Photonic chiral state transfer near the Liouvillian exceptional point

Dengke Qu; Huixia Gao; Konghao Sun; Kunkun Wang; Lei Xiao; Peng Xue; Wei Yi

REVIEW 3 major objections 5 minor 49 references

Photonic chiral state transfer near the Liouvillian exceptional point

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that chiral state transfer near a Liouvillian exceptional point is a transient effect: it appears only for intermediate encircling times, disappears at long times as the system relaxes to its steady state, and obeys a…

desk verdict A careful photonic experiment showing that chiral state transfer near a Liouvillian EP is transient, with a reconstruction-weighting issue in Eq. (12) that needs scrutiny before the quantitative scaling claim can be trusted. read the letter →

arxiv 2501.10349 v1 pith:5KP5WRGI submitted 2025-01-17 cond-mat.mes-hall quant-ph

Huixia Gao , Konghao Sun , Dengke Qu , Kunkun Wang , Lei Xiao , Wei Yi , Peng Xue This is my paper · ORCID

classification cond-mat.mes-hallquant-ph

keywords chiralstatetransferLiouvillianexceptionalpointopenquantumsystemLangevinequationsingle-photoninterferometryuniversalscalingdensity-matrixreconstructionnon-Hermitiandynamics

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 authors set out to show that in a genuinely open quantum system, the direction-dependent state flip associated with encircling a Liouvillian exceptional point is not a long-time feature of the dynamics. Using single-photon interferometry to simulate the density-matrix evolution through the quantum Langevin equation, they find that with dephasing present the chirality survives only for intermediate encircling times, such as their $T=90$ case, and vanishes for long encircling times such as $T=600$. They also report that the chirality obeys the scaling relation $C=f(\gamma_2 T^{1/\nu})$ with a fitted exponent $\nu\approx1.7221$. The result matters because it clarifies when Liouvillian exceptional points, which sit away from the steady state, can produce observable dynamical consequences in open systems.

What carries the argument

The central objects are the Liouvillian superoperator $\mathcal{L}$ of a two-level open system and its stochastic unraveling through the quantum Langevin equation $i\frac{d}{dt}|\psi(t)\rangle=\left(H-\frac{i}{2}L_{\phi}^{\dagger}L_{\phi}+i l(t)L_{\phi}\right)|\psi(t)\rangle$, where $l(t)$ is white noise and $L_{\phi}$ is the dephasing jump operator. The experiment reconstructs the density matrix as an ensemble average of $n=10$ stochastic wave-function evolutions, implemented as nonunitary single-photon interferometry, and quantifies directionality with the chirality $C=\frac{1}{2}\operatorname{Tr}\sqrt{(\tilde{\rho}_{\mathrm{cw}}-\tilde{\rho}_{\mathrm{ccw}})^{\dagger}(\tilde{\rho}_{\mathrm{cw}}-\tilde{\rho}_{\mathrm{ccw}})}$. This machinery connects the observable state flip to the spectral landscape of the Liouvillian and produces the scaling collapse in $\gamma_2 T^{1/\nu}$.

What would settle it

Run the same encircling protocol with the density matrix computed directly from the Lindblad master equation, or with a much larger stochastic ensemble, at the parameters of Fig. 4; if the chirality values and the collapse $C=f(\gamma_2 T^{1/\nu})$ with $\nu\approx1.7221$ do not survive, the observed chirality is an artifact of the ten-realization reconstruction. As a second check, encircle a loop of the same shape that does not enclose the Liouvillian exceptional point: if direction-dependent state flipping persists, the chirality is not caused by exceptional-point encircling.

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Extended reading notes

Core claim

The authors claim that when a Liouvillian exceptional point is parametrically encircled in the presence of dephasing, chiral state transfer is a transient phenomenon. At sufficiently long encircling times the Liouvillian gap makes the system relax toward its instantaneous steady state in both encircling directions, so the final states merge and the chirality disappears; at an intermediate time, one direction follows the Liouvillian spectral landscape nearly adiabatically while the other undergoes a non-adiabatic jump, leaving a mixed final state and a finite chirality. They further claim that this intermediate-time chirality is purely due to the encircling of the Liouvillian exceptional point and that the final-time chirality follows the universal scaling $C=f(\gamma_2 T^{1/\nu})$, with $\nu=1.7221$ determined by fitting the experimental data.

Load-bearing premise

The load-bearing premise is that averaging ten noisy photon trajectories, rescaled by a normalization factor obtained from the evolution operator, faithfully reproduces the true Lindblad density matrix well enough that the measured chirality and scaling reflect the physical Liouvillian dynamics rather than the simulation procedure.

Editorial extensions

If this is right

At long encircling times, any dephased open system will relax toward its instantaneous steady state, so protocols relying on Liouvillian-exceptional-point chirality must operate in an intermediate time window.
The measured scaling $C=f(\gamma_2 T^{1/\nu})$ gives a quantitative rule for choosing encircling time and dephasing rate to maximize the chiral signal.
Comparing the two encircling directions at intermediate times reveals near-adiabatic following in one direction and a non-adiabatic jump in the other, providing a signature for identifying Liouvillian exceptional-point dynamics.
The single-photon stochastic-unraveling scheme reconstructs density-matrix evolution from wave-function trajectories and can therefore simulate other Lindblad open-system dynamics beyond this two-level example.

Reading between the lines

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

A microscopic derivation of the fitted exponent $\nu\approx1.7221$ from the Liouvillian spectrum would test whether the scaling is truly universal or specific to the chosen encircling path; the paper reports the scaling form as universal but the coefficient as parameter-dependent.
Because each reported density matrix uses only ten stochastic realizations, benchmarking the same parameters against an exact Lindblad master-equation solution would show how much of the chirality magnitude depends on the ensemble size.
The same simulation scheme could be applied to bistable or nonlinear open systems, where the paper notes a recent exception to the transient rule, to search for steady-state chiral switching.

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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 core of this paper is the experimental demonstration that chiral state transfer near a Liouvillian exceptional point is a transient effect: at long encircling times the system relaxes to the steady state and chirality disappears, while at intermediate times it survives. That message is plausible, the data in Figs. 2–3 are consistent with numerical master-equation curves, and the single-photon simulation of the quantum Langevin equation with full density-matrix reconstruction is a genuinely useful technical step. The qualitative conclusion is probably right and worth broadcasting.

The soft spots are all in the quantitative claims. The most load-bearing is Eq. (12). The paper renormalizes each tomographically normalized trajectory by max|ξ_j|, the largest singular value squared of U(τ), but the correct unravelling weight for the initial state |1⟩⟨1| is its survival probability ⟨ψ0|U_j†U_j|ψ0⟩. Those coincide only when |ψ0| is the principal right singular vector of every U_j, which is not generally true for the operators generated by their encircling path. Without a derivation or a numerical check, the reconstructed ρ(T), the chirality C, and the scaling collapse in Fig. 4 could be artifacts of the weighting. This is not a fatal flaw in the qualitative story, but it is a real gap and the paper should address it.

Second, n=10 Langevin realizations is small and no convergence analysis is shown for the trace-distance observable C. The error bars from Monte Carlo photon-counting statistics do not capture the ensemble-size bias. Third, the "universal scaling" C = f(γ2 T^(1/ν)) rests on ν = 1.7221 fitted to the same experimental data, so the collapse is a fit, not a prediction. The paper says the exponent is path-independent but parameter-dependent; that is honest, but it lowers the strength of the claim. Fourth, the theoretical framework is largely from the authors' own prior work (Refs. [11,19]), so the new content is the experimental implementation, not the physics.

None of this undermines the main qualitative result, and the citation pattern looks fair. The paper deserves a serious referee: the experiment is real, the technique is interesting, and the reconstruction issue is fixable with a clear derivation and convergence checks. I would engage with it, but I would not cite the scaling exponent as a law until the weighting is sorted out.

Referee Report

3 major / 5 minor

Summary. The paper reports a single-photon interferometric experiment that simulates the Lindblad dynamics of a two-level open system via a quantum Langevin equation. By parametrically encircling a Liouvillian exceptional point with different total encircling times, the authors observe chiral state transfer at an intermediate time (T=90) and its disappearance at long times (T=600), where the system relaxes to the steady state. They quantify the chirality with the trace-distance definition in Eq. (11) and claim a universal scaling C = f(γ2 T^{1/ν}) with an exponent ν=1.7221 obtained by fitting the experimental data.

Significance. If the central claims hold, the paper provides a valuable experimental demonstration that chiral state transfer near a Liouvillian exceptional point is a transient effect, in contrast to the long-time chiral transfer familiar from non-Hermitian Hamiltonian dynamics. The experimental scheme, based on reconstructing density-matrix evolution from stochastic wave-function realizations, is original and the data in Figs. 2 and 3 are shown to be in reasonable agreement with master-equation curves. However, the reconstruction formula in Eq. (12), the absence of a convergence analysis for the n=10 ensemble, and the fitting of the scaling exponent to the same data used to demonstrate collapse leave the quantitative claims—especially the universal scaling—insufficiently supported.

major comments (3)

[Eq. (12), together with Eqs. (4) and (11)] The reconstruction weight in Eq. (12) is not the standard unravelling weight and is not derived. For the linear quantum Langevin equation (4), the unnormalized contribution of trajectory j is U_j|ψ0⟩, whose correct weight in the ensemble density matrix is ⟨ψ0|U_j† U_j|ψ0⟩. Equation (12) instead multiplies the tomographically normalized ρ_j(T) by max|ξ_j|, the largest eigenvalue of U_j U_j† (i.e., the squared largest singular value). These weights coincide only if |ψ0⟩ is the principal right singular vector of every U_j. The initial state in Fig. 4 is |1⟩⟨1|, and no argument is given that this state is the principal singular vector of the operators generated by Eqs. (4)–(10). Because the chirality C in Eq. (11) and the scaling collapse in Fig. 4 are computed from this reconstructed ρ(T), the central quantitative claims rest on an unjustified normalization. Please derive Eq. (12) from Eq. (4), or explicitly benchmark both reconstruction rules against a direct numerical solution of the Lindblad master equation (1) for the same parameters.
[Section 'Simulation of open systems' and Fig. 4] The paper states that n=10 'provides a good enough estimation of the density-matrix dynamics,' but no convergence analysis is shown. For nonunitary trajectories with state-dependent norm fluctuations, ten realizations can bias the ensemble average of ρ(T) and therefore bias the measured chirality C. Please present the ensemble average or the trace-distance observable C as a function of n for representative parameters (for example, T=90, γ2=2), including statistical error bars, and justify why n=10 is sufficient for the scaling collapse in Fig. 4(b).
[Fig. 4(b) and the paragraph 'Chirality'] The universal scaling C = f(γ2 T^{1/ν}) is demonstrated with an exponent ν=1.7221 obtained by fitting the same experimental data that are then collapsed. As written, this is an empirical fit with a free parameter rather than an independent prediction of a scaling law. To substantiate the universality claim, the exponent should be derived from the Liouvillian spectral structure or from an independent numerical dataset, and the fit uncertainty should be reported.

minor comments (5)

[Eq. (12)] Please define ξ_j unambiguously: is it an eigenvalue of U_j U_j†, and is the maximum taken over the eigenvalues of a single trajectory or over trajectories? The current notation 'max|ξ_j|' is unclear.
[Fig. 1(a) caption] The caption contains a grammatical error: 'States |1⟩ is coupled' should read 'State |1⟩ is coupled'.
[Abstract and 'Chirality' section] The abstract states that chirality scales with 1/T^ν, while the main text and Fig. 4 use C = f(γ2 T^{1/ν}); please reconcile this notation.
[Fig. 2] The figure legend distinguishes hollow squares and solid dots, but the caption does not explain which symbol corresponds to clockwise and which to counterclockwise encircling, nor what the solid curves represent.
[Data Availability Statement] The data availability statement says the data are available 'within the Letter [49]', but reference [49] is a supplemental materials file; please provide a persistent repository link or a stable DOI for the raw data.

Circularity Check

1 steps flagged · score 6.0 of 10

Universal scaling exponent is fitted to the same data shown as a collapse; Eq. (12) reconstruction is a validity risk rather than a circular step.

fitted input called prediction [Chirality section, text following Eq. (12) and description of Fig. 4]
"Remarkably, the chirality at the final time exhibits a universal scaling with respect to γ2 and T , i.e., C = f (γ2T 1/ν), as illustrated in Fig. 4(b). We obtain ν = 1 .7221 by fitting the experimental data, which agrees with the numerical calculated result."

The scaling law C=f(γ2 T^{1/ν}) is presented as a universal result, but the exponent ν is explicitly obtained by fitting the same experimental chirality data that are then displayed as a collapse. The data collapse is therefore a post-hoc re-expression of the fit rather than an independent prediction derived from the Liouvillian dynamics. With a free exponent, the collapse is statistically forced, so the claim that the chirality 'exhibits a universal scaling' is not independently tested. The asserted agreement with a numerical calculation is not quantified in the Letter, so the reader cannot verify that the experiment confirms a pre-existing prediction rather than rationalizing the data.

full rationale

The experiment itself is largely self-contained: the Lindblad master equation (1), the quantum-Langevin equivalence (4), and the stroboscopic implementation (5)-(6) are standard, and the central observations (chirality at intermediate T, relaxation to the steady state at long T) are directly shown by the new trajectory data. The main circularity is localized in the 'universal scaling' claim: the exponent ν=1.7221 is explicitly obtained by fitting the experimental data, and the same data are then plotted as a collapse using that fitted exponent. The collapse is therefore a post-hoc fit rather than an independent prediction; asserting agreement with an unspecified numerical result does not supply the missing prediction. The reconstruction formula in Eq. (12) is a separate concern: the weight max|ξ_j| is not the standard trace-weight of the unnormalized trajectory, and it is justified only by references [45-47] (including the same group's [46]) and the supplement. This is a validity or calibration risk rather than a circular step, because Eq. (12) is an input estimator, not a consequence of the claims it supports. The self-citations [11,44,46] are numerous, but the measured trajectories are new, so the circularity score is driven mainly by the fitted scaling exponent, not by the self-citations alone.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new particles or mediators are introduced. The central burden is carried by the QLE-to-Lindblad equivalence ansatz, the n=10 ensemble, the max|ξ_j| renormalization, and the fitted exponent ν.

free parameters (2)

scaling exponent ν = 1.7221 (experimental fit)
Used to collapse C vs γ2 T^(1/ν); no analytical derivation, fitted to the same experimental data.
number of Langevin realizations n = 10
Manual choice; paper says it provides a 'good enough' estimation without a convergence analysis.

assumptions (4)

standard math The quantum Langevin equation (4), averaged over complex white noise, is equivalent to the Lindblad master equation (1).
Invoked in 'Simulation of open systems' with Ref [42]; it is the bridge that makes the photonic simulation meaningful.
ad hoc to paper Ten stochastic realizations suffice for the density-matrix ensemble average ρ(t)=1/n Σ|ψ_j><ψ_j|.
Paper states n=10 'provides a good enough estimation'; no convergence test or central-limit estimate is shown.
ad hoc to paper Multiplying each reconstructed realization by max|ξ_j| in Eq. (12) yields the correct Lindblad density matrix.
The renormalization prescription is asserted without derivation in the main text and deferred to S3.
domain assumption The parameter loop in Eqs. (9)-(10) encircles the Liouvillian EP as well as the Hamiltonian EP.
Chirality is attributed purely to the Liouvillian EP; the loop is defined around the Hamiltonian EP (δ1=0, Γ=2|Ω1|) and its relation to the Liouvillian EP is not shown in the main text.

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Pith. "Pith review of Photonic chiral state transfer near the Liouvillian exceptional point." pith.science (2026). https://pith.science/paper/5KP5WRGI

@misc{pith2026250110349,
  author       = {Pith},
  title        = {Pith review of: Photonic chiral state transfer near the Liouvillian exceptional point},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5KP5WRGI}},
  note         = {Machine review of arXiv:2501.10349}
}

read the original abstract

As branch-point singularities of non-Hermitian matrices, the exceptional points (EPs) exhibit unique spectral topology and criticality, with intriguing dynamic consequences in non-Hermitian settings. In open quantum systems, EPs also emerge in the Liouvillian spectrum, but their dynamic impact often pertains to the transient dynamics and is challenging to demonstrate. Here, using the flexible control afforded by single-photon interferometry, we study the chiral state transfer when the Liouvillian EP is parametrically encircled. Reconstructing the density-matrix evolution by experimentally simulating the quantum Langevin equation, we show that the chirality of the dynamics is only present within an intermediate encircling timescale and dictated by the landscape of the Liouvillian spectrum near the EP. However, the chirality disappears at long times as the system always relaxes to the steady state. We then demonstrate the universal scaling of the chirality with respect to the encircling time. Our experiment confirms the transient nature of chiral state transfer near a Liouvillian EP in open quantum systems, while our scheme paves the way for simulating general open-system dynamics using single photons.

Figures

Figures reproduced from arXiv: 2501.10349 by the authors.

**Figure 2.** FIG. 2. Trajectories of the encircling dynamics for an encircling time [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Trajectories of the encircling dynamics for an encir [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. (a) Chirality as a function of the total encir [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Works this paper leans on

49 extracted references · 39 canonical work pages

[1]

Latinne, N

O. Latinne, N. J. Kylstra, M. D¨ orr, J. Purvis, M. Terao-Dunseath, C. J. Joachain, P. G. Burke, and C. J. Noble, Laser-induced degeneracies involving autoioniz- ing states in complex atoms, Phys. Rev. Lett. 74, 46 (1995)

work page 1995
[2]

Lefebvre, O

R. Lefebvre, O. Atabek, M. ˇSindelka, and N. Moiseyev, Resonance coalescence in molecular photodissociation, Phys. Rev. Lett. 103, 123003 (2009)

2009
[3]

Uzdin, A

R. Uzdin, A. Mailybaev, and N. Moiseyev, On the ob- servability and asymmetry of adiabatic state flips gen- erated by exceptional points, J. Phys. A 44, 435302 (2011)

work page 2011
[4]

M. V. Berry and R. Uzdin, Slow non-Hermitian cy- cling: exact solutions and the Stokes phenomenon, J. Phys. A 44, 435303 (2011)

work page 2011
[5]

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, General description of quasiadi- abatic dynamical phenomena near exceptional points, Phys. Rev. A 92, 052124 (2015)

work page 2015
[6]

Y. Choi, C. Hahn, J.W. Yoon, S.H. Song, and P. Berini, Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quan- tum jumps near exceptional points, Nat. Commun. 8, 14154 (2017)

work page 2017
[7]

S. K. ¨Ozdemir, S. Rotter, F. Nori, and L. Yang, Par- ity–time symmetry and exceptional points in photon- ics, Nat. Mater. 18, 783 (2019)

work page 2019
[8]

Kumar, K

P. Kumar, K. Snizhko, and Y. Gefen, Near-unit effi- ciency of chiral state conversion via hybrid-Liouvillian dynamics, Phys. Rev. A 104, L050405 (2021)

2021

Show all 49 references

[9]

Nasari, G

H. Nasari, G. Lopez-Galmiche, H. E. Lopez-Aviles, A. Schumer, A. U. Hassan, Q. Zhong, S. Rotter, P. LiKamWa, D. N. Christodoulides, and M. Kha- javikhan, Observation of chiral state transfer without encircling an exceptional point, Nature (London) 605, 256 (2022)

2022
[10]

Duan, L.-L

Y.-D. Duan, L.-L. Geng, Q.-Q. Guo, J. Yang, G.-K. Hu, X.-M. Zhou, Acoustic chiral mode switching by dynamic encircling of exceptional points, Appl. Phys. Lett. 123, 101701 (2023)

2023
[11]

Sun, and W

K. Sun, and W. Yi, Chiral state transfer under dephas- ing, Phys. Rev. A 108, 013302 (2023)

2023
[12]

M¨ uller and I

M. M¨ uller and I. Rotter, Exceptional points in open quantum systems, J. Phys. A 41, 244018 (2008)

2008
[13]

Miri and A

M.-A. Miri and A. Al´ u, Exceptional points in optics and photonics, Science 363, 42 (2019)

2019
[14]

Insinga, B

A. Insinga, B. Andresen, P. Salamon, and Ronnie Kosloff, Quantum heat engines: Limit cycles and ex- ceptional points, Phys. Rev. E 97, 062153 (2018)

2018
[15]

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, Dynamically encircling an excep- tional point for asymmetric mode switching, Nature (London) 537, 76 (2016)

2016
[16]

Zhang, S.-B

X.-L. Zhang, S.-B. Wang, B. Hou, and C. T. Chan, Dy- namically encircling exceptional points: in situ control of encircling loops and the role of the starting point, Phys. Rev. X 8, 021066 (2018)

2018
[17]

Q.-H. Song, M. Odeh, J. Z´ u˜ niga-P´ erez, B. Kant´ e, and P. Genevet, Plasmonic topological metasurface by en- circling an exceptional point, Science 373, 1133 (2021)

2021
[18]

W.-J. Chen, M. Abbasi, Yogesh N. Joglekar, and K. W. Murch, Quantum jumps in the non-Hermitian dy- namics of a superconducting qubit, Phys. Rev. Lett. 127, 140504 (2021)

2021
[19]

W.-J. Chen, M. Abbasi, B. Ha, S. Erdamar, Y. N. Joglekar, and K. W. Murch, Decoherence-induced ex- ceptional points in a dissipative superconducting qubit, Phys. Rev. Lett. 128, 110402 (2022)

2022
[20]

Ding, K.-Y

L.-Y. Ding, K.-Y. Shi, Y.-X. Wang, Q.-X. Zhang, C.- H. Zhu, L.-D. Zhang, J.-Q. Yi, S.-N. Zhang, X. Zhang, and W. Zhang, Information retrieval and eigenstate 6 coalescence in a non-Hermitian quantum system with anti-symmetry, Phys. Rev. A 105, L010204 (2022)

2022
[21]

W.-Q. Liu, Y. Wu, C.-K. Duan, X. Rong, and J.-F. Du, Dynamically encircling an exceptional point in a real quantum system, Phys. Rev. Lett. 126, 170506 (2021)

2021
[22]

Z.-J. Ren, D. Liu, E.-T. Zhao, C.-D. He, K. K. Pak, J. Li, and G.-B. Jo, Chiral control of quantum states in non-Hermitian spin–orbit-coupled fermions, Nat. Phys. 18, 385 (2022)

2022
[23]

H. Xu, D. Mason, L. Jiang, and J. G. E. Harris, Topological energy transfer in an optomechanical sys- tem with exceptional points, Nature (London) 537, 80 (2016)

2016
[24]

Doppler, A

J. Doppler, A. A. Mailybaev, P. Rabl, N. Moiseyev, and S. Rotter, Dynamically encircling an exceptional point for asymmetric mode switching, Nature (Lon- don) 537, 76 (2016)

2016
[25]

Q. Liu, S. Li, B. Wang, S. Ke, C. Qin, K. Wang, W. Liu, D. Gao, P. Berini, and P. Lu, Efficient mode trans- fer on a compact silicon chip by encircling moving ex- ceptional points, Phys. Rev. Lett. 124, 153903 (2020)

2020
[26]

A. Li, J. Dong, J. Wang, Z. Cheng, J.S. Ho, D. Zhang, J. Wen, X.-L. Zhang, C.T. Chan, A. Al´ u, C.-W. Qiu, and L. Chen, Hamiltonian hopping for efficient chiral mode switching in encircling exceptional points, Phys. Rev. Lett. 125, 187403 (2020)

2020
[27]

J. W. Yoon, Y. Choi, C. Hahn, G. Kim, S. Ho Song, K.- Y. Yang, J. Yub Lee, Y. Kim, C.S. Lee, J.K. Shin, H.-S. Lee, and P. Berini, Time-asymmetric loop around an exceptional point over the full optical communications band, Nature (London) 562, 86 (2018)

2018
[28]

Khandelwal, W.-J

S. Khandelwal, W.-J. Chen, K. W. Murch, and G. Haack, Chiral Bell-state transfer via dissipative Liou- villian dynamics, Phys. Rev. Lett. 133, 070403 (2024)

2024
[29]

Mathisen and J

T. Mathisen and J. Larson, Liouvillian of the open STIRAP problem, Entropy 20, 20 (2018)

2018
[30]

Hatano, Exceptional points of the Lindblad opera- tor of a two-level system, Mol

N. Hatano, Exceptional points of the Lindblad opera- tor of a two-level system, Mol. Phys. 117, 2121 (2019)

2019
[31]

Minganti, A

F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps, Phys. Rev. A 100, 062131 (2019)

2019
[32]

I. I. Arkhipov, A. Miranowicz, F. Minganti, and F. Nori, Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory, Phys. Rev. A101, 013812 (2020)

2020
[33]

Dalibard, Y

J. Dalibard, Y. Castin, and K. Mølmer, Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett. 68, 580 (1992)

1992
[34]

M. B. Plenio and P. L. Knight, The quantum-jump approach to dissipative dynamics in quantum optics, Rev. Mod. Phys. 70, 101 (1998)

1998
[35]

Minganti, A

F. Minganti, A. Miranowicz, R. W. Chhajlany, I. I. Arkhipov, and F. Nori, Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamil- tonians and Liouvillians via postselection of quantum trajectories, Phys. Rev. A 101, 062112 (2020)

2020
[36]

J.-M. Li, A. K. Harter, J. Liu, L. de Melo, Y. N. Joglekar, and L. Luo, Observation of parity-time sym- metry breaking transitions in a dissipative Floquet sys- tem of ultracold atoms, Nat. Commun. 10, 855 (2019)

2019
[37]

Naghiloo, M

M. Naghiloo, M. Abbasi, Y. N. Joglekar, and K. W. Murch, Quantum state tomography across the excep- tional point in a single dissipative qubit, Nat. Phys. 15, 1232 (2019)

2019
[38]

Abbasi, W

M. Abbasi, W. Chen, M. Naghiloo, Y. N. Joglekar, and K. W. Murch, Topological quantum state control through exceptional-point proximity, Phys. Rev. Lett. 128, 160401 (2022)

2022
[39]

Breuer and F

H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007)

2007
[40]

P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, Marko- vian master equations for quantum thermal machines: local versus global approach, New J. Phys. 19, 123037 (2017)

2017
[41]

P. P. Potts, A. A. S. Kalaee, and A.Wacker, A ther- modynamically consistent Markovian master equation beyond the secular approximation, New J. Phys. 23, 123013 (2021)

2021
[42]

Kampen, and N

V. Kampen, and N. Godfried, Stochastic processes in physics and chemistry, Vol. 1. Elsevier (1992)

1992
[43]

See the Supplemental Materials for details
[44]

L. Xiao, D. Qu, K. Wang, H.-W. Li, J.-Y. Dai, B. D´ ora, M. Heyl, R. Moessner, W. Yi, and P. Xue, Non- hermitian kibble-zurek mechanism with tunable com- plexity in single-photon interferometry, PRX Quantum 2, 020313 (2021)

2021
[45]

P. R. Halmos, Normal dilations and extensions of op- erators, Summ. Bras. Math. 2, 125 (1950)

1950
[46]

H. Gao, K. K. Wang, L. Xiao, M. Nakagawa, N. Mat- sumoto, D. Qu, H. Lin, M. Ueda, and P. Xue, Exper- imental observation of the yang-lee quantum critical- ity in open quantum systems, Phys. Rev. Lett. 132, 176601 (2024)

2024
[47]

Sparrow, E

C. Sparrow, E. Mart ´tn-L´ opez, N. Maraviglia, A. Neville, C. Harrold, J. Carolan, Y. N. Joglekar, T. Hashimoto, N. Matsuda, J. L. O’Brien, D. P. Tew, and A. Laing, Simulating the vibrational quantum dynam- ics of molecules using photonics, Nature (London)557, 660 (2018)

2018
[48]

C. Xie, K. Sun, K.-D. Wu, C.-F. Li, G.-C. Guo, W. Yi, and G.-Y. Xiang, Chiral switching of many- body steady states in a dissipative Rydberg gas, arXiv:2402.02779 (2024)

2024 arXiv
[49]

All raw data supporting the results reported in the Letter can be found in the Supplemental Materials

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Latinne, N

O. Latinne, N. J. Kylstra, M. D¨ orr, J. Purvis, M. Terao-Dunseath, C. J. Joachain, P. G. Burke, and C. J. Noble, Laser-induced degeneracies involving autoioniz- ing states in complex atoms, Phys. Rev. Lett. 74, 46 (1995)

work page 1995

[2] [2]

Lefebvre, O

R. Lefebvre, O. Atabek, M. ˇSindelka, and N. Moiseyev, Resonance coalescence in molecular photodissociation, Phys. Rev. Lett. 103, 123003 (2009)

2009

[3] [3]

Uzdin, A

R. Uzdin, A. Mailybaev, and N. Moiseyev, On the ob- servability and asymmetry of adiabatic state flips gen- erated by exceptional points, J. Phys. A 44, 435302 (2011)

work page 2011

[4] [4]

M. V. Berry and R. Uzdin, Slow non-Hermitian cy- cling: exact solutions and the Stokes phenomenon, J. Phys. A 44, 435303 (2011)

work page 2011

[5] [5]

T. J. Milburn, J. Doppler, C. A. Holmes, S. Portolan, S. Rotter, and P. Rabl, General description of quasiadi- abatic dynamical phenomena near exceptional points, Phys. Rev. A 92, 052124 (2015)

work page 2015

[6] [6]

Y. Choi, C. Hahn, J.W. Yoon, S.H. Song, and P. Berini, Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quan- tum jumps near exceptional points, Nat. Commun. 8, 14154 (2017)

work page 2017

[7] [7]

S. K. ¨Ozdemir, S. Rotter, F. Nori, and L. Yang, Par- ity–time symmetry and exceptional points in photon- ics, Nat. Mater. 18, 783 (2019)

work page 2019

[8] [8]

Kumar, K

P. Kumar, K. Snizhko, and Y. Gefen, Near-unit effi- ciency of chiral state conversion via hybrid-Liouvillian dynamics, Phys. Rev. A 104, L050405 (2021)

2021