Pith. sign in

REVIEW 3 major objections 4 minor 58 references

Unveiling the Self-Orthogonality at Exceptional Points in Driven $\mathcal{PT}$-Symmetric Systems

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read In a driven $\mathcal{PT}$-symmetric three-band lattice, the Rabi frequency of resonant pumping diverges as the target band approaches an exceptional point, and this divergence shows up in the slow oscillations of the total power.

desk verdict A clean three-band PT lattice with a nice finite-distance match, but the RWA breakdown in the divergent regime undermines the power-oscillation claim at the EP. read the letter →

arxiv 2507.10232 v1 pith:TYTKU7EB submitted 2025-07-14 cond-mat.other cond-mat.mes-hallquant-ph

Alexander Fritzsche , Riccardo Sorbello , Ronny Thomale , Alexander Szameit This is my paper · ORCID
classification cond-mat.othercond-mat.mes-hallquant-ph
keywords exceptionalpointsparity-timesymmetrynon-HermitiansystemsRabioscillationsself-orthogonalitydrivenlatticemodelsFloquetstabilitytotalpower
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

The paper establishes that self-orthogonality at an exceptional point—the vanishing overlap between a right eigenstate and its left partner—can be read off from the dynamics of a driven parity-time-symmetric lattice. In a three-band model where two bands meet at an exceptional point and a third band serves as the pumping partner, the Rabi frequency of resonant population transfer diverges as momentum approaches the exceptional point. The paper further argues that the total power of the system, which is far easier to measure than the full state, oscillates with this same diverging Rabi frequency, making power oscillations a direct observable of self-orthogonality. If correct, this gives metamaterial platforms such as photonic lattices or topolectrical circuits a simple route to probing exceptional-point physics without resolving individual eigenstates.

What carries the argument

The central object is the biorthogonal Rabi frequency defined in Eq. (1), $$\Omega_R(k) = \sqrt{|\langle \psi^L_{j;k}|V(k)|\psi^R_{i;k}\rangle| \, |\langle \psi^L_{i;k}|V(k)|\psi^R_{j;k}\rangle|}.$$ It carries the argument because near the exceptional point the target right eigenstate coalesces with its partner, so $\langle \psi^L | \psi^R \rangle = \varepsilon \to 0$; after rescaling only the left eigenstates by $\varepsilon^{-1}$, each matrix element in the product scales as $\varepsilon^{-1/2}$, giving $\Omega_R \propto \varepsilon^{-1/2}$. The companion mechanism is the power formula of Eq. (5), in which the cross-term $\sin(\Omega_R t)\,\mathrm{Re}[\alpha e^{i\Omega_P t} \langle \psi^R_t | \psi^R_{in}\rangle]$ makes the slow envelope of the total power oscillate at exactly $\Omega_R$.

What would settle it

The claim would be falsified if, in a finite chain with $N=60$ unit cells and periodic boundary conditions at $\tau = 10^{-3}$, the slow-oscillation frequency of the metric-tensor-weighted power from Eq. (A2) disagreed with the plain $|\psi(t)|^2$ frequency from Eq. (A16) as $k$ approaches $k_{\mathrm{EP}}^+$; that disagreement would mean the proposed observable depends on the normalization choice.

Watch

Extended reading notes

Core claim

The paper claims that in a driven $\mathcal{PT}$-symmetric three-band sawtooth lattice, resonant pumping between a gapped band and a band that forms an exceptional point with a flat band produces Rabi oscillations whose frequency $\Omega_R$ diverges as $\varepsilon^{-1/2}$, because the target eigenstate becomes self-orthogonal, meaning $\langle \psi^L | \psi^R \rangle = \varepsilon \to 0$. It also claims that the total power $|\psi(t)|^2$ of the $\mathcal{PT}$-symmetric system oscillates with the same slow Rabi frequency, so measuring power oscillations provides a direct experimental observable for self-orthogonality. For a finite chain with $N=60$ unit cells and periodic boundary conditions at driving parameter $\tau = 10^{-3}$, the frequencies extracted from the power oscillations match the analytically expected $\Omega_R(k)$ curve, supporting the claim.

Load-bearing premise

The result stands on the assumption that the measured power signal is independent of how the left eigenstates are normalized, and that the two-level rotating-wave description remains valid at the point where the Rabi frequency and oscillation amplitude diverge.

Editorial extensions

If this is right

  • The slow envelope of the total power oscillates at $\Omega_R$, so a time-resolved measurement of total power at fixed momentum directly maps out the divergence of $\Omega_R$ near the exceptional point.
  • Because the system is translationally invariant, power oscillations within a single unit cell follow the same Rabi frequency as the total power, giving a local observable usable in finite experimental geometries.
  • Near the exceptional point, the divergence of $\Omega_R$ makes the resonant pumping increasingly robust against detuning of the pump frequency.
  • The exceptional points of the Floquet Hamiltonian occur at the same momenta as those of the static Hamiltonian, so the diverging Rabi frequency persists in the stably driven regime.

Reading between the lines

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

  • A testable extension is to repeat the calculation with a metric-tensor-weighted power, as Appendix A1 sets up, and check whether the slow-oscillation frequency still matches $\Omega_R(k)$; if not, the proposed observable is tied to the plain $\mathrm{L}^2$ normalization rather than to normalization-independent physics.
  • If the mechanism is generic, any non-Hermitian platform with a two-level transition coupled to a coalescing eigenstate, not only the sawtooth lattice, should show an $\varepsilon^{-1/2}$ divergence of the Rabi frequency, which could be tested in topolectrical circuits, microwave resonators, or photonic waveguide arrays.
  • The detuning robustness near the exceptional point implies a practical feature: population transfer becomes increasingly insensitive to frequency errors the closer the drive is to the exceptional point, a non-Hermitian effect without a Hermitian counterpart.
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

3 major / 4 minor

Summary. The paper studies a driven three-band PT-symmetric lattice model with a flat band and exceptional points (EPs), and claims that the Rabi frequency associated with resonant pumping diverges as the system approaches an EP due to the self-orthogonality of the coalescing eigenstates. It further proposes that the total power of the system, which oscillates in PT-symmetric systems, exhibits slow oscillations at this Rabi frequency and therefore provides a direct experimental observable for self-orthogonality. The manuscript provides an analytic derivation of the Rabi frequency from biorthogonal perturbation theory, a Floquet stability analysis of the driven model, and numerical simulations of a finite chain with periodic boundary conditions that are compared with the analytic formula.

Significance. If the central claim were fully established, the paper would offer an experimentally accessible signature of self-orthogonality at exceptional points in a tractable lattice model, which would be relevant for photonic and topolectrical metamaterial platforms. The work has clear strengths: the model is concrete, the algebraic derivations in Appendices A and B are internally consistent, the RWA-based formula in Eq. (1) is stated explicitly, and the numerical curves in Figs. 3 and 4 match the derived expressions at finite distances from the EP. The stability analysis via Floquet quasi-energies is a useful practical addition. However, the observable claim is weakened by unresolved normalization and rotating-wave issues, and the numerics do not probe the divergent regime; these concerns are load-bearing for the paper's main message rather than cosmetic.

major comments (3)
  1. [Appendix A.1-A.2, Eqs. (A1)-(A2) and (A16)] The paper asserts in Appendix A.1 that physical observables must be computed with the metric tensor G defined in Eq. (A1) and that expectation values take the form of Eq. (A2) to be independent of the biorthogonal normalization. However, the power formula in Eq. (A16) is the plain L2 norm |ψ_k(t)|^2, not ⟨ψ|G|ψ⟩. Since the wavefunction in Eq. (A14) contains α ~ ε^{-1} while the right target state has unit norm, this L2 power grows like ε^{-2} as the EP is approached. The claimed normalization independence is therefore not actually used in the derivation of the proposed observable, and the power signal may be an artifact of the convention in which only left eigenstates are rescaled by ε^{-1}. This undermines the central claim that power oscillations provide a direct, convention-independent observable of self-orthogonality.
  2. [Appendix A, Eqs. (A8)-(A13)] The rotating-wave approximation is applied by discarding the term e^{-i(Δε+Ω_P)t} in Eq. (A8), which is valid only when the off-diagonal matrix elements are small compared with Δε (or Ω_P). In the biorthonormal convention adopted in the paper, the matrix element ⟨ψ_L^t|V|ψ_R^in⟩ scales as ε^{-1} while the resulting Ω_R scales as ε^{-1/2}. Consequently, for sufficiently small ε the neglected counter-rotating term is no longer perturbative and the two-level truncation breaks down exactly in the regime where the divergence is predicted. The derivation of Eq. (1) and of the power formula in Eq. (5) therefore does not establish the observable divergence without an additional argument or an exact treatment that goes beyond the RWA.
  3. [Section IV, Fig. 4(d)] The red crosses in Fig. 4(d), obtained from the power-oscillation spectra of a finite N=60 chain, sample only momenta where Ω_R is at most about 10 J1(τ). With τ=10^{-3}, J1(τ)≈5×10^{-4} in units of the hopping, so the numerically accessed Ω_R remains much smaller than the pumping frequency Ω_P. These data lie in the RWA-valid regime and are consistent with the theoretical curve, but they do not probe the ε→0 limit; no error bars are shown, and no scaling analysis or extrapolation toward k_EP is presented. Thus the numerical evidence does not support the claimed divergence of the power-oscillation frequency at the exceptional point.
minor comments (4)
  1. [Section III, Eq. (2)] The Bessel-function arguments J0(τ/2) and J1(τ/2) appear in the Bloch Hamiltonian, but the relation of τ to the driving amplitude and the origin of the factor 1/2 are only explained later in Appendix B, Eq. (B25); a sentence in the main text defining τ would improve readability.
  2. [Figure 1] The schematic rows use the notation ⟨ψ_L^2|ψ_R^2⟩ = ε and ⟨ψ_L^2|ψ_R^2⟩ = 0 without clearly indicating which eigenstates are being plotted; adding explicit labels and consistent subscripts for the initial, target, and left states would make the figure less ambiguous.
  3. [Appendix B, Eq. (B5)] The expression 'γϵ0 = 1√ϵ0 sqrt(...)' appears to contain a typographical ambiguity; it should read 1/√ϵ0, and the same notation should be used consistently in Eq. (B9).
  4. [Section IV, Eq. (5)] The notation |ψ(t)|^2 is used both for the L2 norm of the state and for the expectation value of a projector, which can confuse readers; using the norm symbol ∥|ψ(t)⟩∥^2 for the total power would be clearer.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Rabi-frequency divergence and power-oscillation observable are derived within the paper and verified by full numerics; self-citations are contextual only.

full rationale

The central derivation chain is self-contained rather than circular. The Rabi frequency in Eq. (1) is defined through biorthogonal matrix elements and derived in Appendix A.1 from the Schrödinger equation under the rotating-wave approximation. The ε^{-1/2} scaling follows from the chosen biorthonormal normalization in which left eigenstates are rescaled by ε^{-1}, but the product defining Ω_R is invariant under biorthonormal rescalings of left and right states, so the divergence is not merely a normalization artifact. The power-oscillation result, Eq. (5) and Eq. (A16), is obtained by inserting the RWA solution into the L2 norm and is then independently confirmed by real-space Floquet simulations (Fig. 4), where extracted power-oscillation frequencies match the analytical curve without any fitted parameter. The paper's reliance on Ref. [46] for the Rabi-divergence idea and Ref. [48] for the biorthogonal metric formalism uses external prior work, not self-citations. The self-citations present (e.g., Refs. [8,9,26,27]) appear as background on non-Hermitian topology and experimental platforms and are not load-bearing for the derivation. The main caveats—whether the rotating-wave approximation remains valid when one off-diagonal matrix element diverges as ε^{-1}, and whether the L2 power used in Eq. (5) is consistent with the metric-tensor prescription of Appendix A.1—are correctness and robustness concerns, not instances of circularity: the paper's equations do not reduce to their own inputs by construction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central result depends on the biorthogonal normalization convention, the rotating-wave approximation, and a fine-tuned gain/loss value that creates the exceptional points. The parameters v/u and tau are chosen for numerical convenience and stability, not fitted to an external dataset. No new entities are introduced.

free parameters (2)
  • v/u coupling ratio = 1.075
    Chosen so that k+/-EP fall between discrete momenta of the N=60 chain, avoiding exact degeneracy at sampled k; not fitted to a target observable.
  • driving amplitude tau = 10^-3
    Chosen in the Floquet-stable region of Fig. 3(a); small enough for the Jacobi-Anger first-order truncation.
assumptions (5)
  • domain assumption Biorthogonal formalism and metric tensor for non-Hermitian observables
    Used in Section II and Appendix A1; standard in non-Hermitian quantum mechanics, cited to Refs. [1,47,48].
  • domain assumption Rotating wave approximation
    Used to derive the two-level Rabi equations (A8-A13); assumes fast-oscillating terms average out, which may fail when Omega_R diverges.
  • standard math Jacobi-Anger expansion truncated at first order in tau
    Appendix B2, Eq. B22; higher-order terms are neglected because tau << 1 and scale as 1/(2^alpha alpha!).
  • ad hoc to paper Flat-band fine-tuning condition for the gain/loss parameter
    The relation gamma = J0(tau/2) u sqrt(2 - J0(tau/2)^2 u^2 / (J0(tau)^2 v^2)) is enforced so that two bands coalesce at EPs; this is a model design assumption.
  • domain assumption Periodic boundary conditions and momentum conservation under the drive
    Simulations use PBC and assume the drive is translationally invariant so momentum does not mix, as stated in Section III and Appendix D.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Unveiling the Self-Orthogonality at Exceptional Points in Driven $\mathcal{PT}$-Symmetric Systems." pith.science (2026). https://pith.science/paper/TYTKU7EB

@misc{pith2026250710232,
  author       = {Pith},
  title        = {Pith review of: Unveiling the Self-Orthogonality at Exceptional Points in Driven $\mathcalPT$-Symmetric Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TYTKU7EB}},
  note         = {Machine review of arXiv:2507.10232}
}
read the original abstract

We explore the effect of self-orthogonality at exceptional points (EPs) in non-Hermitian Parity-Time-symmetric systems. Using a driven three-band lattice model, we show that the Rabi frequency diverges as the system approaches an EP due to the coalescence of eigenstates. We demonstrate that this divergence manifests in experimentally accessible power oscillations, establishing a direct observable for self-orthogonality. Our results provide a pathway for probing EP physics in various metamaterial platforms.

Figures

Figures reproduced from arXiv: 2507.10232 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of the consequences of the self [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Quasi-one-dimensional three-band model for the re [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Analysis of the dynamical stability with respect to the driving parameter [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Power oscillations as a function of propagation time. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Fig.5. Gain (+i [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Schematic of the unit cell of the static [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Real and imaginary part of the quasi-energy bands [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Bi-orthogonal probability of the wave function onto the three bands at [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Efficiency of the Rabi pumping as a function of the detuning. The efficiency of the process is defined as the maximum [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 42 canonical work pages

  1. [1]

    Moiseyev, Non-Hermitian quantum mechanics(Cam- bridge University Press, 2011)

    N. Moiseyev, Non-Hermitian quantum mechanics(Cam- bridge University Press, 2011)

    2011

  2. [2]

    Z. G. Yuto Ashida and M. Ueda, Ad- vances in Physics 69, 249 (2020), https://doi.org/10.1080/00018732.2021.1876991

    arXiv 2020

  3. [3]

    E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Reviews of Modern Physics 93, 015005 (2021)

    work page 2021

  4. [4]

    Kawabata, K

    K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Phys. Rev. X 9, 041015 (2019)

    2019

  5. [5]

    Y. Cao, Y. Li, and X. Yang, Phys. Rev. B 103, 075126 (2021)

    work page 2021

  6. [6]

    H. Wang, X. Zhang, J. Hua, D. Lei, M. Lu, and Y. Chen, Journal of Optics 23, 123001 (2021)

    work page 2021

  7. [7]

    C. H. Lee and R. Thomale, Phys. Rev. B 99, 201103 (2019)

    work page 2019

  8. [8]

    Hofmann, T

    T. Hofmann, T. Helbig, F. Schindler, N. Salgo, M. Brzezi´ nska, M. Greiter, T. Kiessling, D. Wolf, A. Voll- hardt, A. Kabaˇ si, C. H. Lee, A. Biluˇ si´ c, R. Thomale, and T. Neupert, Phys. Rev. Res. 2, 023265 (2020)

    2020

Show all 58 references
  1. [9]

    Weidemann, M

    S. Weidemann, M. Kremer, T. Helbig, T. Hof- mann, A. Stegmaier, M. Greiter, R. Thomale, and A. Szameit, Science 368, 311 (2020), https://www.science.org/doi/pdf/10.1126/science.aaz8727

    2020 doi

  2. [10]

    C. M. Bender and S. Boettcher, Phys. Rev. Lett.80, 5243 (1998)

    1998

  3. [11]

    C. M. Bender, Journal of Physics: Conference Series 631, 012002 (2015)

    2015

  4. [12]

    Doppler, A

    J. Doppler, A. A. Mailybaev, J. B¨ ohm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moi- seyev, and S. Rotter, Nature 537, 76 (2016)

    2016

  5. [13]

    A. U. Hassan, B. Zhen, M. Soljaˇ ci´ c, M. Khajavikhan, and D. N. Christodoulides, Phys. Rev. Lett. 118, 093002 (2017)

    2017

  6. [14]

    A. V. Sokolov, A. A. Andrianov, and F. Cannata, Jour- nal of Physics A: Mathematical and General 39, 10207 (2006). 6

    2006

  7. [15]

    W. D. Heiss, Journal of Physics A: Mathematical and Theoretical 45, 444016 (2012)

    2012

  8. [16]

    C. H. Lee and S. Longhi, Communications Physics 3, 147 (2020)

    2020

  9. [17]

    Chitsazi, H

    M. Chitsazi, H. Li, F. M. Ellis, and T. Kottos, Phys. Rev. Lett. 119, 093901 (2017)

    2017

  10. [18]

    L. Feng, R. El-Ganainy, and L. Ge, Nature Photonics 11, 752 (2017)

    2017

  11. [19]

    El-Ganainy, K

    R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Na- ture Physics 14, 11 (2018)

    2018

  12. [20]

    Biesenthal, M

    T. Biesenthal, M. Kremer, M. Heinrich, and A. Szameit, Phys. Rev. Lett. 123, 183601 (2019)

    2019

  13. [21]

    Sakhdari, M

    M. Sakhdari, M. Hajizadegan, Q. Zhong, D. N. Christodoulides, R. El-Ganainy, and P.-Y. Chen, Phys. Rev. Lett. 123, 193901 (2019)

    2019

  14. [22]

    Renault, H

    P. Renault, H. Yamaguchi, and I. Mahboob, Phys. Rev. Appl. 11, 024007 (2019)

    2019

  15. [23]

    K.¨Ozdemir, S

    S ¸. K.¨Ozdemir, S. Rotter, F. Nori, and L. Yang, Nature Materials 18, 783 (2019)

    2019

  16. [24]

    Miri and A

    M.-A. Miri and A. Al` u, Science 363, eaar7709 (2019), https://www.science.org/doi/pdf/10.1126/science.aar7709

    2019 doi

  17. [25]

    Parto, Y

    M. Parto, Y. G. N. Liu, B. Bahari, M. Khajavikhan, and D. N. Christodoulides, Nanophotonics 10, 403 (2021)

    2021

  18. [26]

    Stegmaier, S

    A. Stegmaier, S. Imhof, T. Helbig, T. Hofmann, C. H. Lee, M. Kremer, A. Fritzsche, T. Feichtner, S. Klembt, S. H¨ ofling, I. Boettcher, I. C. Fulga, L. Ma, O. G. Schmidt, M. Greiter, T. Kiessling, A. Szameit, and R. Thomale, Phys. Rev. Lett. 126, 215302 (2021)

    2021

  19. [27]

    Fritzsche, T

    A. Fritzsche, T. Biesenthal, L. J. Maczewsky, K. Becker, M. Ehrhardt, M. Heinrich, R. Thomale, Y. N. Joglekar, and A. Szameit, Nature Materials 23, 377 (2024)

    2024

  20. [28]

    F. U. J. Klauck, M. Heinrich, A. Szameit, and T. A. W. Wolterink, Science Advances 11, eadr8275 (2025), https://www.science.org/doi/pdf/10.1126/sciadv.adr8275

    2025 doi

  21. [29]

    Z.-P. Liu, J. Zhang, i. m. c. K. ¨Ozdemir, B. Peng, H. Jing, X.-Y. L¨ u, C.-W. Li, L. Yang, F. Nori, and Y.-x. Liu, Phys. Rev. Lett. 117, 110802 (2016)

    2016

  22. [30]

    J. Li, R. Yu, C. Ding, and Y. Wu, Phys. Rev. A 93, 023814 (2016)

    2016

  23. [31]

    Wiersig, Photon

    J. Wiersig, Photon. Res. 8, 1457 (2020)

    2020

  24. [32]

    Farhat, M

    M. Farhat, M. Yang, Z. Ye, and P.-Y. Chen, ACS Pho- tonics 7, 2080 (2020)

    2020

  25. [33]

    M. I. Rosa, M. Mazzotti, and M. Ruzzene, Journal of the Mechanics and Physics of Solids 149, 104325 (2021)

    2021

  26. [34]

    Goldzak, A

    T. Goldzak, A. A. Mailybaev, and N. Moiseyev, Phys. Rev. Lett. 120, 013901 (2018)

    2018

  27. [35]

    T. T. Koutserimpas, A. Al` u, and R. Fleury, Phys. Rev. A 97, 013839 (2018)

    2018

  28. [36]

    C. Shen, J. Li, X. Peng, and S. A. Cummer, Phys. Rev. Mater. 2, 125203 (2018)

    2018

  29. [37]

    I. I. Rabi, Phys. Rev. 51, 652 (1937)

    1937

  30. [38]

    Braak, Q.-H

    D. Braak, Q.-H. Chen, M. T. Batchelor, and E. Solano, Journal of Physics A: Mathematical and Theoretical 49, 300301 (2016)

    2016

  31. [39]

    Dietz, T

    B. Dietz, T. Friedrich, J. Metz, M. Miski-Oglu, A. Richter, F. Sch¨ afer, and C. A. Stafford, Phys. Rev. E 75, 027201 (2007)

    2007

  32. [40]

    Y. N. Joglekar, R. Marathe, P. Durganandini, and R. K. Pathak, Phys. Rev. A 90, 040101 (2014)

    2014

  33. [41]

    T. E. Lee and Y. N. Joglekar, Phys. Rev. A 92, 042103 (2015)

    2015

  34. [42]

    Q. Xie, S. Rong, and X. Liu, Phys. Rev. A 98, 052122 (2018)

    2018

  35. [43]

    X. Lu, H. Li, J.-K. Shi, L.-B. Fan, V. Mangazeev, Z.- M. Li, and M. T. Batchelor, Phys. Rev. A 108, 053712 (2023)

    2023

  36. [44]

    Y. Liu, L. Duan, and Q.-H. Chen, Analytical study of the non-hermitian semiclassical rabi model (2024), arXiv:2412.02918 [quant-ph]

    2024 arXiv

  37. [45]

    Baradaran, D

    M. Baradaran, D. Braak, L. M. Nieto, and S. Zarrinka- mar, Exact floquet solutions in a parity-time-symmetric rabi model (2025), arXiv:2501.19163 [quant-ph]

    2025 arXiv

  38. [46]

    Alfassi, O

    B. Alfassi, O. Peleg, N. Moiseyev, and M. Segev, Phys. Rev. Lett. 106, 073901 (2011)

    2011

  39. [47]

    D. C. Brody, Journal of Physics A: Mathematical and Theoretical 47, 035305 (2013)

    2013

  40. [48]

    Edvardsson, J

    E. Edvardsson, J. L. K. K¨ onig, and M. St ˚ alhammar, arXiv preprint (2023), arXiv:2212.06004 [quant-ph]

    2023 arXiv

  41. [49]

    [53, 54]

    Appendix containing a detailed derivation of the Rabi frequency, the power oscillations, and the weakly driven Bloch Hamiltonian as well as details on the stability anal- ysis, the definition of the bi-orthogonal probabilities, and the robustness of the transfer efficiency aga...

  42. [50]

    Jotzu, M

    G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Nature 515, 237 (2014)

    2014

  43. [51]

    Ramezani, Phys

    H. Ramezani, Phys. Rev. A 96, 011802 (2017)

    2017

  44. [52]

    Z. Bian, L. Xiao, K. Wang, X. Zhan, F. A. Onanga, F. Ruzicka, W. Yi, Y. N. Joglekar, and P. Xue, Phys. Rev. Res. 2, 022039 (2020)

    2020

  45. [53]

    Longhi, Journal of Physics A: Mathematical and The- oretical 50, 505201 (2017)

    S. Longhi, Journal of Physics A: Mathematical and The- oretical 50, 505201 (2017)

    2017

  46. [54]

    Foot, Atomic physics (Oxford University Press, USA, 2005)

    C. Foot, Atomic physics (Oxford University Press, USA, 2005). 7 Appendix A: Derivation of the Rabi F requency in a non-Hermitian Model and Power Oscillations

    2005

  47. [55]

    Rabi Oscillations in the Vicinity of an Exceptional Point In this section, we want to derive the Rabi frequency in a non-Hermitian system and argue why it diverges in the vicinity of an EP. An important starting remark is that to make the physical observables invariant on the ...

  48. [56]

    Oscillations of the T otal Intensity in a non-Hermitian system with Rabi pumping In this section, we show that the slow oscillation of the total power in the PT -symmetric setup is determined by the Rabi frequency. In a non-Hermitian system where we induce resonant pumping bet...

  49. [57]

    The unit cell of the model with the different couplings u and v and the three sublattices a, b, care presented in Fig.5

    Analytical Calculations for the Static Non-Hermitian Three-Band Model In this section, we repeat the analytical calculations of the static PT -symmetric three-band model presented in [51]. The unit cell of the model with the different couplings u and v and the three sublattice...

  50. [58]

    Effective Hamiltonian of the W eakly Driven PT -Symmetric Three-Band System To derive the effective Hamiltonian for the weakly periodically driven three-band model, whose static properties were discussed in the previous section, we start from the real space tight-binding Hamil...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.