict the evolution time to values where the boundary is not reached, in order to confirm the contrast between caged and uncaged dynamics.
minor comments (7)
  1. [Eq. (3)] The nilpotency condition is misstated: 'I^{m-1}=0, I^m≠0' should read 'I^m=0, I^{m-1}≠0' for a nilpotency index m.
  2. [Eq. (6)] The index convention in the matrices of Eq. (6) appears inconsistent with the vector convention a_n=(a↑,a↓)^T and b_n=(b↑,b↓)^T used in Eq. (1). Please specify whether rows and columns correspond to g/e or e/g indices, or transpose the matrices, so that the mapping between the laser couplings Ω_{g,e} and the link variables U_i is unambiguous.
  3. [Main text, final paragraph of 'Numerical Simulation...'] In the discussion of Fig. 4, 'changing the initial state to A↑2' should read 'to A↓2', since the two panels are initialized in different spin states.
  4. [Eq. (7)] The sqrt(n) factor appears to be an off-by-one convention: with the stated encoding (A_n = |g>⊗|n>, B_n = |e>⊗|n>), the red-sideband matrix element between B_n and A_{n+1} is proportional to sqrt(n+1), not sqrt(n). Please clarify or correct.
  5. [Text after Eq. (7)] The phrase 'as we partly use a boson to simulate a fermion' is unclear; the sqrt(n+1) enhancement is a bosonic factor and does not by itself emulate fermionic statistics. Reword for clarity.
  6. [Effects with Experimental Imperfections] The off-resonant excitation estimate only considers RSB driving the carrier. Since the scheme uses eight carrier and eight red-sideband tones simultaneously, a brief discussion of inter-tone crosstalk or a worst-case estimate would strengthen the feasibility argument.
  7. [Section 'Effects with Experimental Imperfections'] Typo: 'quantas/s' should be 'quanta/s'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the trapped-ion scheme directly implements an externally defined U(2) caging model and tests it by numerical simulation, so the central feasibility claim is not derived from its own inputs.

full rationale

The paper's derivation chain is self-contained. The theoretical framework (Eqs. (1)-(4)) is adopted from Ref. [18] as a modeling input, and the paper does not claim to re-derive non-Abelian caging from scratch; instead, it uses the nilpotency condition on I to choose link variables for the trapped-ion implementation. The central claim, that the laser-ion Hamiltonian of Eq. (7) realizes the U(2) model and that caging is observable under realistic parameters, is supported by direct numerical integration of the simulated dynamics (Figs. 2-5), including a full Lindblad master equation with independently reported decoherence rates. The √n prefactor after Eq. (7) is a genuine modification of the ideal lattice model, and the statement that it does not affect essential caging signatures is presented without a detailed proof; however, this is a correctness/presentation concern rather than a circularity, because it is a factual claim about the simulated dynamics and is not an input reused as an output. Ref. [18] is authored in part by the present authors, and it supplies the parameter-free caging criterion, but that citation is not fitted to the present data, and the claimed exclusivity of the three non-Abelian features is re-proven in Appendix A directly from unitarity. Thus, no load-bearing step reduces by construction or by self-citation to its own inputs.

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

The paper's contribution is an experimental blueprint, not a new dynamical law. The main free choices are the gauge link matrices, which are deliberately selected to realize the known nilpotency condition. The fragile assumptions are the sqrt(n) bosonic modulation and the multi-tone addressability of 16 transitions.

free parameters (5)
  • Link matrices U1, U2, U3, U4 = Specific 2x2 unitaries in Figs. 2-5, e.g., U2=[[0,1],[1,0]] in Fig 2(a)
    Hand-chosen gauge-field links that satisfy the nilpotency condition or illustrate non-nilpotent cases; the simulated dynamics and caging features depend on these choices.
  • Initial state = A-up-2, (A-down-2 + i A-up-2)/sqrt(2), A-down-2
    Selected initial wave packets determine which non-Abelian caging feature is observed; in the non-nilpotent case, caging only occurs for specific states.
  • Phonon truncation n <= 7 = 7
    The simulation truncates the Fock-state ladder at n=7; the paper asserts this does not affect the observation, but no convergence check is shown.
  • Decoherence rates in Lindblad simulation = n-dot = 0.2 quanta/s, T2^m = 35 ms, T2^s = 40 ms
    Chosen as representative ion-trap values from Refs. [52,53]; the imperfection results depend on these choices.
  • Experimental parameters (trap frequency, Lamb-Dicke factor, hopping rate) = omega = 2 pi x 2 MHz, eta = 0.1, J/h = 2.5 kHz
    Chosen to match common 40Ca+ conditions; the feasibility claims assume these values are realizable.
assumptions (5)
  • domain assumption Non-Abelian AB caging occurs iff the interference matrix I = (U2U1+U4U3)/2 is nilpotent
    Taken from Ref [18] and used as the design criterion; not re-derived in this paper.
  • domain assumption The ion-laser interaction in the Lamb-Dicke limit is described by Eq (5) with separate carrier and red-sideband transitions
    Standard trapped-ion physics (Refs. [49,51]); the effective lattice model Eq (7) follows from this.
  • ad hoc to paper The sqrt(n) factor in Eq (7) does not alter the caging signatures
    Asserted after Eq (7) with a heuristic argument (only accelerates evolution), but no proof; this is load-bearing for the mapping.
  • ad hoc to paper The phonon number truncation at n=7 is faithful
    The simulation truncates the state space; the paper states this without affecting the observation but provides no convergence analysis.
  • domain assumption Each of the 16 carrier and red-sideband transitions can be independently programmed in amplitude and phase
    The scheme relies on standard AOM control, but the frequency addressing constraints (magnetic field, polarization rules) and cross-talk between different Zeeman transitions are not quantified.

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Pith. "Pith review of Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion." pith.science (2026). https://pith.science/paper/FFDIVR5Z

@misc{pith2026250500899,
  author       = {Pith},
  title        = {Pith review of: Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FFDIVR5Z}},
  note         = {Machine review of arXiv:2505.00899}
}
abstract

In the lattice system, when the synthetic flux reaches a $\pi$ phase along a closed loop under the synthetic gauge field, destructive interference occurs and gives rise to the localization phenomenon. This is known as the Aharonov-Bohm (AB) caging effect. It provides a powerful tool for the study of quantum transportation and dynamical effects. In the system where lattice sites possess internal structure and the underlying gauge field is non-Abelian, localization can also occur, forming the non-Abelian AB caging. Here, we propose an experimental scheme to synthesize non-Abelian gauge fields with a single trapped ion by coupling multiple internal levels and Fock states in its motion via laser fields. In contrast to the Abelian AB caging, we numerically observe that the non-Abelian AB caging occurs either when the interference matrix is nilpotent, or when the initial state is specifically set. Our experimental scheme broadens the study of localization phenomena and provides a novel tool for the study of non-Abelian physics.

Figures

Figures reproduced from arXiv: 2505.00899 by the authors.

Figure 1
Figure 1. FIG. 1: (a) Schematic illustration of a one-dimensional (1D) periodic rhombic lattice. The lattice is composed of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 5
Figure 5. FIG. 5: Simulation of the non-Abelian AB caging effect by laser-ion interaction under the full Lindblad master [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. FIG. 6: Electron shelving and blue sideband transition protocol for population measurement of (a) [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

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Reference graph

Works this paper leans on

60 extracted references · 50 canonical work pages

  1. [18]

    Gligori´ c, P

    G. Gligori´ c, P. P. Beliˇ cev, D. Leykam, and A. Maluckov, Nonlinear symmetry breaking of aharonov-bohm cages, Phys. Rev. Lett. 99, 013826 (2019)

    work page 2019

  2. [1]

    Liu et al., Synthetic π-flux system in 2d superconduct- ing qubit array with tunable coupling, arXiv e-prints , arXiv:2501.06743 (2025)

    Y. Liu et al., Synthetic π-flux system in 2d superconduct- ing qubit array with tunable coupling, arXiv e-prints , arXiv:2501.06743 (2025)

    arXiv 2025

  3. [2]

    V. Neef, J. Pinske, F. Klauck, L. Teuber, M. Kremer, M. Ehrhardt, M. Heinrich, S. Scheel, and A. Szameit, Three-dimensional non-abelian quantum holonomy, Nat. Phys. 19, 30 (2023)

    work page 2023

  4. [3]

    Shan, Y.-K

    Z.-L. Shan, Y.-K. Sun, R. Tao, Q.-D. Chen, Z.-N. Tian, and X.-L. Zhang, Non-abelian holonomy in degenerate non-hermitian systems, Phys. Rev. Lett. 133, 053802 (2024)

    2024

  5. [4]

    CAR-π” denotes resonant transition between internal states between the S1/2 and D5/2 manifolds. “BSB

    describes the interference of the particle moving leftward. However, since index( I) = index( I†), we only need to focus on one of them in the discussion. To illustrate the role that index(I) plays and for the convenience of the subsequent discussion, we here define the caging size s of the AB caging effect as follows. For a particle initially populated i...

    work page

  6. [5]

    Q. Wang, C. Ye, and L.-B. Fu, Quantum cyclotron orbits of a neutral atom trapped in a triple well with a synthetic gauge field, Chin. Phys. Lett. 29, 060301 (2012)

    work page 2012

  7. [6]

    Zhang et al

    J. Zhang et al. , Synthetic multidimensional aharonov- bohm cages in fock state lattices, Phys. Rev. Lett. 134, 070601 (2025)

    work page 2025

  8. [7]

    Bermudez, T

    A. Bermudez, T. Schaetz, and D. Porras, Synthetic gauge fields for vibrational excitations of trapped ions, Phys. Rev. Lett. 107, 150501 (2011)

    2011

Show all 60 references
  1. [8]

    Vidal, R

    J. Vidal, R. Mosseri, and B. Dou¸ cot, Aharonov-bohm cages in two-dimensional structures, Phys. Rev. Lett. 81, 5888 (1998)

    1998

  2. [9]

    It has provided an impor- tant tool for the study of quantum transportation and dynamical effects [11–16]

    and Rydberg atom [10]. It has provided an impor- tant tool for the study of quantum transportation and dynamical effects [11–16]. However, AB caging has been largely restricted to the system where the lattice sites have no internal structure, and the underlying gauge field is ...

    2025 arXiv

  3. [10]

    H. Li, Z. Dong, S. Longhi, Q. Liang, D. Xie, and B. Yan, Aharonov-bohm caging and inverse anderson transition in ultracold atoms, Phys. Rev. Lett. 129, 220403 (2022)

    2022

  4. [11]

    Mukherjee, M

    S. Mukherjee, M. Di Liberto, P. ¨Ohberg, R. R. Thomson, and N. Goldman, Experimental observation of aharonov- bohm cages in photonic lattices, Phys. Rev. Lett. 121, 075502 (2018)

    2018

  5. [12]

    T. Chen, C. Huang, I. Velkovsky, K. R. Hazzard, J. P. Covey, and B. Gadway, Strongly interacting rydberg atoms in synthetic dimensions with a magnetic flux, Nat. Commun. 15, 2675 (2024)

    2024

  6. [13]

    Kremer, I

    M. Kremer, I. Petrides, E. Meyer, M. Heinrich, O. Zil- berberg, and A. Szameit, A square-root topological insu- lator with non-quantized indices realized with photonic aharonov-bohm cages, Nat. Commun. 11, 907 (2020)

    2020

  7. [14]

    K. Fang, Z. Yu, and S. Fan, Photonic aharonov-bohm effect based on dynamic modulation, Phys. Rev. Lett. 108, 153901 (2012)

    2012

  8. [15]

    Noguchi, Y

    A. Noguchi, Y. Shikano, K. Toyoda, and S. Urabe, Aharonov–bohm effect in the tunnelling of a quantum rotor in a linear paul trap, Nat. Commun. 5, 3868 (2014)

    2014

  9. [16]

    Kawaguchi, D

    Y. Kawaguchi, D. Smirnova, F. Komissarenko1, S. Kir- iushechkina, A. Vakulenko, M. Li, A. Al` u, and A. B. Khanikaev, Pseudo-spin switches and aharonov-bohm effect for topological boundary modes, Sci. Adv. 10, eadn6095 (2024)

    2024

  10. [17]

    M. D. Liberto, S. Mukherjee, and N. Goldman, Nonlinear dynamics of aharonov-bohm cages, Phys. Rev. Lett. 100, 043829 (2019)

    2019

  11. [19]

    Liang, Z

    Q. Liang, Z. Dong, J.-S. Pan, H. Wang, H. Li, Z. Yang, W. Yi, and B. Yan, Chiral dynamics of ultracold atoms under a tunable SU (2) synthetic gauge field, Nat. Phys. 20, 1738 (2024)

    2024

  12. [20]

    Li, Z.-Y

    S. Li, Z.-Y. Xue, M. Gong, and Y. Hu, Non-abelian aharonov-bohm caging in photonic lattices, Phys. Rev. A 102, 023524 (2020)

    2020

  13. [21]

    Zhang, H

    W. Zhang, H. Wang, H. Sun, and X. Zhang, Non- abelian inverse anderson transitions, Phys. Rev. Lett. 130, 206401 (2023)

    2023

  14. [22]

    Foss-Feig, G

    M. Foss-Feig, G. Pagano, A. C. Potter, and N. Y. Yao, Progress in trapped-ion quantum simulation, Annu. Rev. Condens. Matter Phys. 16, 145 (2024)

    2024

  15. [23]

    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 (2022)

    2022

  16. [24]

    Meth et al., Simulating two-dimensional lattice gauge theories on a qudit quantum computer, Nat

    M. Meth et al., Simulating two-dimensional lattice gauge theories on a qudit quantum computer, Nat. Phys. 21, 570 (2025)

    2025

  17. [25]

    Shapira, T

    Y. Shapira, T. Manovitz, N. Akerman, A. Stern, and R. Ozeri, Quantum simulations of interacting systems with broken time-reversal symmetry, Phys. Rev. X 13, 021021 (2023)

    2023

  18. [26]

    Hauke, D

    P. Hauke, D. Marcos, M. Dalmonte, and P. Zoller, Quan- tum simulation of a lattice schwinger model in a chain of trapped ions, Phys. Rev. X 3, 041018 (2013)

    2013

  19. [27]

    Andrade, Z

    B. Andrade, Z. Davoudi, T. Graß, M. Hafezi, G. Pagano, and A. Seif, Engineering an effective three-spin hamilto- nian in trapped-ion systems for applications in quantum simulation, Quant. Sci. Technol. 7, 034001 (2022)

    2022

  20. [28]

    Davoudi, M

    Z. Davoudi, M. Hafezi, C. Monroe, G. Pagano, A. Seif, and A. Shaw, Towards analog quantum simulations of lattice gauge theories with trapped ions, Phys. Rev. Res. 2, 023015 (2020)

    2020

  21. [29]

    Davoudi, N

    Z. Davoudi, N. M. Linke, and G. Pagano, Toward simu- lating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach, Phys. Rev. Res. 3, 043072 (2021)

    2021

  22. [30]

    Calaj´ o, G

    G. Calaj´ o, G. Magnifico, C. Edmunds, M. Ringbauer, S. Montangero, and P. Silvi, Digital quantum simulation of a (1+ 1) D SU (2) lattice gauge theory with ion qudits, PRX Quantum 5, 040309 (2024)

    2024

  23. [31]

    Wang, Y.-K

    Y. Wang, Y.-K. Wu, Y. Jiang, M.-L. Cai, B.-W. Li, Q.- X. Mei, B.-X. Qi, Z.-C. Zhou, and L.-M. Duan, Realiz- ing synthetic dimensions and artificial magnetic flux in a trapped-ion quantum simulator, Phys. Rev. Lett. 132, 130601 (2024)

    2024

  24. [32]

    W. Hou, H. Tang, Q. Xu, and Y. Lin, Experimental pro- posal on non-hermitian skin effect by two-dimensional quantum walk with a single trapped ion, Chin. Phys. Lett. 41, 040301 (2024)

    2024

  25. [33]

    Z. Dong, X. Wu, Y. Yang, P. Yu, X. Chen, and L. Yuan, Temporal multilayer structures in discrete phys- ical systems towards arbitrary-dimensional non-abelian aharonov-bohm interferences, Nat. Commun. 15, 7392 (2024)

    2024

  26. [34]

    Y. Yang, C. Peng, D. Zhu, H. Buljan, J. D. Joannopoulos, 10 B. Zhen, and M. Soljaˇ ci´ c, Synthesis and observation of non-abelian gauge fields in real space, Science 365, 1021 (2019)

    2019

  27. [35]

    Breach, R.-J

    O. Breach, R.-J. Slager, and F. N. ¨Unal, Interferometry of non-abelian band singularities and euler class topology, Phys. Rev. Lett. 133, 093404 (2024)

    2024

  28. [36]

    Y.-F. Wang, H. Yao, Z.-C. Gu, C.-D. Gong, and D. N. Sheng, Non-abelian quantum hall effect in topological flat bands, Phys. Rev. Lett. 108, 126805 (2012)

    2012

  29. [37]

    P. M. Lenggenhager, J. Maciejko, and T. c. v. Bzduˇ sek, Non-abelian hyperbolic band theory from supercells, Phys. Rev. Lett. 131, 226401 (2023)

    2023

  30. [38]

    Q. Wu, A. A. Soluyanov, and T. Bzduˇ sek, Non-abelian band topology in noninteracting metals, Science 365, 1273 (2019)

    2019

  31. [39]

    Zhang, L.-C

    J. Zhang, L.-C. Kwek, E. Sj¨ oqvist, D. M. Tong, and P. Zanardi, Quantum computation in noiseless subsys- tems with fast non-abelian holonomies, Phys. Rev. A 89, 042302 (2014)

    2014

  32. [40]

    O. You, S. Liang, B. Xie, W. Gao, W. Ye, J. Zhu, and S. Zhang, Observation of non-abelian thouless pump, Phys. Rev. Lett. 128, 244302 (2022)

    2022

  33. [41]

    Fan, Simulation of projective non-abelian anyons for quantum computation, Chin

    H. Fan, Simulation of projective non-abelian anyons for quantum computation, Chin. Phys. Lett. 40, 070305 (2023)

    2023

  34. [42]

    Xu et al., Digital simulation of projective non-abelian anyons with 68 superconducting qubits, Chin

    S. Xu et al., Digital simulation of projective non-abelian anyons with 68 superconducting qubits, Chin. Phys. Lett. 40, 060301 (2023)

    2023

  35. [43]

    Abilio, P

    C. Abilio, P. Butaud, T. Fournier, B. Pannetier, J. Vi- dal, S. Tedesco, and B. Dalzotto, Magnetic field induced localization in a two-dimensional superconducting wire network, Phys. Rev. Lett. 83, 5102 (1999)

    1999

  36. [44]

    C. Naud, G. Faini, and D. Mailly, Aharonov-bohm cages in 2d normal metal networks, Phys. Rev. Lett. 86, 5104 (2001)

    2001

  37. [45]

    Fang and L.-L

    M. Fang and L.-L. Sun, Spin filter based on an aharonov– bohm interferometer with rashba spin–orbit effect, Chin. Phys. Lett. 25, 3389 (2008)

    2008

  38. [46]

    Zhang and Y.-S

    X.-M. Zhang and Y.-S. Duan, The topological structure of the su(2) chern-simons topological current in the four- dimensional quantum hall effect, Chin. Phys. Lett. 27, 077301 (2010)

    2010

  39. [47]

    X. Song, T. Liu, J. Bian, P. Lu, Y. Liu, F. Zhu, and L. Luo, Non-hermitian chsh* game with a single trapped- ion qubit, Chin. Phys. Lett. 41, 060301 (2024)

    2024

  40. [48]

    Vidal, B

    J. Vidal, B. Dou¸ cot, R. Mosseri, and P. Butaud, Interac- tion induced delocalization for two particles in a periodic potential, Phys. Rev. Lett. 85, 3906 (2000)

    2000

  41. [49]

    Goldman, A

    N. Goldman, A. Kubasiak, P. Gaspard, and M. Lewen- stein, Ultracold atomic gases in non-abelian gauge po- tentials: The case of constant wilson loop, Phys. Rev. A 79, 023624 (2009)

    2009

  42. [50]

    Meekhof, C

    D. Meekhof, C. Monroe, B. King, W. M. Itano, and D. J. Wineland, Generation of nonclassical motional states of a trapped atom, Phys. Rev. Lett. 76, 1796 (1996)

    1996

  43. [51]

    D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, Experimental issues in coherent quantum-state manipulation of trapped atomic ions, J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998)

    1998

  44. [52]

    Hempel, B

    C. Hempel, B. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, and C. Roos, Entanglement-enhanced detection of single-photon scattering events, Nat. Photonics 7, 630 (2013)

    2013

  45. [53]

    C. J. Foot, Atomic physics , Vol. 7 (Oxford university press, 2005)

    2005

  46. [54]

    C. H. Valahu et al., Direct observation of geometric-phase interference in dynamics around a conical intersection, Nat. Chem. 15, 1503 (2023)

    2023

  47. [55]

    Hempel et al

    C. Hempel et al. , Quantum chemistry calculations on a trapped-ion quantum simulator, Phys. Rev. X 8, 031022 (2018)

    2018

  48. [56]

    Cai and D.-W

    H. Cai and D.-W. Wang, Topological phases of quantized light, Nat. Sci. Rev. 8, nwaa196 (2021)

    2021

  49. [57]

    Deng et al., Observing the quantum topology of light, Science 378, 966 (2022)

    J. Deng et al., Observing the quantum topology of light, Science 378, 966 (2022)

    2022

  50. [58]

    Goldman, G

    N. Goldman, G. Juzeli¯ unas, P. ¨Ohberg, and I. B. Spiel- man, Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys. 77, 126401 (2014)

    2014

  51. [59]

    Di Liberto, N

    M. Di Liberto, N. Goldman, and G. Palumbo, Non- abelian bloch oscillations in higher-order topological in- sulators, Nat. Commun. 11, 5942 (2020)

    2020

  52. [60]

    Goldman, I

    N. Goldman, I. Satija, P. Nikolic, A. Bermudez, M. A. Martin-Delgado, M. Lewenstein, and I. Spielman, Real- istic time-reversal invariant topological insulators with neutral atoms, Phys. Rev. Lett. 105, 255302 (2010)

    2010

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