Pith. sign in

REVIEW 4 major objections 5 minor 71 references

Goos-Hanchen Shift with a rotating atomic superfluid in a ring

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read With quantized circulation in a ring BEC, optomechanical interference turns the Goos-Hanchen shift of a transmitted probe into a power-tunable, rotation-biased displacement, reaching about 1.0 × 10^-4 for Lp = 1 and 1 fW control power.

desk verdict Good platform idea undercut by non-reproducible equations: the printed GH formula is not the phase derivative and Eq. (33) makes transmission constant. read the letter →

arxiv 2509.04148 v1 pith:AEHOJURQ submitted 2025-09-04 cond-mat.quant-gas

Ghaisud Din , Muqaddar Abbas , Pei Zhang This is my paper · ORCID
classification cond-mat.quant-gas
keywords Goos-HanchenshiftringBose-Einsteincondensatecavityoptomechanicsoptomechanicallyinducedtransparencyquantizedcirculationdouble-OMITtransmissionphasebeamsteering
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 proposes that the rotation of a ring-trapped Bose-Einstein condensate can be converted into a large, controllable sideways displacement of a transmitted light beam—the Goos-Hanchen shift—inside an optical cavity. The central step is that quantized circulation splits the condensate's two Bragg-scattered mechanical side modes, so the usual single optomechanically induced transparency window becomes a double transparency with steep dispersive flanks. Because the beam shift is proportional to the angular derivative of the transmitted phase, those flanks amplify the shift and bias its sign, making it grow with control-laser power and peak at red-sideband detuning. If correct, this yields two practical outputs: a non-destructive, in-situ way to read the circulation state, and a femto-watt-level beam-steering and phase-gradient sensing mechanism.

What carries the argument

The carrying mechanism is the pair of Bragg-scattered mechanical side modes c and d of the condensate, with bare frequencies ωc = ℏ(Lp + 2l)^2/2Ia and ωd = ℏ(Lp − 2l)^2/2Ia. At Lp = 0 they are degenerate and the probe sees ordinary optomechanically induced transparency; circulation splits them into a double-OMIT profile whose central absorption width grows with |Ωc − Ωd|. The Goos-Hanchen shift is the Artmann-type angular derivative of the transmitted phase, St = −(λ/2π|Tt|^2)[Re Tt d/dθ Im Tt + Im Tt d/dθ Re Tt], evaluated from the transfer-matrix coefficient Tt. The split side modes supply the steep phase dispersion that inflates this derivative. The angular-lattice coupling G = u0√(n/2)/2

What would settle it

Solve the few-mode many-body problem (or run a truncated-Wigner simulation) for small N with the same ring-BEC parameters and compare the probe transmission to Eqs. (20)-(22): if no double-OMIT doublet appears at δ ≈ Ωc, Ωd for Lp ≠ 0, the mean-field ansatz is the source of the effect. Alternatively, measure the transmitted-probe Goos-Hanchen shift versus incidence angle for Lp = 1, Plc = 1 fW at Δ̃ = −Ωm and check whether the peak reaches about 1.0 × 10^-4 and drops to about 3 × 10^-6 at Δ̃ = −1.2Ωm, as claimed.

Watch

Extended reading notes

Core claim

The paper's central claim is that the transmitted probe's Goos-Hanchen shift—the angular derivative of its transmission phase, Eq. (34)—can be amplified and sign-biased by the ring BEC's quantized circulation. With Lp = 0, the two Bragg-scattered mechanical side modes are degenerate, giving standard OMIT and a strictly positive, bounded shift near 3 × 10^-6 controlled by cooperativity. With Lp ≠ 0, the side modes split into frequencies ωc and ωd, producing paired transparency windows around a central absorption; the steep dispersive flanks make the phase derivative large. For Lp = 1, a 1 fW control field at the red sideband yields a shift up to about 1.0 × 10^-4, roughly thirty times the non

Load-bearing premise

The load-bearing premise is that the transition operator moving an atom from the condensate mode into a Bragg-scattered side mode can be replaced by the square root of a number, turning the condensate's two-mode dynamics into linear oscillators; if that replacement is not a valid mean-field linearization, the split side-mode frequencies and the double-transparency spectrum that generate the enhanced shift do not follow.

Editorial extensions

If this is right

  • With quantized circulation switched on, the peak Goos-Hanchen shift grows monotonically with control power over the range shown, rising from about 6 × 10^-5 at 0.05 fW to 1.2 × 10^-4 at 1.5 fW.
  • At fixed power the maximum shift occurs at the red-sideband detuning Δ̃ = −Ωm; moving to −1.1Ωm cuts it to about 6 × 10^-6, and farther detunings reduce it to about 3 × 10^-6.
  • Increasing the winding number Lp broadens the central absorption between the two transparency windows and steepens the sampled phase gradients, further increasing the attainable shift.
  • Without circulation the shift stays positive and capped near 3 × 10^-6 regardless of detuning offsets, with only a weak transient sign change from Fano asymmetry at intermediate power.
  • Interatomic interactions have negligible influence on the transmission features that set the phase slope, so the prediction is stable against the condensate's s-wave collisions.

Reading between the lines

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

  • An extension not developed in the paper: the double-OMIT peak separation |Ωc − Ωd| is a non-destructive readout of the winding number Lp, so the same transmitted-probe spectrum could serve as a continuous rotation sensor, complementing the destructive time-of-flight imaging the paper cites as motivation.
  • Testable prediction: the monotonic power growth is a low-power-regime effect; at higher control powers power broadening should flatten the dispersion and cap the shift, so mapping St(Plc) beyond 1.5 fW would separate the linearized-coupling regime from saturation.
  • Because Eq. (34) is an angular derivative of an analytically known Tt, the predicted 30-fold enhancement is directly checkable in a transfer-matrix calculation with independently measured cavity parameters; no new many-body physics is needed to test the magnitude.
  • The linearization step √nc = c_p† c_+ and √nd = c_p† c_− could be stress-tested by an exact few-mode simulation of the full many-body Hamiltonian for small atom number: if the double transparency and its steep flanks survive without this replacement, the mechanism is robust; if not, the shift enhancement may be an artifact of the mean-field ansatz.
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 scheme to realize a rotation-tunable Goos-Hänchen shift for a probe beam transmitted through a Fabry-Pérot cavity containing a ring-trapped Bose-Einstein condensate with quantized circulation. The authors model the Bragg-scattered mechanical side modes of the condensate, derive linearized Heisenberg-Langevin equations, and compute probe transmission and a Goos-Hänchen shift as functions of control power, cavity detuning, winding number, and incidence angle. They report that without circulation the shift is positive and bounded, while with circulation the split side modes produce a double-OMIT dispersion whose steep phase flanks amplify the shift, with numerical peak values up to 1.0e-4.

Significance. If the model and the computed quantity were correct, the proposed platform would offer a new way to read out persistent currents in ring BECs with an all-optical, minimally invasive probe, and would connect OMIT physics to beam-displacement metrology. The qualitative mechanism—rotation splitting of Bragg side modes producing double-OMIT—is plausible and follows from earlier work (Refs. [19,34]). However, the manuscript as written does not establish this result: the central observable is defined by an expression that is not the Goos-Hänchen phase derivative, the printed transmission formula in Eq. (33) is inconsistent with all displayed spectra, and the transformation from atomic operators to mechanical side-mode oscillators in Sec. II is unjustified. These are not cosmetic deficiencies; they affect every plotted curve and every quantitative claim. The paper is not circular in the sense of fitting parameters to targets, and no code or machine-checkable derivations are supplied, so the numerical values cannot be independently audited.

major comments (4)
  1. [Sec. II, Eqs. (7)-(11)] The replacement sqrt(n_c) = c_p^dagger c_+ and sqrt(n_d) = c_p^dagger c_- is introduced without justification. The operator c_p^dagger c_+ is a transition operator, not the square root of an occupation number. Equations (7), (10), and (11), and the subsequent mechanical equations (20)-(22), all depend on this replacement. A proper mean-field/Bogoliubov linearization—for example, treating c_p as a c-number condensate amplitude and expanding to leading order in side-mode operators—must be supplied. As written, the side-mode frequencies and the coupling G that generate the double-OMIT and the GH shift are not derived.
  2. [Sec. III B, Eq. (33)] The printed transmission formula T = |1 - mu gamma_0|^2 contains no dependence on the probe detuning delta, control power P_lc, winding number L_p, side-mode frequencies, or incidence angle theta. This cannot be the transmission plotted in Figs. 2-7, which show strong dependence on these parameters. The transmission amplitude t_S in Eq. (32) is the quantity that should enter the GH formula, but the connection between t_S and the printed T is missing. As written, the spectra and all subsequent GH curves are not reproducible from the Eqs. (30)-(33).
  3. [Sec. III B, Eq. (34)] Equation (34) defines S_t = -lambda/(2 pi |T_t|^2)[Re T_t d_theta Im T_t + Im T_t d_theta Re T_t]. The standard Artmann relation for the transmitted-beam GH shift is proportional to d(arg T_t)/d_theta = (Re T_t Im' - Im T_t Re')/|T_t|^2, with a minus sign between the two terms. The printed expression equals -lambda/(4 pi) d(ln |T_t|^2)/d_theta, i.e., the derivative of the log-amplitude, not the phase derivative. Since the abstract and Sec. III B attribute the effect to 'steep dispersive flanks that strongly amplify the phase derivative', the quantity plotted in all GH figures is not the quantity claimed. A corrected calculation must use the proper phase derivative and the reported values, including the 1.0e-4 peak in Fig. 9, must be recomputed.
  4. [Sec. III B, Eqs. (31)-(35)] The manuscript never specifies how the optomechanical transmission coefficient t_S from Eq. (32) is related to the transfer-matrix transmission coefficient T_t in Eq. (35). The GH shift is defined through T_t, while the OMIT calculation yields t_S. Without an explicit mapping between the two, the theta-dependent GH curves are not connected to the detuning- and power-dependent OMIT spectra that are used to explain them. This is a load-bearing gap in the derivation of the central observable.
minor comments (5)
  1. [Sec. III B] Text says the GHS is 'evaluated from Equation (35)', but the shift is defined in Eq. (34) and Eq. (35) is the transfer-matrix expression. Please correct the cross-reference; a similar typo appears as 'In equation (36) Q_0'.
  2. [Sec. II, Eq. (10)] Subscripts are inconsistent: c_p^dagger and c_P^dagger, and c_p versus c_P, are used interchangeably. Use a single notation throughout.
  3. [Sec. II after Eq. (30)] In Eq. (30) the line 'slc = slc = sqrt(mu gamma_0) alpha_s - eta_c/(sqrt(mu gamma_0))' contains a duplicated symbol. This is likely a typographical error but should be fixed.
  4. [Sec. II around Eq. (15)] The definitions of g' are not mutually consistent: Eq. (15) gives g' = omega_rho a_s n_a/(2 pi R), while later g' = g/(4 pi hbar) with g = 2 hbar omega_rho a_s/R. Please define a single set of interaction parameters and use it consistently.
  5. [Reference [66]] The reference list entry for J. Phys. B '54, 125302' lacks a full publication year or DOI; please complete the citation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the rotation-tunable GH-shift prediction is computed from the stated Hamiltonian and external model references; no fitted parameter or self-citation chain is used to force the target result.

full rationale

I walked the derivation chain from the Hamiltonian (Sec. II) through the transmission formula and the GH-shift definition (Sec. III B). The claimed rotation-induced side-mode splitting follows from the ansatz in Eq. (4): side modes carry angular momenta Lp±2l, so their rotational kinetic energies in Eq. (7) differ as a direct algebraic consequence. This is a model construction, not a circular reduction: the splitting is not used to define Lp or the frequencies, and no GH-shift value is an input to any of the parameters. The double-OMIT spectrum is inherited from external references [19,34], not from a self-citation chain. The only self-citations are Ref. [33] (background on optomechanical GH shifts) and Ref. [65] (transfer-matrix method); both are non-load-bearing because the relevant formula is printed in Eq. (35) and the transfer-matrix method is independently standard. I also considered the asserted replacement sqrt(n_c)=c_p^dagger c_+ and sqrt(n_d)=c_p^dagger c_- in Eqs. (7)-(11). This is an unproved mean-field identity and a validity/derivation gap, but it is not circular: it does not assume the target GH shift or the rotation-dependent dispersion, it merely attempts to linearize the interaction. The skeptic's objections about Eq. (33) making T parameter-independent and Eq. (34) not being the standard phase-derivative expression are reproducibility/correctness concerns, not instances of assuming the conclusion. No fitted input is renamed as a prediction, and no uniqueness theorem from the authors' prior work is invoked. Hence no circular step is present.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The calculation uses no new particles or forces. Its physical content is carried by assumptions about truncating the BEC mode expansion, the legality of the square-root mode amplitudes, the neglect of interactions, and the validity of the plane-wave GH relation as printed.

free parameters (3)
  • Cavity linewidth gamma0
    Appears in Eqs. (20), (27), (31)-(33) and controls the OMIT window width, but no numeric value is provided, so the reported spectra cannot be reproduced.
  • Mechanical damping rate gamma_m
    Appears in Eqs. (21)-(22) and sets the side-mode linewidth, but no numeric value is stated.
  • Atom-light coupling u0 = g_a^2 / Delta_a
    Sets the optomechanical coupling G used throughout; referenced to Ref. [19] but not given numerically.
assumptions (4)
  • domain assumption Three-mode ansatz truncating the angular momentum ladder to modes with angular momenta Lp and Lp +/- 2l
    Eqs. (4)-(5) restrict psi to three momentum modes; higher side modes and their effects on the spectrum are neglected without a validity estimate.
  • ad hoc to paper sqrt(n_c) = c_p^dagger c_+ and sqrt(n_d) = c_p^dagger c_- are valid collective mode amplitudes
    Used in Eqs. (7) and (11); no derivation or justification is given beyond naming them mode operators, and it is not an operator identity.
  • domain assumption Interatomic interactions can be dropped in the numerics (g' = 0)
    Stated in Sec. III A as checked 'negligible', but no comparison plot or error bound is shown.
  • domain assumption The GH shift of the transmitted beam is given by the plane-wave phase derivative via Eq. (34)
    The Artmann relation for transmitted multilayer systems is standard, but the printed Eq. (34) is not the phase derivative; finite beam width and angular-spectrum corrections are not discussed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Goos-Hanchen Shift with a rotating atomic superfluid in a ring." pith.science (2026). https://pith.science/paper/AEHOJURQ

@misc{pith2026250904148,
  author       = {Pith},
  title        = {Pith review of: Goos-Hanchen Shift with a rotating atomic superfluid in a ring},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AEHOJURQ}},
  note         = {Machine review of arXiv:2509.04148}
}
read the original abstract

We investigate the Goos Hanchen shift of the transmitted probe and show that optomechanical interference in a ring Bose Einstein condensate provides a sensitive, rotation tunable beam shift response at ultralow optical powers. Without quantized circulation, conventional optomechanically induced transparency produces a strictly positive and bounded shift whose magnitude is governed primarily by cooperativity; small detuning offsets can introduce a weak, transient sign change consistent with a Fano type asymmetry, but the overall response remains limited. With circulation, the Bragg scattered mechanical side modes split, yielding a double transparency dispersion with steep dispersive flanks that strongly amplify the phase derivative and bias its sign. In this regime, the peak shift grows monotonically with control field strength, reflecting enhanced linearized coupling and increased transmission across the angular scan. At fixed power, the detuning dependence is decisive: the shift is maximized at the red sideband condition and diminishes away from resonance, tracking how effectively the scan samples the rotation split dispersive flanks. Increasing the winding number broadens the central absorption and steepens accessible phase gradients, further boosting the attainable shift. The protocol remains minimally invasive under experimentally realistic conditions, and interatomic interactions have a negligible influence on the transmission features that set the phase slope. These results identify circulation, control power, and cavity detuning as practical knobs for in situ control of the Goos Hanchen shift, enabling interferometric beam steering and phase gradient metrology in hybrid atom optomechanical platforms.

Figures

Figures reproduced from arXiv: 2509.04148 by the authors.

Figure 1
Figure 1. FIG. 1. A Fabry-P´erot cavity with fixed mirrors [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Transmission T of the probe field against the pump-pro [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Transmission T of the probe field against the pump-pro [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Transmission T of the probe field against the pump-pro [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Transmission T of the probe field against the pump-pro [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Transmission T of the probe field against the pump-pro [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Transmission T of the probe field against the pump-pro [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. GHS [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. GHS [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. GHS [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. GHS [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 62 canonical work pages

  1. [34]

    Ullah, A

    M. Ullah, A. Abbas, J. Jing, and L.-G. Wang, Phys. Rev. A 100, 063833 (2019)

    work page 2019

  2. [1]

    K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Phys. Rev. Lett. 110, 025302 (2013)

    2013

  3. [2]

    C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, Phys. Rev. Lett. 111, 205301 (2013)

    2013

  4. [3]

    The two transmission maxima occur at δ+ = Ω d and δ− = Ω c, respectively, where δ+ (δ−) denotes the peak on the positive (nega- tive) side of Ω m

    In particular, a double-OMIT profile appears: two transparency windows flank an absorption region whose width is approximately ∼ |Ωc − Ωd|, centered at δ = Ω m. The two transmission maxima occur at δ+ = Ω d and δ− = Ω c, respectively, where δ+ (δ−) denotes the peak on the positive (nega- tive) side of Ω m. The origin of this double-OMIT structure can be und...

    work page

  5. [4]

    ¨Ohberg and E

    P. ¨Ohberg and E. M. Wright, Phys. Rev. Lett. 123, 250402 (2019)

    work page 2019

  6. [5]

    G. E. Marti, R. Olf, and D. M. Stamper-Kurn, Phys. Rev. A 91, 013602 (2015)

    work page 2015

  7. [6]

    Exactly at the red sideband, ˜∆/Ωm = −1, these flanks are sym- metric and maximally steep, so the GHS rises from 0 to a much larger value, ≈ 1.0 × 10−4

    Rotation splits the side modes and creates a central absorption, yielding two steep dispersive flanks. Exactly at the red sideband, ˜∆/Ωm = −1, these flanks are sym- metric and maximally steep, so the GHS rises from 0 to a much larger value, ≈ 1.0 × 10−4. When the cavity is detuned to ˜∆/Ωm = −1.1, the angular scan overlaps only one (partially shifted) stee...

    work page 2023

  8. [7]

    A. L. Fetter, Rev. Mod. Phys. 81, 647 (2009)

    work page 2009

Show all 71 references
  1. [8]

    Freilich, D

    D. Freilich, D. Bianchi, A. Kaufman, T. Langin, and D. Hall, Science 329, 1182 (2010)

    2010

  2. [9]

    C. Ryu, M. F. Andersen, P. Clad´ e, V. Natara- jan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007)

    2007

  3. [10]

    N. R. Cooper, Advances in Physics 57, 539 (2008)

    2008

  4. [11]

    Y. Shin, M. Saba, M. Vengalattore, T. A. Pasquini, C. Sanner, A. E. Leanhardt, M. Prentiss, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 93, 160406 (2004)

    2004

  5. [12]

    D. R. Tilley, Superfluidity and superconductivity (Rout- ledge, 2019)

    2019

  6. [13]

    Mehdi, A

    Z. Mehdi, A. Bradley, J. Hope, and S. Szigeti, SciPost physics 11, 080 (2021)

    2021

  7. [14]

    Pandey, H

    S. Pandey, H. Mas, G. Vasilakis, and W. von Klitzing, Phys. Rev. Lett. 126, 170402 (2021)

    2021

  8. [15]

    Amico, M

    L. Amico, M. Boshier, G. Birkl, A. Minguzzi, C. Miniatura, L.-C. Kwek, D. Aghamalyan, V. Ahufinger, D. Anderson, N. Andrei, et al. , A VS Quantum Science 3, https://doi.org/10.1116/5.0026178 (2021)

    2021 doi

  9. [16]

    J. Polo, V. Ahufinger, F. W. J. Hekking, and A. Min- guzzi, Phys. Rev. Lett. 121, 090404 (2018)

    2018

  10. [17]

    Del Pace, K

    G. Del Pace, K. Xhani, A. Muzi Falconi, M. Fedrizzi, N. Grani, D. Hernandez Rajkov, M. Ingus- cio, F. Scazza, W. J. Kwon, and G. Roati, Phys. Rev. X 12, 041037 (2022)

    2022

  11. [18]

    Y. Cai, D. G. Allman, P. Sabharwal, and K. C. Wright, Phys. Rev. Lett. 128, 150401 (2022)

    2022

  12. [19]

    J. W. Park, B. Ko, and Y. Shin, Phys. Rev. Lett. 121, 225301 (2018)

    2018

  13. [20]

    Eckel, J

    S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature 506, 200 (2014)

    2014

  14. [21]

    Kumar, T

    P. Kumar, T. Biswas, K. Feliz, R. Kanamoto, M.-S. Chang, A. K. Jha, and M. Bhattacharya, Phys. Rev. Lett. 127, 113601 (2021)

    2021

  15. [22]

    Aspelmeyer, T

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

    2014

  16. [23]

    P. R. Berman, Phys. Rev. E 66, 067603 (2002)

    2002

  17. [24]

    Qamar, and M

    Ziauddin, S. Qamar, and M. S. Zubairy, Phys. Rev. A 81, 023821 (2010)

    2010

  18. [25]

    Wang, S.-Y

    L.-G. Wang, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. Lett. 111, 223901 (2013)

    2013

  19. [26]

    Goos and H

    F. Goos and H. H¨ anchen, Annalen der Physik 436, 333 (1947)

    1947

  20. [27]

    Goos and H

    F. Goos and H. Lindberg-H¨ anchen, Annalen der Physik 440, 251 (1949)

    1949

  21. [28]

    Artmann, Annalen der Physik 437, 87 (1948)

    K. Artmann, Annalen der Physik 437, 87 (1948)

    1948

  22. [29]

    R. H. Renard, Journal of the Optical Society of America 54, 1190 (1964)

    1964

  23. [30]

    Puri and J

    A. Puri and J. L. Birman, Journal of the Optical Society of America A 3, 543 (1986)

    1986

  24. [31]

    Aiello and J

    A. Aiello and J. Woerdman, Optics letters 33, 1437 (2008)

    2008

  25. [32]

    K. Y. Bliokh and A. Aiello, Journal of Optics 15, 014001 (2013)

    2013

  26. [33]

    Bretenaker, A

    F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992)

    1992

  27. [35]

    A. A. Khan, M. Abbas, Y.-L. Chaung, I. Ahmed, and Ziauddin, Phys. Rev. A 102, 053718 (2020)

    2020

  28. [36]

    Kalita, P

    S. Kalita, P. Kumar, R. Kanamoto, M. Bhattacharya, and A. K. Sarma, Phys. Rev. A 107, 013525 (2023)

    2023

  29. [37]

    G. S. Agarwal and S. Huang, Phys. Rev. A 81, 041803 (2010)

    2010

  30. [38]

    S. Weis, R. Rivi` ere, S. Del´ eglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, science 330, 1520 (2010)

    2010

  31. [39]

    A. H. Safavi-Naeini, T. M. Alegre, J. Chan, M. Eichen- field, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011)

    2011

  32. [40]

    Ma, J.-Q

    P.-C. Ma, J.-Q. Zhang, Y. Xiao, M. Feng, and Z.-M. Zhang, Phys. Rev. A 90, 043825 (2014)

    2014

  33. [41]

    Huang, Journal of Physics B: Atomic, Molecular and Optical Physics

    S. Huang, Journal of Physics B: Atomic, Molecular and Optical Physics

  34. [42]

    J.-X. Peng, Z. Chen, Q.-Z. Yuan, and X.-L. Feng, Physics Letters A 384, 126153 (2020)

    2020

  35. [43]

    S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989)

    1989

  36. [44]

    S. E. Harris, J. E. Field, and A. Imamo˘ glu, Phys. Rev. Lett. 64, 1107 (1990)

    1990

  37. [45]

    J. P. Marangos, Journal of modern optics 45, 471 (1998)

    1998

  38. [46]

    Qu and G

    K. Qu and G. S. Agarwal, Phys. Rev. A 87, 063813 (2013)

    2013

  39. [47]

    Chen, Phys

    H.-J. Chen, Phys. Rev. A 104, 013708 (2021)

    2021

  40. [48]

    Tian, Phys

    L. Tian, Phys. Rev. Lett. 108, 153604 (2012)

    2012

  41. [49]

    Wang and A

    Y.-D. Wang and A. A. Clerk, Phys. Rev. Lett. 108, 153603 (2012)

    2012

  42. [50]

    Zhang, J

    Z. Zhang, J. Pei, Y.-P. Wang, and X. Wang, Frontiers of Physics 16, 32503 (2021)

    2021

  43. [51]

    Stern, M

    L. Stern, M. Grajower, and U. Levy, Nature communications 5, 4865 (2014) . 14

    2014

  44. [52]

    H. L¨ u, Y. Jiang, Y.-Z. Wang, and H. Jing, Photonics Research 5, 367 (2017)

    2017

  45. [53]

    J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, Nature communications 3, 1196 (2012)

    2012

  46. [54]

    Lesanovsky and W

    I. Lesanovsky and W. von Klitzing, Phys. Rev. Lett. 99, 083001 (2007)

    2007

  47. [55]

    B. E. Sherlock, M. Gildemeister, E. Owen, E. Nugent, and C. J. Foot, Phys. Rev. A 83, 043408 (2011)

    2011

  48. [56]

    Y. Guo, R. Dubessy, M. d. G. de Herve, A. Kumar, T. Badr, A. Perrin, L. Longchambon, and H. Perrin, Phys. Rev. Lett. 124, 025301 (2020)

    2020

  49. [57]

    Morizot, Y

    O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway, Phys. Rev. A 74, 023617 (2006)

    2006

  50. [58]

    Corman, L

    L. Corman, L. Chomaz, T. Bienaim´ e, R. Desbuquois, C. Weitenberg, S. Nascimb` ene, J. Dalibard, and J. Beugnon, Phys. Rev. Lett. 113, 135302 (2014)

    2014

  51. [59]

    K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Phys. Rev. A 88, 063633 (2013)

    2013

  52. [60]

    Naidoo, K

    D. Naidoo, K. A ¨ ıt-Ameur, M. Brunel, and A. Forbes, Applied Physics B 106, 683 (2012)

    2012

  53. [61]

    Padhi and S

    B. Padhi and S. Ghosh, Phys. Rev. Lett. 111, 043603 (2013)

    2013

  54. [62]

    J. Polo, R. Dubessy, P. Pedri, H. Perrin, and A. Minguzzi, Phys. Rev. Lett. 123, 195301 (2019)

    2019

  55. [63]

    Benguria and M

    R. Benguria and M. Kac, Phys. Rev. Lett. 46, 1 (1981)

    1981

  56. [64]

    Bowen, in Conference on Lasers and Electro-Optics/Pacific Rim (Optica Publishing Group, 2015) p

    W. Bowen, in Conference on Lasers and Electro-Optics/Pacific Rim (Optica Publishing Group, 2015) p. 25G1 1

    2015

  57. [65]

    Brennecke, S

    F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, Science 322, 235 (2008)

    2008

  58. [66]

    L.-G. Wang, M. Ikram, and M. S. Zubairy, Phys. Rev. A 77, 023811 (2008)

    2008

  59. [67]

    Abbas, A

    M. Abbas, A. A. Khan, H. Ali, et al. , Physica Scripta 96, 125104 (2021)

    2021

  60. [68]

    M. d. G. de Herve, Y. Guo, C. De Rossi, A. Kumar, T. Badr, R. Dubessy, L. Longchambon, and H. Perrin, Journal of Physics B: Atomic, Molecular and Optical Physics 54, 125302

  61. [69]

    Xiong and Y

    H. Xiong and Y. Wu, Applied physics reviews 5, https://doi.org/10.1063/1.5027122 (2018)

    2018 doi

  62. [70]

    Kronwald and F

    A. Kronwald and F. Marquardt, Phys. Rev. Lett. 111, 133601 (2013)

    2013

  63. [71]

    Børkje, A

    K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, Phys. Rev. Lett. 111, 053603 (2013)

    2013

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.