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Strong Molecule-Light Entanglement with Molecular Cavity Optomechanics

T0 review · 2 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that a single molecule in a hybrid plasmonic–whispering-gallery-mode cavity can sustain steady photon–phonon entanglement at room temperature, reaching logarithmic negativity $E_N^{a|b} = 1.05$ and surpassing the $\ln 2…

desk verdict A careful theoretical proposal with a genuinely new redirection mechanism, but the headline E_N=1.05 rests on an unvalidated assumption that the WGM keeps its ultrahigh Q while strongly coupled to a lossy nanoparticle. read the letter →

arxiv 2505.21227 v1 pith:5LS2RKBE submitted 2025-05-27 quant-ph

Hong-Yun Yu , Ya-Feng Jiao , Jie Wang , Feng Li , Bin Yin , Tian Jiang , Qi-Rui Liu , Hui Jing
show 1 more author
Ke Wei
This is my paper · ORCID
classification quant-ph PACS 03.65.Ud42.50.Pq42.50.Wk
keywords molecularoptomechanicsphoton-phononentanglementwhispering-gallery-moderesonatorplasmonicnanocavitystationarylogarithmicnegativityground-statecoolingroom-temperaturequantumoptics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether a single molecule can hold steady quantum entanglement between cavity light and its own molecular vibration at room temperature, a regime where thermal noise usually destroys quantum correlations. It claims yes, if the molecule sits in a plasmonic hotspot that is also evanescently coupled to an ultrahigh-quality whispering-gallery-mode (WGM) resonator. In the blue-detuned regime the lossy plasmonic mode generates photon-phonon correlations, while the long-lived WGM collects the Stokes photons and suppresses molecular absorption, cooling the 30 THz vibration near its ground state. Solving the linearized three-mode model, the paper finds stationary photon-phonon logarithmic negativity up to $E_N^{a|b} = 1.05$, exceeding the $\ln 2 \approx 0.69$ bound for conventional two-mode stationary squeezing.

What carries the argument

The argument rests on a linearized three-mode Gaussian model: the WGM photon mode $\hat{a}$, the molecular vibration $\hat{b}$, and the plasmonic mode $\hat{c}$, coupled by beam-splitter strength $J$ and effective radiation-pressure coupling $G = 2g_c c_s$. The steady state is obtained from the $6\times 6$ covariance matrix $V$ that solves the Lyapunov equation $AV + VA^T = -D$, and bipartite entanglement is quantified by logarithmic negativity $E_N = \max[0, -\ln(2\nu^-_{m,n})]$, where $\nu^-_{m,n}$ is the minimum symplectic eigenvalue of the partial transpose of the reduced covariance matrix. Two analytic objects carry the physics: the photon-redirection ratio $R_{ac} = -iJ/[\kappa_a + i(\omega_b + \Delta_a)]$, which measures how much of a Stokes photon produced in the plasmon mode ends up in the WGM, and the absorption rate $A_+ \approx G^2\kappa_a/(2J^2)$ for $J\gg\kappa_a$, whose suppression keeps $\langle \hat{N}_b\rangle < 1$. The relevant regime is the Stokes sideband $\Delta_a = \Delta_c = -\omega_b$, where the pump is effectively decoupled from the WGM while Stokes photons are redirected into it.

What would settle it

One concrete check is to measure the effective linewidth of the WGM-like mode in a fabricated hybrid device with a metal nanoparticle in the evanescent field: if $\kappa_a^{\mathrm{eff}}/2\pi \gtrsim 0.1$ THz at $J/2\pi = 1.5$ THz, the predicted $E_N^{a|b} = 1.05$ would fall below $\ln 2 \approx 0.69$ and the central claim would fail. Alternatively, the paper's two-WGM homodyne protocol can be run at room temperature, and failure to observe the Duan inseparability criterion $\langle(\Delta X_S + \Delta X_{AS})^2\rangle + \langle(\Delta P_S - \Delta P_{AS})^2\rangle < 2$ would refute the predicted entanglement.

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Extended reading notes

Core claim

The central claim is that stationary photon-phonon entanglement in a single-molecule optomechanical system can surpass the conventional two-mode stationary squeezing bound. With a 30 THz molecular vibration, a 330 THz plasmon mode of linewidth $\kappa_c/2\pi = 15$ THz, and a high-Q WGM of linewidth $\kappa_a/2\pi = 10^{-4}$ THz, the model yields $E_N^{a|b} = 1.05$ at photon-plasmon coupling $J/2\pi = 1.5$ THz and effective plasmon-phonon coupling $G/2\pi = 2$ THz, while the plasmon-phonon entanglement $E_N^{c|b}$ is pushed toward zero. The mechanism is twofold: the beam-splitter coupling $J$ redirects Stokes photons from the lossy plasmon mode into the high-Q WGM (response ratio $R_{ac}\gg 1$), and the reduced optical absorption rate $A_+$ keeps the phonon occupancy $\langle \hat{N}_b\rangle$ below unity. The paper therefore claims that this hybrid architecture realizes ground-state cooling of the molecular vibration at ambient temperature, separating entanglement generation at the lossy hotspot from entanglement storage in the quiet WGM.

Load-bearing premise

The load-bearing premise is that the ultrahigh-Q WGM mode keeps its bare narrow linewidth ($\kappa_a/2\pi = 10^{-4}$ THz) even while evanescently coupled to a lossy plasmonic nanocavity containing a metal nanoparticle, since the model treats $\kappa_a$ as an independent constant and does not include the extra loss channels that a metal nanoparticle in the evanescent field would open; if the effective linewidth grew to roughly 0.1 THz, the absorption rate $A_+$ would rise, ground-state cooling would fail, and the $E_N^{a|b} > \ln 2$ result would collapse.

Editorial extensions

If this is right

  • Stationary entanglement between a single molecule's vibration and cavity photons becomes feasible at room temperature, because the 30 THz vibration has thermal occupancy $\bar{n}\approx 0.01$ and the WGM suppresses reabsorption.
  • The stationary logarithmic negativity can exceed the $\ln 2 \approx 0.69$ bound of conventional two-mode optomechanical squeezing, reaching $1.05$ in the predicted parameter window.
  • Entanglement generation and storage are spatially separated: the lossy plasmonic hotspot creates the photon-phonon correlations, while the high-Q WGM stores them, making the entanglement insensitive to plasmonic dissipation.
  • The hybrid architecture widens the dynamical stability region: larger $J$ raises the instability threshold in $G$, permitting stronger effective coupling and larger entanglement.
  • A two-WGM extension with zero pump detuning provides a concrete path to experimental verification through homodyne detection of Stokes and anti-Stokes outputs.

Reading between the lines

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

  • This suggests a general design principle: generate fragile quantum correlations in a strongly coupled but lossy element, then transfer them to a quiet high-Q element, a strategy that could apply to other solid-state quantum emitters such as color centers or excitons.
  • If the two-WGM verification protocol works, experimenters would not need to detect terahertz radiation directly; homodyne detection of the optical outputs would certify the phonon entanglement, sidestepping a major experimental bottleneck.
  • The claim implicitly predicts that the bare WGM linewidth is largely unchanged by the nearby nanoparticle; an independent linewidth measurement would be a sharper test than the entanglement measurement itself.
  • A directly measurable optical signature of the mechanism is that, at the Stokes sideband, the ratio of Stokes emission into the WGM versus the plasmon mode should scale as $|R_{ac}|^2 \approx J^2/\kappa_a^2$, which could be checked in a Raman scattering experiment.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The manuscript proposes a hybrid optomechanical setup in which a single molecule in a plasmonic nanocavity (NPoM) is evanescently coupled to a high-Q WGM microdisk resonator. The authors linearize the quantum Langevin equations around a driven steady state, solve the Lyapunov equation for the 6×6 covariance matrix, and compute logarithmic negativity for the bipartitions. The central finding is that at Stokes-sideband (blue-detuned) driving, the photon-phonon logarithmic negativity E_N^{a|b} reaches approximately 1.05 for J/2π=1.5 THz and G/2π=2 THz, exceeding the often-quoted ln2 stationary bound for conventional two-mode optomechanical squeezing. The explanation is a combination of Stokes-photon redirection into the low-loss WGM and suppression of the molecular absorption rate A_+, which keeps the phonon near its ground state. The SI contains derivations of the Stokes response functions, the absorption/emission rates, a finite-γ correction to A_+, and a two-WGM detection protocol.

Significance. If the predicted regime is physically realizable, the result is significant: it would be a concrete proposal for stationary, ambient-temperature photon-phonon entanglement in a single-molecule platform, with a clear mechanism (photon redirection plus heating suppression) and a detection scheme. The linearized QLE/Lyapunov treatment is standard and internally consistent; the SI is unusually careful in validating the S_FF(ω) approach against the covariance-matrix result, including the κa<<γ correction to A_+ in Sec. V. The paper also gives a plausible experimental protocol with two WGMs for homodyne verification. The main weakness is not in the mathematics but in the physical modeling of the high-Q WGM when it is strongly coupled to a lossy metal nanoparticle, which is the load-bearing idealization behind the headline number.

major comments (2)
  1. [The System (parameter list) and SI Eq. (S18)] The headline value E_N=1.05 at J/2π=1.5 THz, G/2π=2 THz assumes κa/2π=10^-4 THz while the WGM is strongly evanescently coupled to a plasmonic nanocavity containing a metal nanoparticle. The model treats κa as an independent constant and includes no extra loss channel for the WGM. If the nanoparticle loads the WGM so that κa/2π rises to only 0.1 THz (Q≈3×10^3 rather than 3×10^6), then Eq. (S18) gives A+≈(G^2/2)κa/(J^2+κaκc)≈0.053 THz at the optimum, exceeding 2γ=0.02 THz. In that case the denominator in Eq. (S15) becomes negative and the steady state used for Fig. 3(c) does not exist. The manuscript should provide a model or experimental bound for the J-induced loading of κa, or demonstrate that the bound-breaking regime survives under a realistic loaded linewidth; without this, the central claim is contingent on an unvalidated idealization.
  2. [Fig. 3 and Eq. (S15)] The manuscript states that all points in Fig. 3 are in the stable parameter region but does not show the stability boundary. The maximum in Fig. 3(c) is controlled by the competition between A+ and 2γ in Eq. (S15): as A+ approaches 2γ, the stationary phonon occupation diverges and the linearized steady state ceases to exist. Because the optimal point lies near this boundary, the authors should provide a stability diagram in the (J,G) plane for the stated κa and also for modest perturbations of κa, so the reader can judge how fragile the E_N≈1.05 result is to parameter uncertainty.
minor comments (6)
  1. [Introduction and Entanglement Trade-off] The phrase 'plasmon-photon subsystem' appears where 'plasmon-phonon subsystem' is meant (the bipartition in question is c–b); please correct this terminology throughout.
  2. [Abstract] The abstract's claim of 'robust entanglement among bosonic modes' overstates the results, since only bipartite entanglement measures are reported and no tripartite measure is computed; please adjust the wording.
  3. [SI Eq. (S13b) and Eq. (S16)] The denominators in these equations contain an extra closing parenthesis; please fix the typography.
  4. [Fig. 3(c)] The maximum E_N≈1.05 is reported at J/2π=1.5 THz and G/2π=2 THz, which is the edge of the plotted parameter window; please state explicitly whether this is an interior maximum of the optimization or a boundary value of the chosen range.
  5. [SI Sec. VI] The 'optimal pump power P=8.24 mW' should be accompanied by the corresponding steady-state amplitude |c_s| and the resulting G value, so that the consistency of the parameter set can be checked.
  6. [Breaking the entanglement bound] The statement that E_N exceeds the 'theoretical bound' should clarify that the bound applies to stationary two-mode optomechanical systems without auxiliary modes; in a three-mode system with an auxiliary mode the bound does not apply, as the authors themselves note via Refs. [39,44-46].

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: E_N is a direct Lyapunov-equation output with independent analytical cross-checks and no fitted target.

full rationale

The central claim (stationary E_N^{a|b}=1.05 at J/2π=1.5 THz, G/2π=2 THz) is obtained by numerically solving the linearized Lyapunov equation AV+VA^T=-D (SI Eq. S9) for the stated Hamiltonian and parameters; no parameter is fitted to this result and no measured data are invoked. The explanatory quantities introduced afterwards—R_ac (Eq. 2/S14), A_+ (Eq. S18), and the mean phonon number (Eq. 3/S15)—are derived analytically from the same linearized equations, but they are not used as inputs to compute E_N; instead the paper explicitly checks them against the covariance-matrix solution (Fig. 4(a) and Fig. S2), which is a consistency test, not a circular reduction. The ln2 comparison is an external benchmark from the cited optomechanics literature, rather than an input or a self-citation. The only self-citations (Refs. [15] and [47], by Jiao/Jing) appear in contextual or feasibility remarks—single-mode backscattering and synthetic gauge fields—and do not carry the derivation of the entanglement result. The acknowledged limitation in SI Sec. VI (neglect of WGM-induced renormalization of g_c and practical detuning challenges) concerns the physical validity of parameter assumptions, not definitional circularity. Accordingly, no step of the claimed derivation reduces to its own inputs.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central prediction is computed from a linearized three-mode Gaussian model with no fitting; the inputs are physical parameters chosen within claimed feasible ranges. The most consequential choices are the large couplings J and G (peaking at the boundary of the scanned ranges) and the assumption that the WGM linewidth stays at 10^-4 THz despite the presence of a metal nanoparticle. The model adds no new physical entities.

free parameters (3)
  • Effective plasmon-phonon coupling G/2π = 0 to 2 THz, peak result at 2 THz
    Defined as G = 2 g_c c_s; depends on laser power, molecular position, and single-photon coupling gc. Treated as an adjustable input; the E_N = 1.05 result sits at the upper end of the scanned range.
  • Plasmon-WGM coupling J/2π = 0 to 1.5 THz, peak result at 1.5 THz
    Controlled by the nanoparticle position in the WGM evanescent field; scanned as an input; the maximum E_N occurs at the upper end of the range.
  • WGM linewidth κa/2π = 10^-4 THz
    Chosen from ultrahigh-Q microdisk literature; load-bearing because R_ac >> 1 and A+ suppression require κa << J. No model for degradation by the metal nanoparticle.
assumptions (7)
  • standard math Markovian white-noise quantum Langevin equations with delta-correlated input noises
    Used throughout Eq. (S1); valid for mechanical quality factor Q satisfying ωb/γ >> 1.
  • standard math Linearization around a stable steady state under strong driving
    Main text after Eq. (1); second-order fluctuation terms neglected; standard for optomechanics with |cs| >> 1.
  • domain assumption Neglect of direct WGM-molecular vibration coupling
    Main text: 'we neglect the WGM-molecular vibration coupling... the radiation pressure from the WGM field... negligible.' No quantitative estimate is given; Stokes photons in the WGM could interact with the molecule.
  • domain assumption Neglect of the increase of plasmonic mode volume due to plasmon-WGM coupling
    Main text cites [50] but does not quantify the effect on gc or G.
  • domain assumption WGM retains its bare ultrahigh Q (κa/2π = 10^-4 THz) in the hybrid metal-nanoparticle structure
    Load-bearing for the redirection ratio and ground-state cooling; the paper does not model additional absorption/scattering losses from the metallic nanoparticle overlapping the WGM field.
  • domain assumption Single-mode operation of the WGM (CW mode only)
    SI Sec IV relies on asymmetric backscattering to suppress the CCW mode; the paper notes that with two modes E_N^{a|b} drops by about 50%.
  • domain assumption Stability of the molecule under the required pump power (~8 mW)
    SI Sec VI asserts the power 'matches the thermal stable condition' citing [5], but no thermal model of the single molecule is provided.

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Cite this review

Pith. "Pith review of Strong Molecule-Light Entanglement with Molecular Cavity Optomechanics." pith.science (2026). https://pith.science/paper/5LS2RKBE

@misc{pith2026250521227,
  author       = {Pith},
  title        = {Pith review of: Strong Molecule-Light Entanglement with Molecular Cavity Optomechanics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5LS2RKBE}},
  note         = {Machine review of arXiv:2505.21227}
}
read the original abstract

We propose a molecular optomechanical platform to generate robust entanglement among bosonic modes-photons, phonons, and plasmons-under ambient conditions. The system integrates an ultrahigh-Q whispering-gallery-mode (WGM) optical resonator with a plasmonic nanocavity formed by a metallic nanoparticle and a single molecule. This hybrid architecture offers two critical advantages over standalone plasmonic systems: (i) Efficient redirection of Stokes photons from the lossy plasmonic mode into the long-lived WGM resonator, and (ii) Suppression of molecular absorption and approaching vibrational ground states via plasmon-WGM interactions. These features enable entanglement to transfer from the fragile plasmon-phonon subsystem to a photon-phonon bipartition in the blue-detuned regime, yielding robust stationary entanglement resilient to environmental noise. Remarkably, the achieved entanglement surpasses the theoretical bound for conventional two-mode squeezing in certain parameter regimes. Our scheme establishes a universal approach to safeguard entanglement in open quantum systems and opens avenues for noise-resilient quantum information technologies.

Figures

Figures reproduced from arXiv: 2505.21227 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic diagram of single-molecule optomechanical system with WGM (denoted as [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The line plots of the logarithmic negativity [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Contour-filled plot of the stationary thermal excita [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Forward citations

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    quant-ph 2025-10 conditional novelty 5.0 of 10

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Reference graph

Works this paper leans on

81 extracted references · 68 canonical work pages · cited by 1 Pith paper

  1. [2]

    Zhao, S.-D

    W. Zhao, S.-D. Zhang, A. Miranowicz, and H. Jing, Sci. China- Phys. Mech. Astron. 63, 224211 (2020)

    work page 2020

  2. [3]

    Wilson-Rae, N

    I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, New J. Phys.10, 095007 (2008)

    work page 2008

  3. [4]

    Millen, T

    J. Millen, T. S. Monteiro, R. Pettit, and A. N. Vamivakas, Rep. Prog. Phys. 83, 026401 (2020)

    work page 2020

  4. [5]

    Roelli, C

    P. Roelli, C. Galland, N. Piro, and T. J. Kippenberg, Nat. Nan- otechnol. 11, 164 (2016)

    work page 2016

  5. [6]

    Roelli, H

    P. Roelli, H. Hu, E. Verhagen, S. Reich, and C. Galland, ACS Photonics 11, 4486 (2024)

    work page 2024

  6. [7]

    M. K. Schmidt, R. Esteban, A. Gonz ´alez-Tudela, G. Giedke, and J. Aizpurua, ACS Nano 10, 6291 (2016)

    work page 2016

  7. [8]

    M. K. Schmidt, R. Esteban, F. Benz, J. J. Baumberg, and J. Aizpurua, Faraday Discuss. 205, 31 (2017)

    work page 2017

  8. [9]

    Esteban, J

    R. Esteban, J. J. Baumberg, and J. Aizpurua, Acc. Chem. Res. 55, 1889 (2022)

    work page 2022

Show all 81 references
  1. [10]

    L. A. Jakob, W. M. Deacon, Y . Zhang, B. De Nijs, E. Pavlenko, S. Hu, C. Carnegie, T. Neuman, R. Esteban, J. Aizpurua, and J. J. Baumberg, Nat. Commun. 14, 3291 (2023)

    2023

  2. [11]

    Y . Xu, H. Hu, W. Chen, P. Suo, Y . Zhang, S. Zhang, and H. Xu, ACS Nano 16, 12711 (2022)

    2022

  3. [12]

    Lombardi, M

    A. Lombardi, M. K. Schmidt, L. Weller, W. M. Deacon, F. Benz, B. De Nijs, J. Aizpurua, and J. J. Baumberg, Phys. Rev. X 8, 011016 (2018)

    2018

  4. [13]

    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, Science 374, 1264 (2021)

    2021

  5. [14]

    Xomalis, X

    A. Xomalis, X. Zheng, R. Chikkaraddy, Z. Koczor-Benda, E. Miele, E. Rosta, G. A. E. Vandenbosch, A. Mart ´ınez, and J. J. Baumberg, Science 374, 1268 (2021). 6

    2021

  6. [15]

    Abutalebi, S

    S. Abutalebi, S. M. Ashrafi, H. Ranjbar Askari, and A. Bahram- pour, Opt. Mater. Express 14, 2134 (2024)

    2024

  7. [16]

    Moradi Kalarde, F

    F. Moradi Kalarde, F. Ciccarello, C. S ´anchez Mu ˜noz, J. Feist, and C. Galland, Nanophotonics 14, 59 (2025)

    2025

  8. [17]

    J. Liu, F. He, and K. D. Zhu, EPL 137, 25002 (2022)

    2022

  9. [18]

    S. M. Ashrafi, R. Malekfar, A. R. Bahrampour, and J. Feist, Phys. Rev. A 100, 013826 (2019)

    2019

  10. [19]

    Carretta, D

    S. Carretta, D. Zueco, A. Chiesa, A. G ´omez-Le´on, and F. Luis, Appl. Phys. Lett. 118, 240501 (2021)

    2021

  11. [20]

    D. K. Ruttley, T. R. Hepworth, A. Guttridge, and S. L. Cornish, Nature 637, 827 (2025)

    2025

  12. [21]

    S. L. Cornish, M. R. Tarbutt, and K. R. A. Hazzard, Nat. Phys. 20, 730 (2024)

    2024

  13. [22]

    Y . Li, W. Chen, X. He, J. Shi, X. Cui, J. Sun, and H. Xu, Adv. Mater. 36, 2405186 (2024)

    2024

  14. [23]

    Chiesa, P

    A. Chiesa, P. Santini, E. Garlatti, F. Luis, and S. Carretta, Rep. Prog. Phys. 87, 034501 (2024)

    2024

  15. [24]

    Weedbrook, S

    C. Weedbrook, S. Pirandola, R. Garc´ıa-Patr´on, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012)

    2012

  16. [25]

    C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Woot- ters, Phys. Rev. A 54, 3824 (1996)

    1996

  17. [26]

    Raussendorf and H

    R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

    2001

  18. [27]

    T. D. Ladd, F. Jelezko, R. Laflamme, Y . Nakamura, C. Monroe, and J. L. O’Brien, Nature 464, 45 (2010)

    2010

  19. [28]

    Y . Xia, W. Li, W. Clark, D. Hart, Q. Zhuang, and Z. Zhang, Phys. Rev. Lett. 124, 150502 (2020)

    2020

  20. [29]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Rev. Mod. Phys. 89, 035002 (2017)

    2017

  21. [30]

    Z. Zhao, Y . A. Chen, A. N. Zhang, T. Yang, H. J. Briegel, and J. W. Pan, Nature 430, 54 (2004)

    2004

  22. [31]

    A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. An- dersson, Nat. Phys. 7, 677 (2011)

    2011

  23. [32]

    Mazzanti, R

    M. Mazzanti, R. X. Schussler, J. D. A. Espinoza, Z. Wu, R. Ger- ritsma, and A. Safavi-Naini, Phys. Rev. Lett. 127, 260502 (2021)

    2021

  24. [33]

    Haffner, C

    H. Haffner, C. F. Roos, and R. Blatt, Phys. Rep. 469, 155 (2008)

    2008

  25. [34]

    Clarke and F

    J. Clarke and F. K. Wilhelm, Nature 453, 1031 (2008)

    2008

  26. [35]

    Kotler, G

    S. Kotler, G. A. Peterson, E. Shojaee, F. Lecocq, K. Cicak, A. Kwiatkowski, S. Geller, S. Glancy, E. Knill, R. W. Sim- monds, J. Aumentado, and J. D. Teufel, Science 372, 622 (2021)

    2021

  27. [36]

    Mercier de L ´epinay, C

    L. Mercier de L ´epinay, C. F. Ockeloen-Korppi, M. J. Woolley, and M. A. Sillanp¨a¨a, Science 372, 625 (2021)

    2021

  28. [37]

    Vitali, S

    D. Vitali, S. Gigan, A. Ferreira, H. R. B ¨ohm, P. Tombesi, A. Guerreiro, V . Vedral, A. Zeilinger, and M. Aspelmeyer, Phys. Rev. Lett. 98, 030405 (2007)

    2007

  29. [38]

    T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehn- ert, Science 342, 710 (2013)

    2013

  30. [39]

    Wang and A

    Y .-D. Wang and A. A. Clerk, Phys. Rev. Lett. 110, 253601 (2013)

    2013

  31. [41]

    Wang, X.-Y

    M. Wang, X.-Y . L¨u, Y .-D. Wang, J. Q. You, and Y . Wu, Phys. Rev. A 94, 053807 (2016)

    2016

  32. [42]

    Hu, L.-T

    C.-S. Hu, L.-T. Shen, Z.-B. Yang, H. Wu, Y . Li, and S.-B. Zheng, Phys. Rev. A 100, 043824 (2019)

    2019

  33. [43]

    Huang and A

    S. Huang and A. Chen, Phys. Rev. A 98, 063843 (2018)

    2018

  34. [44]

    Zhang, C.-S

    Y .-L. Zhang, C.-S. Yang, Z. Shen, C.-H. Dong, G.-C. Guo, C.- L. Zou, and X.-B. Zou, Phys. Rev. A 101, 063836 (2020)

    2020

  35. [45]

    Liao, R.-X

    C.-G. Liao, R.-X. Chen, H. Xie, and X.-M. Lin, Phys. Rev. A 97, 042314 (2018)

    2018

  36. [46]

    Tian, Phys

    L. Tian, Phys. Rev. Lett. 110, 233602 (2013)

    2013

  37. [47]

    Liu, Y .-F

    J.-X. Liu, Y .-F. Jiao, Y . Li, X.-W. Xu, Q.-Y . He, and H. Jing, Sci. China-Phys. Mech. Astron. 66, 230312 (2023)

    2023

  38. [48]

    Huang, D

    J. Huang, D. Lei, G. S. Agarwal, and Z. Zhang, Phys. Rev. B 110, 184306 (2024)

    2024

  39. [49]

    K. B. Emale, J.-X. Peng, A. Sohail, P. Djorwe, A.-H. Abdel- Aty, N. Alessa, K. S. Nisar, and S. G. N. Engo, (2025), 2501.14045

    2025 arXiv

  40. [50]

    H. M. Doeleman, E. Verhagen, and A. F. Koenderink, ACS Photonics 3, 1943 (2016)

    2016

  41. [52]

    J. Sun, H. Hu, Y . Xu, Y . Li, and H. Xu, Laser Photonics Rev. 16, 2100564 (2022)

    2022

  42. [53]

    Shlesinger, J

    I. Shlesinger, J. Vandersmissen, E. Oksenberg, E. Verhagen, and A. F. Koenderink, Sci. Adv.9, eadj4637 (2023)

    2023

  43. [54]

    Shlesinger, K

    I. Shlesinger, K. G. Cogn ´ee, E. Verhagen, and A. F. Koen- derink, ACS Photonics 8, 3506 (2021)

    2021

  44. [56]

    Liu, Y .-W

    Y .-C. Liu, Y .-W. Hu, C. W. Wong, and Y .-F. Xiao, Chinese Phys. B 22, 114213 (2013)

    2013

  45. [57]

    Genes, D

    C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A 77, 033804 (2008)

    2008

  46. [58]

    W. Mao, Y . Li, X. Jiang, Z. Liu, and L. Yang, Light Sci. Appl. 12, 247 (2023)

    2023

  47. [59]

    Chikkaraddy, A

    R. Chikkaraddy, A. Xomalis, L. A. Jakob, and J. J. Baumberg, Light Sci. Appl. 11, 19 (2022)

    2022

  48. [60]

    Zhang, S

    Z. Zhang, S. Mouradian, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. Lett. 114, 110506 (2015)

    2015

  49. [61]

    Sunami, S

    S. Sunami, S. Tamiya, R. Inoue, H. Yamasaki, and A. Goban, PRX Quantum 6, 010101 (2025)

    2025

  50. [62]

    Aghaee Rad, T

    H. Aghaee Rad, T. Ainsworth, R. N. Alexander, B. Altieri, and M. F. Askarani, Nature 638, 912 (2025). Supplemental Information: Strong Molecule-Light Entanglement with Molecular Cavity Optomechanics Hong-Yun Yu,1 Ya-Feng Jiao,2, 3 Jie Wang,4 Feng Li,5 Bin Yin,4 Tian Jiang,6, 1...

    2025 arXiv

  51. [63]

    Coupling asymmetry: Small discrepancies betweenJ1 andJ2 (< 10%) induce bearable entanglement degradation (Fig. S4(b))

  52. [64]

    S4(c)), achievable through thermal compensa- tion of WGMs and pump tuning

    Detuning mismatch: Strict maintenance of ∆a1≈− ∆a2 is crucial (Fig. S4(c)), achievable through thermal compensa- tion of WGMs and pump tuning

  53. [65]

    Pump detuning tolerance: Moderate ∆c variations preserve entanglement (Fig. S4(d))

  54. [66]

    For κa/2π <10−4 THz, the improvement in entanglement becomes negligible (Fig

    High-Q resonator requirement While a higher Q factor ( κa) enhances the entanglement strength ENa 1|a2, ultra-high Q values are not strictly necessary. For κa/2π <10−4 THz, the improvement in entanglement becomes negligible (Fig. S4(e)). Then by measuring the quadrature operat...

  55. [67]

    S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , second edition ed. (Westview Press, 2015)

    2015

  56. [68]

    E. X. DeJesus and C. Kaufman, Phys. Rev. A 35, 5288 (1987)

    1987

  57. [69]

    Adesso, A

    G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A 70, 022318 (2004)

    2004

  58. [70]

    Roelli, C

    P. Roelli, C. Galland, N. Piro, and T. J. Kippenberg, Nat. Nanotechnol. 11, 164 (2016)

    2016

  59. [71]

    J. Sun, H. Hu, Y . Xu, Y . Li, and H. Xu, Laser Photon. Rev.16, 2100564 (2022)

    2022

  60. [72]

    Shlesinger, J

    I. Shlesinger, J. Vandersmissen, E. Oksenberg, E. Verhagen, and A. F. Koenderink, Sci. Adv. 9, eadj4637 (2023)

    2023

  61. [73]

    Shlesinger, K

    I. Shlesinger, K. G. Cogn ´ee, E. Verhagen, and A. F. Koenderink, ACS Photonics 8, 3506 (2021)

    2021

  62. [74]

    Genes, A

    C. Genes, A. Mari, P. Tombesi, and D. Vitali, Phys. Rev. A 78, 032316 (2008)

    2008

  63. [75]

    Wang and A

    Y .-D. Wang and A. A. Clerk, Phys. Rev. Lett.110, 253601 (2013)

    2013

  64. [76]

    Liu, Y .-W

    Y .-C. Liu, Y .-W. Hu, C. W. Wong, and Y .-F. Xiao, Chinese Phys. B22, 114213 (2013)

    2013

  65. [77]

    Aspelmeyer, T

    M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014)

    2014

  66. [78]

    A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Rev. Mod. Phys. 82, 1155 (2010)

    2010

  67. [79]

    A. O. Svela, J. M. Silver, L. Del Bino, S. Zhang, M. T. M. Woodley, M. R. Vanner, and P. Del’Haye, Light Sci. Appl. 9, 204 (2020)

    2020

  68. [80]

    Wiersig, Phys

    J. Wiersig, Phys. Rev. A 84, 063828 (2011)

    2011

  69. [81]

    Jiao, S.-D

    Y .-F. Jiao, S.-D. Zhang, Y .-L. Zhang, A. Miranowicz, L.-M. Kuang, and H. Jing, Phys. Rev. Lett.125, 143605 (2020)

    2020

  70. [82]

    Marquardt, J

    F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, Phys. Rev. Lett. 99, 093902 (2007)

    2007

  71. [83]

    Shlesinger, I

    I. Shlesinger, I. M. Palstra, and A. F. Koenderink, Phys. Rev. Lett. 130, 016901 (2023)

    2023

  72. [84]

    L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000)

    2000

  73. [85]

    T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, Science 342, 710 (2013)

    2013

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.