Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Nonreciprocal entanglement in a molecular optomechanical system

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read A spinning whispering-gallery-mode resonator coupled to an auxiliary cavity can generate nonreciprocal quantum entanglement between light and molecular vibrations, with direction and strength set by rotation sense and detuning.

desk verdict A clean linearized optomechanics calculation whose 'nonreciprocal' headline result is planted by an unexplained J1≠J2 coupling and a contrast measure that compares two different rotation configurations. read the letter →

arxiv 2501.14045 v3 pith:2KLZ4VZZ submitted 2025-01-23 quant-ph

E. Kongkui Berinyuy , Jia-Xin Peng , A. Sohail , P. Djorwe , A.-H. Abdel-Aty , N. Alessa , K.S. Nisar , S. G. Nana Engo This is my paper · ORCID
classification quant-ph
keywords nonreciprocalentanglementmolecularoptomechanicsSagnac-Fizeaueffectwhispering-gallery-moderesonatorvibration-vibrationcavitylogarithmicnegativityquantuminformation
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 argues that placing many molecules inside a spinning whispering-gallery-mode (WGM) resonator, itself coupled to an auxiliary optical cavity, turns the Sagnac-Fizeau frequency shift into a directional resource: photon-vibration and vibration-vibration entanglement become strong for one sense of rotation and weak for the other. The authors show this through a linearized quantum Langevin treatment and the logarithmic negativity of the steady-state covariance matrix. They find CCW spinning with blue-detuned driving gives the largest entanglement, that vibration-vibration entanglement grows with the number of molecules and survives relatively high temperatures, and that the degree of nonreciprocity can be switched on and off by tuning the auxiliary cavity detuning. If correct, the system would be a tunable source of one-way quantum correlations, relevant for unidirectional quantum information transfer and nonreciprocal devices.

What carries the argument

The machinery that carries the argument is the Sagnac-Fizeau effect in a spinning WGM resonator: rotation shifts the resonance frequency by $\Delta_F = \pm \frac{n\Omega R \omega_{c1}}{c}\left(1-\frac{1}{n^2}\right)$, and this shift is taken to convert the otherwise symmetric cavity-cavity coupling into the unequal strengths $J_1$ and $J_2$ in $J_1 a_1^\dagger a_2 + J_2 a_2^\dagger a_1$. The quantitative tool is the covariance-matrix formalism: after linearizing the quantum Langevin equations around the steady state, the $8\times8$ drift matrix $A$ and the Lyapunov equation $AV+VA^T=-D$ give the covariance matrix, and entanglement is read from the logarithmic negativity $E_N=\max[0,-\ln(2\zeta)]$ of the relevant two-mode submatrices. Nonreciprocity is then quantified by the bidirectional contrast ratio $C_{kl}$ defined from the entanglement under $\Delta_F>0$ versus $\Delta_F<0$. The collective vibrational modes $B_1$ and $B_2$ are defined from the same molecular ensemble and carry the vibration-vibration entanglement.

What would settle it

Measure the effective coupling strengths $J_1$ and $J_2$ between the spinning WGM mode and a stationary auxiliary cavity as a function of rotation speed and direction; if $J_1 = J_2$ whenever the Sagnac shift $\Delta_F$ is nonzero, the predicted nonreciprocal entanglement cannot occur. Alternatively, swap the rotation from CW to CCW while holding all other parameters fixed and look for the predicted asymmetry in logarithmic negativity; its absence would falsify the central claim.

Watch

Extended reading notes

Core claim

The central claim is that nonreciprocal bipartite entanglement can be generated in a hybrid molecular cavity optomechanical system consisting of $N$ molecules inside a spinning WGM resonator whose mode $a_1$ is coupled to the molecular vibrations and to an auxiliary cavity mode $a_2$. With experimentally motivated parameters ($\omega_m/2\pi=30\ \mathrm{THz}$, $g_m/2\pi=30\ \mathrm{GHz}$, $T=312\ \mathrm{K}$), the Sagnac-Fizeau shift makes the inter-cavity coupling direction-dependent, $J_1\neq J_2$, and the computed logarithmic negativities $E_{a_2B_1}$ and $E_{B_1B_2}$ acquire a nonzero bidirectional contrast ratio. The paper reports that counter-clockwise rotation ($\Delta_F<0$) and blue-detuned driving optimize both types of entanglement, and that vibration-vibration entanglement is enhanced by a larger molecular number $N$ and remains robust at higher temperatures, while photon-vibration entanglement is stronger but more fragile at small $N$. The two collective vibrational modes $B_1$ and $B_2$ are a theoretical split of the same set of $N$ molecules, not physically distinct groups.

Load-bearing premise

The load-bearing assumption is that the spinning resonator actually makes the two inter-cavity coupling constants unequal ($J_1 \neq J_2$); the paper states this directionality follows from the Sagnac-Fizeau effect but does not derive the unequal couplings from the frequency shift in equation (2).

Editorial extensions

If this is right

  • A spinning molecular optomechanical resonator can act as a switchable nonreciprocal entangler: the bidirectional contrast ratio can be tuned from 0 to 1 by adjusting the auxiliary cavity detuning.
  • Vibration-vibration entanglement is predicted to grow with the number of molecules and to persist at temperatures where photon-vibration entanglement has already degraded, suggesting a scalable route to robust macroscopic entanglement.
  • Blue-detuned driving combined with counter-clockwise rotation gives the optimal parameter regime, while red detuning cools the molecular vibrations; the two detuning signs give different, tunable behavior.
  • Larger molecular ensembles favour vibration-vibration entanglement over photon-vibration entanglement, so the same device can be tailored to either type of correlation by choosing $N$.
  • These results point toward unidirectional quantum information transfer and nonreciprocal quantum devices that operate at molecular vibrational frequencies (tens of THz) rather than low-frequency mechanical modes.

Reading between the lines

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

  • If the assumed inequality $J_1\neq J_2$ is replaced by a microscopic derivation from the Sagnac shift, the scheme becomes testable; without such a derivation, the predicted directionality rests entirely on that assumption.
  • A natural extension would be to look for nonreciprocal tripartite entanglement among $a_1$, $a_2$, and the collective vibrations, or to use the same platform for one-way squeezing transfer; the paper only analyses bipartite correlations.
  • The split into two collective modes $B_1$ and $B_2$ is a bookkeeping device; an experimental test could target the cross-correlation between two frequency-resolved subsets of molecular vibrations rather than two physically separated groups.
  • Because the predicted contrast ratio depends on detuning, a similar molecular system without spinning might still show entanglement asymmetries from detuning alone; comparing a stationary resonator with equal nominal couplings would isolate the Sagnac contribution.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript proposes a theoretical scheme to generate nonreciprocal bipartite entanglement in a molecular cavity optomechanical system consisting of a spinning whispering-gallery-mode (WGM) resonator hosting N molecules and coupled to an auxiliary optical cavity. The authors write a Hamiltonian with nonreciprocal intermode couplings J1 and J2, linearize the quantum Langevin equations, solve the Lyapunov equation for the covariance matrix, and compute logarithmic negativity for photon-vibration and vibration-vibration entanglement. They report that counter-clockwise rotation and blue-detuned driving enhance both types of nonreciprocal entanglement, and that increasing the number of molecules strengthens vibration-vibration entanglement and its robustness to temperature.

Significance. If the underlying model were physically justified, the proposal would be interesting for tunable nonreciprocal quantum devices exploiting molecular vibrations. The linearized fluctuation analysis and the Lyapunov calculation are internally consistent, and the stability analysis follows standard methods. However, the central claim of nonreciprocal entanglement generation is not supported because the nonreciprocal coupling J1≠J2 is assumed in Eq. (1) without a derivation, and the stated physical origin, the Sagnac-Fizeau frequency shift of Eq. (2), does not by itself yield direction-dependent hopping amplitudes. The quantitative predictions in Section III therefore follow from an input assumption rather than from a demonstrated physical mechanism.

major comments (4)
  1. [Sec. II.A, Eq. (1) and Eq. (2)] The interaction term J1 a1†a2 + J2 a2†a1 in Eq. (1) is non-Hermitian when J1≠J2, since its adjoint is J1 a2†a1 + J2 a1†a2. No reservoir, synthetic-gauge, or dynamical-modulation mechanism is provided to justify an effective non-Hermitian description, and Eq. (2) only gives a Sagnac-Fizeau frequency shift that cannot by itself produce unequal hopping amplitudes between modes a1 and a2. The numerical results in Section III, including Figures 3–6, are driven by an assumed asymmetry rather than by the physics of a spinning resonator. The authors must either derive J1 and J2 from a microscopic model or clearly state the model as an assumption; in the latter case, the abstract's claim to demonstrate nonreciprocal entanglement generation should be revised.
  2. [Sec. III.C, Eq. (19)] The bidirectional contrast ratio Ckl is defined by comparing entanglement for ΔF>0 and ΔF<0, i.e., for two different rotation directions or configurations. Nonreciprocity in a device typically means a directional asymmetry within a single configuration, such as forward versus backward propagation. The quantity in Eq. (19) therefore does not measure the directional asymmetry claimed in the abstract, and the conclusion that nonreciprocal entanglement can be switched on and off may be a statement about parameter dependence rather than about nonreciprocity in a fixed device.
  3. [Sec. II.A, Eq. (3)] The collective modes B1 and B2 are constructed by partitioning the same set of N molecules into two groups. Because both modes are built from the same physical degrees of freedom, the logarithmic negativity EB1B2 between them does not describe entanglement between independent subsystems; it may be an artifact of the arbitrary partition. The paper acknowledges this as a 'theoretical construct' but still presents the vibration-vibration entanglement as a physical prediction in Figures 3–6. A justification that this quantity corresponds to physically meaningful, detectable entanglement is needed.
  4. [Sec. II.A and Sec. III] The text states that the Sagnac-Fizeau shift is 'the physical origin of the nonreciprocal coupling in our system, distinguishing J1 and J2,' but no equation links J1 and J2 to the rotation rate Ω, radius R, or refractive index n. The parameters J1/ωm=0.3 and J2/ωm=1 are simply chosen at the beginning of Section III, so the central results have no falsifiable dependence on the spinning rate. This further supports that the claimed mechanism is not actually used in the calculations.
minor comments (5)
  1. [Introduction, paragraph 5] The phrase 'the Sagnac effect induces noreciprocity in our system' contains a typo; 'noreciprocity' should be 'nonreciprocity'.
  2. [Eq. (6)] The definition of B_in^2 is garbled: it should be B_in^2 = (1/sqrt(N−M)) Σ_{j=M+1}^N b_in_j, but the text repeats the expression for B_in^1. Please correct this and ensure the noise correlation functions in Eq. (7) are indexed consistently.
  3. [Sec. II.A and Sec. III] The notation for the cavity detunings is inconsistent: Eq. (1) uses Δc2, Eq. (5) uses Δ2c, and Section III uses Δ1c and Δ2c. Please unify the notation throughout.
  4. [Eq. (7)] The thermal phonon number is defined as n_j = {exp(ℏω_j/k_B T) − 1}^{−1}, but the correlation functions use n_k. Clarify the subscript convention.
  5. [Fig. 6 caption] The caption lists '(a) Bidirectional contrast ratio C ... (b) Photon-vibration Ea2B1 ...' but the main text appears to reference Figure 6(b) when discussing the contrast ratio and Figure 6(a) when discussing molecular number. Please verify the panel labels and the in-text references.

Circularity Check

2 steps flagged · score 4.0 of 10

Partial circularity: the nonreciprocal coupling J1≠J2 is assumed in Eq. (1), and the 'nonreciprocal entanglement' contrast of Eq. (19) reports that same assumed asymmetry; the entanglement magnitudes and parameter trends are genuine outputs.

  1. self definitional [Section II.A, around Eqs. (1) and (2)]
    "The nonreciprocal coupling between a1 and the auxiliary cavity mode a2 (represented by the terms J1a†1a2 and J2a†2a1) arises from the Sagnac-Fizeau effect on the spinning WGM resonator, which makes the effective coupling strength dependent on the direction of energy transfer between the modes."

    This statement is the load-bearing premise for the abstract's claim that 'nonreciprocal entanglements arise due to the Sagnac-Fizeau effect.' The only Sagnac formula supplied, Eq. (2), is a frequency shift ΔF = ±nΩRωc1/c(1 − 1/n² − λ/n dn/dλ); it gives no expression for J1 or J2. The simulations then simply fix J1/ωm = 0.3 and J2/ωm = 1. The direction asymmetry J1≠J2 is therefore an input to Eq. (1), and the computed direction-dependent entanglement is the same asymmetry propagated through the Lyapunov equation, not an independent consequence of the Sagnac shift.

  2. other [Section III.C, Eq. (19)]
    "we use the following bidirectional contrast ratio C for bipartite entanglement to quantitatively describe nonreciprocal entanglement [31], Ckl = |Ekl(ΔF > 0) − Ekl(ΔF < 0)| / (Ekl(ΔF > 0) + Ekl(ΔF < 0))."

    Nonreciprocity is operationally defined by comparing ΔF > 0 with ΔF < 0. In the model, ΔF enters only through the detuning Δ = Δc1 − ΔF; the asymmetric couplings J1≠J2 are kept fixed in both cases. A nonzero C is therefore largely a consequence of the assumed J1≠J2 input combined with a sign-dependent detuning, rather than a measured forward/backward asymmetry independently derived from Sagnac physics. The 'switchable nonreciprocity' displayed in Fig. 6(b) is thus a contrast between two parameter settings of the same assumed-asymmetric Hamiltonian.

full rationale

The paper's central novelty is the claim that the Sagnac-Fizeau effect produces nonreciprocal entanglement. Tracing the derivation, the only explicit Sagnac input is the frequency shift ΔF in Eq. (2), which enters the detuning Δ. The asymmetry that actually makes the entanglement direction-dependent is the unequal hopping amplitudes J1≠J2 in Eq. (1). No equation connects J1 or J2 to Ω, R, n, or ΔF; the text simply asserts that the Sagnac-Fizeau effect 'distinguishes J1 and J2,' and the numerics fix J1/ωm = 0.3, J2/ωm = 1. Therefore the 'nonreciprocal' part of the main result is an input, not a derived prediction. The entanglement values, detuning dependence, thermal robustness, and N-scaling are genuine outputs of the linearized Langevin/Lyapunov calculation from that Hamiltonian, so the circularity is partial rather than total. The non-Hermitian character of Eq. (1) for J1≠J2 and the missing microscopic derivation of J1,J2 are correctness and completeness concerns, not additional circularity; they would remain even if the calculation were fully self-contained.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The central claims rest on two domain assumptions: the nonreciprocal coupling form and the collective-mode partition. Both are stated in the paper but not independently validated. All other quantitative inputs are literature values, and no fitting to external data is performed.

free parameters (2)
  • M, molecular distribution number = 50
    Arbitrary split of N molecules into two collective groups; sets g1 = gm√M and g2 = gm√(N-M), and therefore controls the magnitude and N-scaling of vibration-vibration entanglement. It is a theoretical construct, not a physical parameter.
  • Nonreciprocal coupling strengths J1/ωm and J2/ωm = 0.3 and 1
    Chosen values create the coupling asymmetry that the nonreciprocal entanglement result directly depends on; they are not derived from the Sagnac-Fizeau shift.
assumptions (4)
  • domain assumption The Sagnac-Fizeau effect in a spinning WGM resonator produces an effective nonreciprocal (non-Hermitian) coupling J1 a1†a2 + J2 a2†a1 with J1≠J2.
    Invoked in Eq. (1) and the text after Eq. (2); the paper derives only a frequency shift ΔF, not the coupling asymmetry, and no microscopic derivation of J1≠J2 is given.
  • domain assumption N identical molecular vibrations can be represented by two collective modes B1, B2 (split into groups of M and N-M), with the remaining orthogonal modes decoupled and negligible.
    Eq. (3) and Figure 1 caption; the split is exact if dark modes are included, but the physical meaning of B1-B2 entanglement and its N-scaling depends on the arbitrary choice of M.
  • standard math Standard linearized quantum Langevin equations, Routh-Hurwitz stability, and Lyapunov equation for the covariance matrix are valid for this driven-dissipative system.
    Used in Section II B and III A; standard tools in continuous-variable optomechanics.
  • domain assumption Optical thermal noise is negligible and the mechanical bath is Markovian with thermal phonon number n̄.
    Eq. (7) and diffusion matrix Eq. (16); standard for optical frequencies, but it shapes the temperature robustness claim.
invented entities (1)
  • Collective vibrational modes B1 and B2
    purpose: Create two vibrational modes coupled to the cavity so that vibration-vibration entanglement can be computed and scaled with N.
    The paper calls this separation 'a theoretical construct' (Fig. 1 caption). The physically unique bright mode is √M B1 + √(N-M) B2 over √N; the orthogonal combination does not couple to the cavity, so B1-B2 entanglement is not between two independent physical reservoirs.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Nonreciprocal entanglement in a molecular optomechanical system." pith.science (2026). https://pith.science/paper/2KLZ4VZZ

@misc{pith2026250114045,
  author       = {Pith},
  title        = {Pith review of: Nonreciprocal entanglement in a molecular optomechanical system},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2KLZ4VZZ}},
  note         = {Machine review of arXiv:2501.14045}
}
abstract

We propose a theoretical scheme to generate nonreciprocal bipartite entanglement between a cavity mode and vibrational modes in a molecular cavity optomechanical system. Our system consists of $\mathcal{N}$ molecules placed inside a spinning whispering-gallery-mode (WGM) resonator. The vibrational modes of these molecules are coupled to the WGM resonator mode (which is analogous to a plasmonic cavity) and the resonator is also coupled to an auxiliary optical cavity. We demonstrate that nonreciprocal photon-vibration entanglement and nonreciprocal vibration-vibration entanglement can be generated in this system, even at high temperatures. These nonreciprocal entanglements arise due to the Sagnac-Fizeau effect induced by the spinning WGM resonator. We find that spinning the WGM resonator in the counter-clockwise (CCW) direction enhances both types of nonreciprocal entanglement, especially under blue-detuned driving of the optical cavity mode. Furthermore, we show that vibration-vibration entanglement can be significantly enhanced by increasing the number of molecules. Our findings have potential applications in quantum information transmission and in the development of nonreciprocal quantum devices.

Figures

Figures reproduced from arXiv: 2501.14045 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of a molecular optomechanical system which consists of a spinning whispering gallery mode (WGM) and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The dependence of the system stability on the driving amplitude [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Photon-vibration entanglement versus the normalized cavity detuning ∆ [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Photon-vibration entanglement versus the distribution number of molecular collective mode M, and (b) vibration [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Panels (a)–(c); contour plot of photon-vibration entanglement [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Bidirectional contrast ratio [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strong Molecule-Light Entanglement with Molecular Cavity Optomechanics

    quant-ph 2025-05 conditional novelty 5.0 of 10

    Coupling a plasmonic nanocavity to a high-Q whispering-gallery resonator transfers molecular vibration entanglement to long-lived photons, yielding stationary photon-phonon entanglement that can exceed the standard tw...

Reference graph

Works this paper leans on

44 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    + p 2γ1Bin 1 , δ ˙B2 = − (iωm + γ2)δB2 − i(G∗ 2δa1 + G2δa†

    work page

  2. [2]

    In our model, a1 represents a single effective mode of the WGM resonator relevant to the interactions

    and bj(b† j) are the annihilation (creation) operators of the WGM resonator mode (analogous to the plasmonic cavity mode), auxiliary optical cavity mode and the jth molecular mode, respectively. In our model, a1 represents a single effective mode of the WGM resonator relevant to the interactions. The nonreciprocal coupling between a1 and the auxiliary cav...

    work page

  3. [3]

    + p 2γ2Bin 2 , (9) where ∆′ = ∆ +P2 k=1 2gkRe[βk] is the effective detuning, G1 = √ M gmα1, and G2 = √ N −M gmα1, are the effective optomechanical coupling strengths. In order to study the entanglement, we define the following quadrature operators, δxk = (δak + δa† k)√ 2 , δyk = (δak − δa† k) i √ 2 , δqk = (δBk + δB † k)√ 2 , δpk = (δBk − δB † k) i √ 2 , ...

    work page 2024

  4. [4]

    Stannigel, P

    K. Stannigel, P. Ko3, S. Habraken, S. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, Optomechanical quantum information processing with photons and phonons, Physical review letters 109, 013603 (2012)

    work page 2012

  5. [5]

    Blais, S

    A. Blais, S. M. Girvin, and W. D. Oliver, Quantum information processing and quantum optics with circuit quantum electrodynamics, Nature Physics 16, 247 (2020)

    work page 2020

  6. [6]

    J. Liu, F. He, and K. D. Zhu, Optomechanical controlling of intermolecular interaction and the application in molecular self-assembly, Opt. Express 29, 23357 (2021)

    work page 2021

  7. [7]

    Zhang, J

    Y. Zhang, J. Aizpurua, and R. Esteban, Optomechanical collective effects in surface-enhanced raman scattering from many molecules, ACS Photonics 7, 1676 (2020)

    work page 2020

  8. [8]

    Roelli, C

    P. Roelli, C. Galland, N. Piro, and T. J. Kippenberg, Molecular cavity optomechanics as a theory of plasmon-enhanced raman scattering, Nature Nanotechnology 11, 164 (2015)

    work page 2015

Show all 44 references
  1. [9]

    F. Zou, L. Du, Y. Li, and H. Dong, Amplifying frequency up-converted infrared signals with a molecular optomechanical cavity, Phys. Rev. Lett. 132, 153602 (2024)

    2024

  2. [10]

    Esteban, J

    R. Esteban, J. J. Baumberg, and J. Aizpurua, Molecular optomechanics approach to surface-enhanced raman scattering, Accounts of Chemical Research 55, 1889 (2022)

    2022

  3. [11]

    Roelli, D

    P. Roelli, D. Martin-Cano, T. J. Kippenberg, and C. Galland, Molecular platform for frequency upconversion at the single-photon level, Physical Review X 10, 10.1103/PhysRevX.10.031057 (2020)

    2020 doi

  4. [12]

    W. Chen, P. Roelli, H. Hu, S. Verlekar, S. P. Amirtharaj, A. I. Barreda, T. J. Kippenberg, M. Kovylina, E. Verhagen, A. Mart ´ ınez, and C. Galland, Continuous-wave frequency upconversion with a molecular optomechanical nanocavity, Science 374, 1264 (2021)

    2021

  5. [13]

    Koczor-Benda, P

    Z. Koczor-Benda, P. Roelli, C. Galland, and E. Rosta, Molecular vibration explorer: an online database and toolbox for surface-enhanced frequency conversion and infrared and raman spectroscopy, The Journal of Physical Chemistry A 126, 4657 (2022)

    2022

  6. [14]

    Koner, M

    A. Koner, M. Du, S. Pannir-Sivajothi, R. H. Goldsmith, and J. Yuen-Zhou, A path towards single molecule vibrational strong coupling in a fabry–p´ erot microcavity, Chemical Science14, 10.1039/d3sc01411h (2023)

    2023 doi

  7. [15]

    Roelli, H

    P. Roelli, H. Hu, E. Verhagen, S. Reich, and C. Galland, Nanocavities for molecular optomechanics: Their fundamental description and applications, ACS Photonics 11, 4486 (2024). 13

    2024

  8. [16]

    J. P. Pezacki, J. A. Blake, D. C. Danielson, D. C. Kennedy, R. K. Lyn, and R. Singaravelu, Chemical contrast for imaging living systems: molecular vibrations drive cars microscopy, Nature chemical biology 7, 137 (2011)

    2011

  9. [17]

    Liu and K.-D

    J. Liu and K.-D. Zhu, Coupled quantum molecular cavity optomechanics with surface plasmon enhancement, Photon. Res. 5, 450 (2017)

    2017

  10. [18]

    Flamini, N

    F. Flamini, N. Spagnolo, and F. Sciarrino, Photonic quantum information processing: a review, Reports on Progress in Physics 82, 016001 (2018)

    2018

  11. [19]

    Shoji and T

    Y. Shoji and T. Mizumoto, Magneto-optical non-reciprocal devices in silicon photonics, Science and Technology of Advanced Materials 15, 014602 (2014)

    2014

  12. [20]

    Vitali, S

    D. Vitali, S. Gigan, A. Ferreira, H. R. B¨ ohm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, Optomechanical entanglement between a movable mirror and a cavity field, Phys. Rev. Lett. 98, 030405 (2007)

    2007

  13. [21]

    Djorw´ e, A.-H

    P. Djorw´ e, A.-H. Abdel-Aty, K. Nisar, and S. Engo, Optomechanical entanglement induced by backward stimulated brillouin scattering, Optik 319, 172097 (2024)

    2024

  14. [22]

    D. R. K. Massembele, P. Djorw´ e, A. K. Sarma, A.-H. Abdel-Aty, and S. G. N. Engo, Quantum entanglement assisted via duffing nonlinearity, Physical Review A 110, 10.1103/PhysRevA.110.043502 (2024)

    2024 doi

  15. [23]

    Massembele, P

    D. Massembele, P. Djorw´ e, K. Emale, J.-X. Peng, A.-H. Abdel-Aty, and K. Nisar, Low threshold quantum correlations via synthetic magnetism in brillouin optomechanical system, Physica B: Condensed Matter 697, 416689 (2025)

    2025

  16. [24]

    Djorwe, Y

    P. Djorwe, Y. Pennec, and B. Djafari-Rouhani, Exceptional point enhances sensitivity of optomechanical mass sensors, Physical Review Applied 12, 10.1103/PhysRevApplied.12.024002 (2019)

    2019 doi

  17. [25]

    S. M. Tchounda, P. Djorw´ e, S. N. Engo, and B. Djafari-Rouhani, Sensor sensitivity based on exceptional points engineered via synthetic magnetism, Physical Review Applied 19, 10.1103/PhysRevApplied.19.064016 (2023)

    2023 doi

  18. [26]

    Chen, X.-G

    J. Chen, X.-G. Fan, W. Xiong, D. Wang, and L. Ye, Nonreciprocal photon-phonon entanglement in kerr-modified spinning cavity magnomechanics, Phys. Rev. A 109, 043512 (2024)

    2024

  19. [27]

    Chakraborty and C

    S. Chakraborty and C. Das, Nonreciprocal magnon-photon-phonon entanglement in cavity magnomechanics, Phys. Rev. A 108, 063704 (2023)

    2023

  20. [28]

    Z.-Q. Liu, J. Liu, L. Tan, and W.-M. Liu, Twice-enhanced quantum entanglement in a dual-coupled auxiliary-sphere- assisted cavity magnomechanical system, Physical Review A 110, 023707 (2024)

    2024

  21. [29]

    Zheng, W

    Q. Zheng, W. Zhong, G. Cheng, and A. Chen, Nonreciprocal macroscopic tripartite entanglement in atom- optomagnomechanical system, EPJ Quantum Technology 11, 1 (2024)

    2024

  22. [30]

    P. E. J., Sagnac effect, Reviews of Modern Physics 39, 475 (1967)

    1967

  23. [31]

    Jiao, S.-D

    Y.-F. Jiao, S.-D. Zhang, Y.-L. Zhang, A. Miranowicz, L.-M. Kuang, and H. Jing, Nonreciprocal optomechanical entangle- ment against backscattering losses, Phys. Rev. Lett. 125, 143605 (2020)

    2020

  24. [32]

    long Ren, Nonreciprocal optical–microwave entanglement in a spinning magnetic resonator, Opt

    Y. long Ren, Nonreciprocal optical–microwave entanglement in a spinning magnetic resonator, Opt. Lett. 47, 1125 (2022)

    2022

  25. [33]

    Zheng, W

    Q. Zheng, W. Zhong, G. Cheng, and A. Chen, Nonreciprocal tripartite entanglement based on magnon kerr effect in a spinning microwave resonator, Optics Communications 546, 129796 (2023)

    2023

  26. [34]

    Chen, X.-G

    J. Chen, X.-G. Fan, W. Xiong, D. Wang, and L. Ye, Nonreciprocal entanglement in cavity-magnon optomechanics, Phys. Rev. B 108, 024105 (2023)

    2023

  27. [35]

    Huang, Y.-F

    Z.-H. Huang, Y.-F. Jiao, L.-L. Yan, D.-Y. Wang, S.-L. Su, and H. Jing, Nonreciprocal enhancement of macroscopic entanglement with noise tolerance, Phys. Rev. A 110, 012423 (2024)

    2024

  28. [36]

    Emale, J.-X

    K. Emale, J.-X. Peng, P. Djorw´ e, A. Sarma, Abdourahimi, A.-H. Abdel-Aty, K. Nisar, and S. Engo, Quantum correlations enhanced in hybrid optomechanical system via phase tuning, Physica B: Condensed Matter 701, 416919 (2025)

    2025

  29. [37]

    Amazioug, S

    M. Amazioug, S. Singh, B. Teklu, and M. Asjad, Feedback control of quantum correlations in a cavity magnomechanical system with magnon squeezing, Entropy 25, 1462 (2023)

    2023

  30. [38]

    Xiao, Y.-C

    Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, Strongly enhanced light-matter interaction in a hybrid photonic-plasmonic resonator, Phys. Rev. A 85, 031805 (2012)

    2012

  31. [39]

    Maayani, R

    S. Maayani, R. Dahan, Y. Kligerman, E. Moses, A. U. Hassan, H. Jing, F. Nori, D. N. Christodoulides, and T. Carmon, Flying couplers above spinning resonators generate irreversible refraction, Nature 558, 569 (2018)

    2018

  32. [40]

    Huang, D

    J. Huang, D. Lei, G. S. Agarwal, and Z. Zhang, Collective quantum entanglement in molecular cavity optomechanics, Phys. Rev. B 110, 184306 (2024)

    2024

  33. [41]

    E. J. POST, Sagnac effect, Rev. Mod. Phys. 39, 475 (1967)

    1967

  34. [42]

    E. X. DeJesus and C. Kaufman, Routh-hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations, Phys. Rev. A 35, 5288 (1987)

    1987

  35. [43]

    M. B. Plenio, Logarithmic negativity: A full entanglement monotone that is not convex, Phys. Rev. Lett. 95, 090503 (2005)

    2005

  36. [44]

    M. K. Schmidt and M. J. Steel, Molecular optomechanics in the anharmonic regime: from nonclassical mechanical states to mechanical lasing, New Journal of Physics 26, 033041 (2024)

    2024

Pith tools

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