Pith. sign in

REVIEW 3 major objections 4 minor 51 references

The transverse-to-longitudinal frequency ratio of a levitated particle's motion is a power-independent gauge of trap quality, and the cleanest beam is the one that maximizes the axial frequency.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-04 08:59 UTC pith:MUNJXLK7

load-bearing objection Useful figure of merit and credible GLMT curves, but the experiment's centerpiece agreement depends on a reported-never filling factor. the 3 major comments →

arxiv 2510.17654 v2 pith:MUNJXLK7 submitted 2025-10-20 physics.optics

Controlling the centre of mass motion of levitated particles using structured wavefronts

Shah Jee Rahman , Quimey Pears Stefano , Angel Cifuentes , Jason T Francis , Iker G\'omez-Viloria , Rub\'en Pellicer-Guridi , Miguel Varga , Gabriel Molina-Terriza This is my paper
classification physics.optics PACS 42.50.Wk
keywords optical levitationZernike polynomialsfrequency ratiowavefront shapingGeneralized Lorentz-Mie theoryoptical trappingaberration correctioncenter-of-mass motion
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that the ratio of the transverse to longitudinal center-of-mass oscillation frequencies of an optically levitated particle is a better way to judge the quality of an optical trap than any single frequency, because the ratio is independent of laser power and, for sufficiently small particles, independent of particle size. Combining experiments with a spatial light modulator that shapes the wavefront using Zernike polynomials and full multipolar light-scattering calculations, the authors show that correcting aberrations so that the measured frequency ratios match the theoretically predicted curve also maximizes the longitudinal (axial) trap frequency, at the cost of the transverse frequencies. The result gives experimenters an explicit recipe: measure the three resonance frequencies, compute the GLMT ratio curve, and tune the wavefront until the ratios fall on it. This matters because a cleaner trap reduces optical backaction and thermal decoherence, which is relevant for quantum sensing and quantum-superposition experiments with levitated nanoparticles.

Core claim

The central claim is that the ratio of transverse to longitudinal CoM oscillation frequencies (Ωx/Ωz, Ωy/Ωz) is a superior, power-independent figure of merit for the tightness and quality of an optical trap. Using Generalized Lorentz-Mie Theory to compute the forces on a trapped silica sphere for a range of filling factors (the ratio of input beam diameter to objective back aperture), the authors predict how these ratios depend on filling for both linear and circular polarization. They then use a spatial light modulator to apply Zernike-polynomial phase corrections to the trapping beam, recording the particle's power spectral density and hence the three resonance frequencies. In their experi

What carries the argument

The central object is the frequency-ratio curve computed from Generalized Lorentz-Mie Theory (GLMT): for a given particle size, numerical aperture and polarization, the transverse-to-longitudinal frequency ratios are plotted as a function of the filling factor Fr. This curve, along with the paraxial-dipolar approximation Ωi/Ωz = √2/(NA·Fr), is used as a target that the experimental frequency ratios must match in order to verify that the trap is clean and optimally focused. The experimental control mechanism is a phase-only spatial light modulator programmed with Zernike polynomials (Defocus, Spherical, Astigmatism, Coma) that reshape the wavefront; the measured PSD frequencies and their rati

Load-bearing premise

The agreement between experiment and theory rests on the independently measured filling factor Fr (the ratio of input beam diameter to objective back aperture), whose value and uncertainty are not reported; and the size-independence claim holds only up to the 177 nm particle diameter used in the experiment.

What would settle it

Measure the three CoM frequencies of a levitated particle over a range of laser powers (keeping wavefront fixed) and check whether the frequency ratios remain constant; and measure the filling factor with an independent method (e.g., knife-edge) and verify the reported ratio match without adjusting Fr to force agreement. If the ratios shift with power, or if the ratio match disappears with an independent Fr measurement, the central claim fails.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • An experimentalist can judge trap quality and aberration correction without knowing the laser power or the exact particle size (for particles smaller than ~177 nm in this setup), by simply comparing the measured frequency ratios to the GLMT prediction.
  • The optimal wavefront for a clean trap is the one that maximizes the axial (z-axis) frequency; transverse-frequency maximization requires a deliberately aberrated beam.
  • The method provides a rule for when to stop an iterative aberration-correction loop: stop when the measured ratios match the theoretically predicted curve, rather than when a weighted sum of frequencies is maximized.
  • Because the trap is then cleaner, photon-recoil/backaction heating is reduced, aiding ground-state cooling and quantum-superposition proposals for levitated nanoparticles.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The frequency-ratio criterion could be applied to non-spherical or arbitrary-shape particles only if GLMT or similar multipolar calculations are available for those shapes; the paper does not demonstrate this.
  • The claim that the optimal ratio coincides with maximal axial frequency is established experimentally for a single particle size and NA 0.9; if true generally, it suggests that maximizing axial frequency alone might be a simpler proxy for trap quality in setups without a full GLMT curve.
  • The filling factor Fr enters the prediction as 1/Fr; since the experimental points are placed on the curve by an independent beam-size measurement whose uncertainty is not reported, a systematic check would be to measure Fr with a second method (e.g., knife-edge scan of the input beam) and see whether the ratios still match.
  • Since the ratio is power-independent but the frequencies themselves scale with power, this figure of merit could also be used to compare traps across different laser powers or different experimental setups, as a normalised metric.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes the ratio of transverse to longitudinal center-of-mass oscillation frequencies of an optically levitated nanoparticle as a power-independent figure of merit for trap quality, and uses Generalized Lorenz–Mie Theory (GLMT) to predict this ratio versus the objective back-aperture filling factor for a tightly focused 1064 nm beam (NA=0.9). Experimentally, the authors use an SLM to apply Zernike wavefront corrections, measure the three CoM frequencies from PSDs, and sweep the Zernike coefficients until the measured ratios match the GLMT prediction. They report that a corrected 'clean' beam yields ratios that fall on the predicted curve and that this condition coincides with maximizing the longitudinal frequency at the expense of the transverse frequencies, giving a recipe for systematic aberration correction in levitated-particle experiments.

Significance. If the central claims hold, the work provides a practically useful, power-independent diagnostic for optimizing optical traps for levitated nanoparticles: the transverse-to-longitudinal frequency ratio, computed from GLMT, is independent of particle size below 177 nm for the tested parameters and is insensitive to laser power. The systematic Zernike-sweep study of Spherical, Defocus, Astigmatism, and Coma is a useful contribution, and the use of a public GLMT toolbox (MOFT) makes the theoretical curves reproducible. The proposed recipe could help experimentalists avoid iterative, figure-of-merit-dependent aberration corrections. However, the experimental validation currently rests on an incompletely reported filling-factor measurement and on an optimization protocol that uses the theory itself as the target, so the claims are only partially supported by the data as presented.

major comments (3)
  1. [Section V, Fig. 3; Supplementary A] The 'independently measured' filling factor Fr is never reported numerically or with an uncertainty. The predicted ratios are steep functions of Fr (Eq. 3 gives Ω_i/Ω_z ∝ 1/Fr, and the GLMT curves in Fig. 2 vary strongly with Fr). Since the red-star experimental points are placed on the curve using this Fr, the claimed 'exact' agreement cannot be distinguished from a fit unless the Fr value and its uncertainty are given and the experimental ratios are shown with error bars. Please report Fr and its uncertainty and, ideally, plot the data with an Fr-uncertainty band.
  2. [Section IV, Methodology; Section V] The optimization procedure explicitly sweeps the Zernike coefficients until the ratios match the theoretical prediction, so the final point lying on the GLMT curve is by construction not an independent validation of the theory. The additional claim that the ratio-matched point coincides with the global maximum of Ω_z (Figs. 4–5) is read from the same selected point. To make the validation load-bearing, an out-of-sample check is needed: for example, an independent wavefront measurement (e.g., Shack–Hartmann or caustic-based) confirming that the selected SLM phase mask is aberration-free, or a prediction of the absolute frequencies that is not used as a fitting target.
  3. [Section II and Section IV, particle size] The size-independence claim is stated for d < 177 nm at Fr > 0.5, and the experimental particle is described as 'around 177 nm' (Supplementary A). The particle sits exactly on the boundary of the size-independent region, so the manufacturer's diameter tolerance directly shifts the predicted curve. Please report the size distribution/tolerance for the Bangs Labs particles and show the corresponding band of predicted ratios (e.g., for 177±10 nm) to establish that the experimental agreement is robust to particle-size uncertainty.
minor comments (4)
  1. [Section II, Eq. (3)] The derivation of the paraxial ratio formula should explicitly state the definitions of NA and Fr and note the approximation's validity range (small particle, low Fr), since the dotted curve in Fig. 2 is only close to the GLMT result for 5 nm particles and low Fr.
  2. [Fig. 3 caption] The caption contains typographical and grammatical issues ('represents thePower spectrum densityof levitated nanoparticle', 'F requency ratios'); please proofread and ensure the axes and curves are clearly identified, including which curves correspond to the prediction and which to the experimental points.
  3. [Section IV] Minor typo: 'sweeped' should be 'swept'. Also, the units of the Zernike coefficients in Table I (Supplementary) are not stated; clarify whether they are in radians or waves.
  4. [Section V, Fig. 4] The statement that the ratio-optimal point 'is closer to the peak of z-axis frequency' is qualitative. Quantify the location of the maximum of Ω_z and the ratio target (e.g., with the coefficient values and a confidence interval) so the reader can assess the alignment.

Circularity Check

1 steps flagged

Corrected-beam ratio agreement is a termination condition of the optimization, not an independent validation; filling-factor audit trail is missing.

specific steps
  1. fitted input called prediction [Section IV (Methodology) and Section V (Results), Fig. 3(c)-(d)]
    "Then, we will explore different wavefront corrections. This is done systematically with the use of superpositions of Zernike polynomials, whose coefficients are sweeped simultaneously until we find a configuration which match the theoretically predicted frequency ratio values. ... The ratios of the frequencies shown in Fig.3(c)-(d), fall exactly onto the predicted curve, once we take into account the difference in the filling factor, which we independently measure. This ensures that our correction process has achieved an optimal beam."

    The red-star ratios in Fig. 3 are not independent experimental predictions of GLMT: they are produced by an explicit search whose objective is the theoretical ratio curve. The statement that they 'fall exactly onto the predicted curve' is therefore the termination condition of the sweep, not a test of the theory. The plotted agreement is forced by construction. The independent content is limited to the separate observation that the same coefficient choice maximizes the z-axis frequency (Figs. 4-5), which is what keeps the central practical claim from being fully circular.

full rationale

The GLMT frequency-ratio calculations (Section II, Fig. 2) are parameter-free once NA=0.9, 1064 nm, silica size/refractive index and the measured filling factor Fr are fixed, so the theoretical side is anchored externally rather than fitted to the experimental frequencies. The principal circularity is in the validation loop: the corrected-beam data points are obtained by sweeping Zernike coefficients until the measured ratios match the theoretically predicted curve, so the reported 'exact' agreement in Fig. 3(c)-(d) is a self-consistent output of the optimization procedure, not an independent check. This is partially offset by the independent observation that the same corrected setting coincides with the maximum of the longitudinal frequency in the two-dimensional coefficient maps (Figs. 4-5), which gives the central 'maximize the longitudinal frequency' claim empirical content beyond the fit. The filling factor is asserted to be independently measured, and no evidence shows that it was adjusted to force agreement; however, its numerical value and uncertainty are never reported, and Eq. (3) makes the predicted ratio proportional to 1/Fr, so the tightness of the claimed agreement cannot be fully audited. That is a reporting/correctness concern rather than a demonstrated additional circular step. Net result: one load-bearing validation statement reduces to the optimization target, but the central practical result has independent support; score 4.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The core theoretical content (Eqs. 1-3) is standard paraxial/Gaussian-trap physics used only for intuition; the quantitative predictions come from GLMT as implemented in the authors' public MOFT toolbox. The experimental control parameters are the Zernike coefficients, chosen by manual sweeps to match the predicted ratios, and the filling factor, measured but reported without uncertainty. No new entities (particles, forces, dimensions) are introduced.

free parameters (2)
  • Zernike coefficients (Defocus, Spherical, Astig-X, Astig-D, Coma-X, Coma-Y) = -1.25, 0.50, -0.10, 0.23, -0.40, 0.40 (Table I)
    Chosen by manual sweeps (Section V, Supp. D) until the measured frequency ratios match the GLMT prediction; the 'optimal beam' claim depends on this hand-chosen set.
  • Filling factor F_r = not stated
    Independently measured via CCD at the back-aperture conjugate (Section III, Supp. A) and used to position the experimental points on the predicted ratio curves; its numerical value and uncertainty are not reported, and the ratio curves are steep functions of F_r.
axioms (4)
  • standard math Paraxial Gaussian-beam trap model: k_trap = alpha E0^2/w0^2, k_z = alpha E0^2/(2 z_R^2) and ratio sqrt(2)/(NA * F_r) (Eqs. 2-3)
    Standard textbook result (refs. 32-33), used only for intuition; the authors themselves note it fails for tight focus, so the quantitative claims run through GLMT instead.
  • domain assumption GLMT accurately gives optical forces and trapping frequencies for a spherical particle in a tightly focused vector beam carrying the programmed Zernike phase
    The Fig. 2 ratio curves are computed with MOFT (refs. 28, 36); both the focused-beam decomposition and the Mie coefficients must be correct, and the toolbox's validation is in the authors' prior work.
  • domain assumption Particles are homogeneous dielectric spheres of the nominal 177 nm diameter
    Size-independence of the ratios is claimed only for d <= 177 nm in the simulations (Fig. 2); the experimental particle sits exactly at this boundary, so deviations of the real size or refractive index would shift the predicted curve.
  • domain assumption Trap dynamics are harmonic so that PSD peaks map to stiffnesses k = m Omega^2
    The paper itself cites ref. 23 showing that aberrations introduce nonlinearities; strong Zernike coefficients used in the sweeps may enter anharmonic regimes, yet every PSD peak is treated as a harmonic resonance.

pith-pipeline@v1.3.0-alltime-deepseek · 12772 in / 14677 out tokens · 121168 ms · 2026-08-04T08:59:16.597641+00:00 · methodology

0 comments
read the original abstract

Optically levitated particles have great potential to form the basis of novel quantum- enhanced sensors. These systems are very well suited for inertial sensing, as the particles are isolated from the environment when they are levitated at low pressures. However, there are many challenges in the experimental realization that may affect the performance of these systems. For example, optical aberrations in the wavefront of the trapping laser which arise from optical elements or misalignment have a great impact on the trapping potential. The detrimental effect of optical aberrations has not been thoroughly studied, and usually they are iteratively corrected, giving some conflicting results depending on the figures of merit that are used. In this work, we present a thorough study of the effects of structuring the wavefront of the trapping beams. We observe that clean beams, i.e. highly focused beams with unaberrated wavefronts, may be used to optimize the longitudinal frequencies, at the cost of the transversal ones. Our work is based in a combination of experimental studies using a complete basis of orthogonal polynomials (Zernike polynomials) to control the wavefront and a set of numerical calculations, which allow us to compare the impact of structured wavefronts on the quality of traps for optically levitated particles in vacuum. This will have direct applications in quantum sensing and fundamental studies of quantum mechanics, as it allows the reduction of optical backaction and thermal decoherence of the particles.

Figures

Figures reproduced from arXiv: 2510.17654 by Angel Cifuentes, Gabriel Molina-Terriza, Iker G\'omez-Viloria, Jason T Francis, Miguel Varga, Quimey Pears Stefano, Rub\'en Pellicer-Guridi, Shah Jee Rahman.

Figure 2
Figure 2. Figure 2: FIG. 2. Theoretical simulation of of back aperture filling of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a)-(b) represents the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Maps of the CoM frequencies for the (a) z, (b) x and (c) for for a grid sweep of the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Surface plots of Zernike polynomials with the names from left to right and their associated aberrations up to 4th order. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. PSDs of trapped particle in uncorrected (green) and corrected wavefront (orange) along x, y and z-axis, respectively. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The effects of Astigmatism-X & Astigmatism-D on the CoM motion of levitated particle. The green curve in (a), (d) [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The observed effects of Coma-X & Coma-Y on the CoM motion of optically levitated particle. The green curve in [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

51 extracted references · 2 linked inside Pith

  1. [1]

    In this last respect, optical levitation gives us the advantage of observing the real-time dynamical proper- ties (i.e

    The effect of optical aberrations on arbitrary particles is not well understood theoretically, and 2) different fig- ures of merit can be used to iteratively improve an optical trap. In this last respect, optical levitation gives us the advantage of observing the real-time dynamical proper- ties (i.e. CoM motion) of the levitated particles. The three-dime...

  2. [2]

    Ashkin, Phys

    A. Ashkin, Phys. Rev. Lett.24, 156 (1970)

    1970

  3. [3]

    Ashkin and J

    A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett.28, 333 (1976)

    1976

  4. [4]

    Dania, D

    L. Dania, D. S. Bykov, F. Goschin, M. Teller, A. Kassid, and T. E. Northup, Phys. Rev. Lett.132, 133602 (2024)

    2024

  5. [5]

    Liang, S

    T. Liang, S. Zhu, P. He, Z. Chen, Y. Wang, C. Li, Z. Fu, X. Gao, X. Chen, N. Li, Q. Zhu, and H. Hu, Fundamental Research3, 57 (2023)

    2023

  6. [6]

    A. A. Geraci, S. B. Papp, and J. Kitching, Phys. Rev. Lett.105, 101101 (2010)

    2010

  7. [7]

    T. M. Hoang, J. Ahn, J. Bang, and T. Li, Nature com- munications7, 12250 (2016)

    2016

  8. [8]

    S. Zhu, Z. Fu, X. Gao, C. Li, Z. Chen, Y. Wang, X. Chen, and H. Hu, Photon. Res.11, 279 (2023)

    2023

  9. [9]

    Aspelmeyer, T

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

    2014

  10. [10]

    J. Ahn, Z. Xu, J. Bang, P. Ju, X. Gao, and T. Li, Nat. Nanotechnol.15, 89 (2020)

    2020

  11. [11]

    Y. Jin, J. Yan, S. J. Rahman, J. Li, X. Yu, and J. Zhang, Photon. Res.9, 1344 (2021)

    2021

  12. [12]

    Reimann, M

    R. Reimann, M. Doderer, E. Hebestreit, R. Diehl, M. Frimmer, D. Windey, F. Tebbenjohanns, and L. Novotny, Phys. Rev. Lett.121, 033602 (2018)

    2018

  13. [13]

    Manjavacas and F

    A. Manjavacas and F. J. Garc ´ ıa de Abajo, Phys. Rev. Lett.105, 113601 (2010)

    2010

  14. [14]

    Deli´ c, M

    U. Deli´ c, M. Reisenbauer, K. Dare, D. Grass, V. Vuleti´ c, N. Kiesel, and M. Aspelmeyer, Science367, 892 (2020)

    2020

  15. [15]

    Piotrowski, D

    J. Piotrowski, D. Windey, J. Vijayan, C. Gonzalez- Ballestero, A. de los R ´ ıos Sommer, N. Meyer, R. Quidant, O. Romero-Isart, R. Reimann, and L. Novotny, Nature Physics19, 1009 (2023)

    2023

  16. [16]

    Roda-Llordes, A

    M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Grochowski, and O. Romero-Isart, Phys. Rev. Lett.132, 023601 (2024)

    2024

  17. [17]

    Bassi, K

    A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ul- bricht, Rev. Mod. Phys.85, 471 (2013)

    2013

  18. [18]

    M. A. Taylor, M. Waleed, A. B. Stilgoe, H. Rubinsztein- Dunlop, and W. P. Bowen, Nature Photonics9, 669 (2015)

    2015

  19. [19]

    U. G. B¯ utait˙ e, C. Sharp, M. Horodynski, G. M. Gibson, M. J. Padgett, S. Rotter, J. M. Taylor, and D. B. Phillips, Science Advances10, eadi7792 (2024)

    2024

  20. [20]

    G´ omez-Viloria, A

    I. G´ omez-Viloria, A. Nodar, M. Molezuelas-Ferreras, J. Olmos-Trigo, A. Cifuentes, M. Mart ´ ınez, M. Varga, and G. Molina-Terriza, ACS Photonics11, 626 (2024), https://doi.org/10.1021/acsphotonics.3c01499

    doi:10.1021/acsphotonics.3c01499 2024

  21. [21]

    H¨ upfl, N

    J. H¨ upfl, N. Bachelard, M. Kaczvinszki, M. Horodyn- ski, M. K¨ uhmayer, and S. Rotter, Phys. Rev. Lett.130, 083203 (2023)

    2023

  22. [22]

    Yu and X

    J. Yu and X. Mao, Photonics (2025)

    2025

  23. [23]

    Schkolnik, B

    V. Schkolnik, B. Leykauf, M. Hauth, C. Freier, and A. Pe- ters, Appl. Phys. B120, 311 (2015)

    2015

  24. [24]

    M. T. Cuairan, J. Gieseler, N. Meyer, and R. Quidant, Phys. Rev. Lett.128, 213601 (2022)

    2022

  25. [25]

    ˇCiˇ zm´ ar, H

    T. ˇCiˇ zm´ ar, H. I. C. Dalgarno, P. C. Ashok, F. J. Gunn- Moore, and K. Dholakia, Journal of Optics13, 044008 (2011)

    2011

  26. [26]

    Ashkin, J

    A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett.11, 288 (1986)

    1986

  27. [27]

    Antonello and M

    J. Antonello and M. Verhaegen, J. Opt. Soc. Am. A32, 1160 (2015)

    2015

  28. [28]

    R. J. Noll, J Opt Soc Am66, 207 (1976). 8

    1976

  29. [29]

    G´ omez-Viloria, E

    I. G´ omez-Viloria, E. A. Garc ´ ıa, J. Olmos-Trigo, Q. P. Stefano, J. Lasa-Alonso, M. Molezuelas-Ferreras, and G. Molina-Terriza, APL Photonics10, 051101 (2025)

    2025

  30. [30]

    Kleine, M

    M. Kleine, M. Horodynski, S. Rotter, Y. Amarouch- ene, Y. Louyer, M. Perrin, and N. Bachelard, Wave- front shaping of scattering forces enhances optical trap- ping of levitated nanoparticles (2025), arXiv:2504.20702 [physics.optics]

    Pith/arXiv arXiv 2025

  31. [31]

    Y. Jin, K. Shen, P. Ju, and T. Li, arXiv preprint arXiv:2407.12496 (2024)

    Pith/arXiv arXiv 2024

  32. [32]

    Gieseler,Dynamics of optically levitated nanoparticles in high vacuum, Ph.D

    J. Gieseler,Dynamics of optically levitated nanoparticles in high vacuum, Ph.D. thesis, Universitat Polit` ecnica de Catalunya (2014)

    2014

  33. [33]

    Gieseler, B

    J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, Physical Review Letters109, 103603 (2012)

    2012

  34. [34]

    Harada and T

    Y. Harada and T. Asakura, Optics Communications124, 529 (1996)

    1996

  35. [35]

    Novotny and B

    L. Novotny and B. Hecht,Principles of nano-optics (Cambridge university press, 2012)

    2012

  36. [36]

    J. P. Barton, D. R. Alexander, and S. A. Schaub, Journal of Applied Physics66, 4594 (1989)

    1989

  37. [37]

    Code available in the Github repository MOFT

  38. [38]

    Zambrana-Puyalto, X

    X. Zambrana-Puyalto, X. Vidal, and G. Molina-Terriza, Opt. Express20, 24536 (2012)

    2012

  39. [39]

    Molezuelas-Ferreras, A

    M. Molezuelas-Ferreras, A. Nodar, M. Barra-Burillo, J. Olmos-Trigo, J. Lasa-Alonso, I. G´ omez-Viloria, E. Posada, J. J. M. Varga, R. Esteban, J. Aizpurua, L. E. Hueso, C. Lopez, and G. Molina-Terriza, Laser & Pho- tonics Reviews , 2300665 (2023)

    2023

  40. [40]

    Lakshminarayanan and A

    V. Lakshminarayanan and A. Fleck, Journal of Modern Optics58, 545 (2011)

    2011

  41. [41]

    Bellando, M

    L. Bellando, M. Kleine, Y. Amarouchene, M. Perrin, and Y. Louyer, Phys. Rev. Lett.129, 023602 (2022)

    2022

  42. [42]

    S. Kuhn, B. A. Stickler, A. Kosloff, F. Patolsky, K. Horn- berger, M. Arndt, and J. Millen, Nat. Commun.8, 1670 (2017)

    2017

  43. [43]

    Y. Jin, K. Shen, P. Ju, X. Gao, C. Zu, A. J. Grine, and T. Li, Nat Commun15, 5063 (2024)

    2024

  44. [44]

    Rossi, A

    M. Rossi, A. Militaru, N. Carlon Zambon, A. Riera- Campeny, O. Romero-Isart, M. Frimmer, and L. Novotny, Phys. Rev. Lett.135, 083601 (2025). VII. SUPPLEMENT AR Y DOCUMENT A. Details of the experimental setup L L SF BS BS BS D-M D-M MM LASER WPs PBS CMOS OBJ TELESCOPE Vacuum chamber LL L L M M M LL Lc SLM M Spectrum Analyzer & DAQ FIG. 6.The schematic diag...

    2025

  45. [45]

    The usual cause of astigmatism in an optical system is the lens or mirrors

    Astigmatisms Astigmatism is an aberration in optics in which different parts of rays do not focus at a single point. The usual cause of astigmatism in an optical system is the lens or mirrors. Introduces asymmetry in the trapping potential, and the stiffness varies along different axes. In a highly focused linearly polarized beam, it is hard to point out ...

  46. [46]

    Comas Although the effect of higher order cylindrically asymmetric Zernike polynomials is small, Comas-X and Coma-Y have slightly noticeable effects and can increase the longitudinal frequency up to 5%, which suggests that Comas compensates for aberration along the laser axis as well. In Fig. 10, we show the behavior of Comas on optically levitated nanopa...

  47. [47]

    Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode,

    Z. von F, “Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode,” Physica1, 689–704 (1934)

    1934

  48. [48]

    Born and E

    M. Born and E. Wolf,Principles of optics: electromagnetic theory of propagation, interference and diffraction of light(Elsevier, 2013)

    2013

  49. [49]

    Zernike polynomials and atmospheric turbulence,

    R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J Opt Soc Am66, 207–211 (1976)

    1976

  50. [50]

    Modal-based phase retrieval for adaptive optics,

    J. Antonello and M. Verhaegen, “Modal-based phase retrieval for adaptive optics,” J. Opt. Soc. Am. A32, 1160–1170 (2015)

    2015

  51. [51]

    Quantum delocalization of a levitated nanoparticle,

    M. Rossi, A. Militaru, N. Carlon Zambon,et al., “Quantum delocalization of a levitated nanoparticle,” Phys. Rev. Lett.135, 083601 (2025)

    2025