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Quantum walks of correlated photons in non-Hermitian photonic lattices
Open accessAbstract
Quantum walks have demonstrated capabilities that surpass classical approaches across a range of applications, including quantum computing, quantum simulation, quantum information processing, etc. Recently, quantum walks in non-Hermitian systems have garnered significant attention. The authors experimentally realize here a non-Hermitian photonic lattice on a silicon chip, observing asymmetric quantum walks of single photons induced by the non-Hermitian skin effect. Notably, they investigate the entanglement dynamics of correlated photons, revealing a suppression of entanglement in these non-Hermitian systems.
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TL;DR
The paper experimentally realizes quantum walks of single and two indistinguishable photons in engineered non-Hermitian silicon photonic lattices, observing skin-effect-induced unidirectional propagation and suppression of entanglement entropy. It validates the entanglement suppression theoretically and experimentally through measured correlation matrices and second-order Rényi entropy.
Key findings
- Single-photon quantum walks show unidirectional wave-packet shift in the bulk for nonzero Lyapunov exponent, with no shift at zero Lyapunov exponent; experimental and theoretical probability distributions agree with a least similarity of 85.3% ± 1.9%.
- Two-photon coincidence patterns shift toward the corner for nonzero Lyapunov exponent, with more pronounced shifting for larger |Lyapunov exponent| and longer evolution periods; the measured correlation matrices agree well with theory.
- The Rényi entropy in the asymmetric lattice (λ ≠ 0) is lower than in the symmetric one (λ = 0), and the suppression becomes stronger as evolution proceeds; experiments cover periods 3π–6π, while extended theory up to 40π shows more profound suppression.
- Identical photon pairs used for the two-photon walks have a Hong-Ou-Mandel dip visibility of 97.32% ± 0.17%.
Methods
- Fabricated silicon-on-insulator waveguide arrays with nine straight waveguides and eight auxiliary waveguides; auxiliary waveguides are cut off to introduce loss and asymmetric nearest-neighbor coupling, with parameters a = 0.9 μm, R = 0.21 μm, and L = 40 μm. Evolution periods are Ω = 3π, 4π, 5π, 6π.
- Photon pairs are generated by spontaneous parametric down-conversion in a type-II periodically poled lithium-niobate waveguide, producing 1550.92 nm photons from a 775.46 nm pump. Single photons are injected at site n0 = 6; two indistinguishable photons are injected at sites n0 = 5 and l0 = 6. Coincidence measurements use superconducting nanowire single-photon detectors and a PicoHarp 300, with accidental coincidences subtracted.
- Analysis uses a Lindblad master equation and effective non-Hermitian Hamiltonian, Lyapunov exponent and generalized Brillouin zone calculations, and second-order Rényi entropy extracted from the measured correlation matrix; experiment and theory are compared via a similarity measure Q.
Limitations
- Stated: the current experiment uses second-order Rényi entropy only considering diagonal elements of the density matrix; full density-matrix reconstruction is left for future work with precise phase measurement.
- Stated: longer evolution periods are not experimentally achievable due to lossy signals, so the extended theoretical results up to 40π are not experimentally measured.
- Evident from the text: the study is limited to one and two indistinguishable photons, not general many-body systems; the Rényi entropy extraction also relies on neglecting off-diagonal summation terms as a reasonable approximation.
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Claims the paper makes
24 Own result · 15 Own interpretation · 10 No basis given · 7 Sources not found · 2 Own method
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In the paper
“We have successfully observed the unidirectional behavior of quantum walks in the bulk far from the edges induced by the skin effect.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > Abstract
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In the paper
“And we find that the least similarity is still up to 85.3% ± 1.9% .”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > B. The master equation for correlated photons in open systems
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In the paper
“From these results, it is evident that the Lyapunov exponents are a monotonic function of the geometric phase 𝜑𝜑 in a range from 0 to 𝜋𝜋/2.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > A. The engineered non-Hermitian photonic lattices
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In the paper
“In short, we utilize the additional loss in the auxiliary waveguide to create a non-Hermitian photonic lattice with intentionally designed asymmetric coupling.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > A. The engineered non-Hermitian photonic lattices
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“Moreover, we experimentally reveal the suppression of entanglement that is caused by the skin effect in non-Hermitian systems.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > Abstract
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“The real part is always zero for all the hopping terms.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“However, for the case with 𝜑𝜑 = 𝜋𝜋/2, the energy spectrum for OBCs becomes a repeated straight line.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“we find that the deterministically separated identical photon-pair has a very high visibility of the quantum interferences, characterized by a Hong-Ou-Mandel (HOM) dip with 97.32% ± 0.17% visibility.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > Additional information
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In the paper
“We find that the solution derived from the single-photon transmission matrix aligns closely with the results obtained using the master equation method, as demonstrated in Fig. 1(b).”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“and the entropy in the asymmetric system is suppressed more heavily as the evolution proceeds.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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- It may state two separate claims as one. 7
- Probably not a substantial claim. 6
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“Here, we propose and experimentally realize quantum walks of two indistinguishable photons in engineered non-Hermitian photonic lattices.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > Abstract
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“Moreover, we find that the effective Hamiltonian under PBC not only exhibits nonreciprocal nearest-neighbor coupling terms but also reveals the presence of higherorder long-distance coupling terms (see details inTable I), which are not negligible.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“Note that a system with the NHSE will render GBZ as a nonunit circle on the complex 𝛽𝛽 plane [Fig.1(f)], and the NHSE leads to unidirectional propagation in bulk”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“which illustrates that the wave packet exhibits unidirectional (unitary) diffusion in the photonic lattice with a non-zero (zero) Lyapunov exponent.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“Note that the Lyapunov exponent describes the asymptotic growth rate of light intensity at the excitation position [34], which indicates the shifting behavior of the wave packet in the lattices as it propagates.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > A. The engineered non-Hermitian photonic lattices
What the sources say
- Not matchedcites [34]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Notably, when the evolution of quantum walks involves more than one particle [36][37][38][39], their dynamics exhibit a hallmark feature of multiparticle interference and lack a classical analog.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > I. INTRODUCTION
What the sources say
- Not matchedcites [36]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [37]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [38]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [39]
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In the paper
“and our theory can then be validated by the experimental results below.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“Among these, photonic quantum walks [30] have emerged as a competent platform to study the underlying mechanism of non-Hermitian physics.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > I. INTRODUCTION
What the sources say
- Not matchedcites [30]
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In the paper
“Although the measurement of correlation for longer evolution periods is not achievable in current experiments due to the lossy signals”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > APPENDIX B: EFFECTIVE NON-HERMITIAN HAMILTONIAN
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In the paper
“Given that in the quantum optical experiment only the intensity of each correlation term (𝛽𝛽 𝑖𝑖𝑗𝑗 ) can be measured”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > Additional information
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In the paper
“Significantly, the Rényi entropy can be retrieved from the coincident matrix [52,53] (see details in Appendix D), which can be observed directly in the experiment.”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > B. The master equation for correlated photons in open systems
What the sources say
- Not matchedcites [52]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [53]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The second-order Rényi entropy can be calculated from the correlation probability distribution, following the approach outlined in several papers [52,53].”
§ Quantum walks of correlated photons in non-Hermitian photonic lattices > Additional information
What the sources say
- Not matchedcites [52]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [53]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
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The paper relies on this without support.
Few experiments have been conducted to investigate quantum walks of many bodies in non-Hermitian systems.
“Unfortunately, few experiments have been conducted to investigate the quantum walks of many bodies in non-Hermitian systems.”
The paper relies on this without support.
There have been no reports on experimentally studying the quantum dynamics of correlated photons in an engineered non-Hermitian system.
“Nonetheless, there have been no reports on experimentally studying the quantum dynamics of correlated photons in an engineered non-Hermitian system.”
The paper relies on this without support.
The experimental realization of exploring entanglement dynamics in open condensed matter systems remains challenging.
“Although there have been theoretical studies on the suppression of entanglement induced by the intrinsic NHSE in open condensed matter systems [42], the experimental realization of exploring this entanglement dynamic in such systems remains challenging.”
The authors state this as an assumption.
The environment consists of a large resonant chamber containing multiple electromagnetic eigenmodes, with which the auxiliary waveguides may interact.
“Additionally, we assume that the environment consists of a large resonant chamber containing multiple electromagnetic eigenmodes, with which the auxiliary waveguides may interact.”
The authors state this as an assumption.
There is no nonlinear term in our system.
“Considering that there is no nonlinear term in our system, we should remove the 𝑙𝑙 𝑘𝑘 𝑏𝑏 𝑘𝑘 † 𝑎𝑎 𝑗𝑗 † and 𝑙𝑙 𝑘𝑘 𝑏𝑏 𝑘𝑘 𝑎𝑎 𝑗𝑗 terms above.”
The authors state this as an assumption.
The initial state of the environment is the vacuum state.
“We can substitute the above term into the density matrix equation and assume that the initial state of the environment is the vacuum state.”
The authors state this as an assumption.
The spectrum of the mode is approximately continuous, allowing summation to be changed into integration.
“Because the environment works as a resonant chamber, which is relatively much larger than the cross-face of the waveguides, the spectrum of the mode is approximately continuous, and one can change the summation into integration.”
The authors state this as an assumption.
The j ≠ j' terms in the summation representing inter-coupling between auxiliary waveguides via the environment reservoir can be ignored.
“Here, we ignore the 𝑗𝑗 ≠ 𝑗𝑗 ′ terms in the summation which represent the inter-coupling between the auxiliary waveguides with the help of the environment reservoir.”
The authors state this as an assumption.
The period length is long enough that the difference in propagation direction between the straight and auxiliary waveguides is negligible.
“Since the period length is long enough, we can reasonably assume that the difference in propagation direction between the straight and auxiliary waveguides is negligible.”
The authors state this as an assumption.
The coupling mode equation serves as an analog to the Schrödinger equation.
“Provided the coupling mode equation serves as an analog to the Schrödinger equation, the Hamiltonian of the system over a single period becomes time-dependent.”
The authors state this as an assumption.
All the energy at auxiliary waveguides will be lost at the ends of every period when performing a simulation.
“Considering the energy loss caused by the periodic cut-off in the auxiliary waveguide, all the energy at auxiliary waveguides will be lost at the ends of every period when performing a simulation.”
The paper relies on this without support.
The coupling coefficient is reciprocal between straight waveguides.
“Note that the coupling coefficient is reciprocal between straight waveguides.”
The authors state this as an assumption.
The Fock state component only contains states no more than two photons.
“For the concern we are studying, we solve the master equation considering the Fock state component only containing the state no more than two photons”
The authors state this as an assumption.
During the process, the system and the environment are completely decoupled, so the density operator of the total system is separable.
“During this process, the system and the environment are completely decoupled, rendering the density operator of the total system separatable.”
The authors state this as an assumption.
The evolution of the density operator during this process is governed solely by the Hamiltonian of the system, equivalent to the standard Hamiltonian formalism.
“The evolution of the density operator during this process is governed solely by the Hamiltonian of the system, which is equivalent to the standard Hamiltonian formalism.”
The authors state this as an assumption.
The approximation neglecting off-diagonal terms (i≠j) in the Rényi entropy calculation is reasonable.
“we adopt a reasonable approximation by neglecting the summation terms where 𝑙𝑙 ≠ 𝑗𝑗”
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Metadata
- Authors
- Gao, M., Sheng, C., Zhao, Y., He, R., Lu, L., Chen, W., Ding, K., Zhu, S., & Liu, H.
- Affiliations
- Nanjing University (CN)
- Southeast University (CN)
- Nanjing Normal University (CN)
- Fudan University (CN)
- Corresponding author
- Gao, Mingyuan
- Sheng, Chong
- Zhao, Yule
- ORCID
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2024-09-09
- Volume
- 110
- Issue
- 9
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W4402360208
- Cited by
- 16
- References
- 55
- Citations by year
- 2026: 8 · 2025: 7 · 2024: 1
- FWCI
- 2.29
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- public-domain
- link.aps.org/licenses/aps-default-license (vor)
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (submittedVersion, public-domain)
- arXiv (Cornell University) (public-domain)
- Funders
- National Key Research and Development Program of China (2023YFB2805700)
- National Natural Science Foundation of China (12174187, 62288101, 92163216, 92150302, 2021hwyq05)
- Natural Science Foundation of Jiangsu Province (BK20240164, BK20243009)
- Fundamental Research Funds for the Central Universities (2024300329)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Random lasers and scattering media
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum walks, non-Hermitian skin effect, correlated photons, entanglement dynamics, entanglement suppression, silicon photonics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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