High-purity quantum optomechanics at room temperature

Carlos Gonzalez-Ballestero; Davide Candoli; Jayadev Vijayan; Johannes Piotrowski; Lorenzo Dania; Lukas Novotny; Martin Frimmer; Oriol Romero-Isart; Oscar Schmitt Kremer

REVIEW 3 major objections 4 minor 4 cited by

High-purity quantum optomechanics at room temperature

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read A room-temperature optical trap has cooled the twisting motion of a levitated silica nanoparticle into a 92% pure quantum state, with a mean phonon occupation of 0.04, by scattering light into an optical cavity and actively cancelling…

desk verdict A genuine room-temperature record if the calibration checks in the supplement hold up; worth a serious referee. read the letter →

arxiv 2412.14117 v1 pith:4BUF5VQ3 submitted 2024-12-18 quant-ph

Lorenzo Dania , Oscar Schmitt Kremer , Johannes Piotrowski , Davide Candoli , Jayadev Vijayan , Oriol Romero-Isart , Carlos Gonzalez-Ballestero , Lukas Novotny

show 1 more author

Martin Frimmer

This is my paper · ORCID

classification quant-ph

keywords optomechanicslevitatednanoparticlelibrationalmodecoherentscatteringsidebandthermometrycavitycoolingquantumgroundstatelaserphasenoise

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 aims to show that a mechanical oscillator can be brought to a high-purity quantum state without cryogenic cooling: the 1.08 MHz librational (twisting) mode of an optically levitated silica nanoparticle is cooled from room temperature to a mean phonon occupation of $n = 0.04(1)$ quanta, corresponding to a state purity of $P = 92\%$. Cooling is achieved by coherent scattering of the trapping laser into a high-finesse Fabry-Perot cavity operated in the resolved-sideband regime, with an active phase-noise eater that suppresses laser phase noise otherwise capable of heating the motion. The occupation is inferred by Raman sideband thermometry, using the Stokes/anti-Stokes sideband asymmetry in a free-space heterodyne detector. If correct, this places room-temperature levitated oscillators ahead, in terms of quantum state purity, of the cryogenic clamped opto- and electromechanical systems cited as benchmarks.

What carries the argument

The central mechanism is coherent-scattering resolved-sideband cooling of the librational mode: the particle's angular motion inelastically scatters tweezer photons into the cavity at the Stokes and anti-Stokes frequencies, and with cavity detuning $\Delta \approx \Omega_\alpha$ the anti-Stokes process is resonantly enhanced, removing phonons from the motion. Thermometry is performed with a free-space balanced heterodyne detector that measures both motional sidebands directly, using the sideband asymmetry $a_{aS}/a_S = n/(n+1)$ to infer the occupation without relying on the cavity output spectrum. A phase-noise eater, consisting of a Mach-Zehnder interferometer for noise detection and an electro-optic phase modulator for feedback, suppresses laser phase noise that would otherwise heat the motion and corrupt the sideband ratio.

What would settle it

Thermalize the same nanoparticle at a higher gas pressure where the librational occupation is set by the bath temperature ($n \approx k_B T/(\hbar\Omega_\alpha)$), measure the Stokes/anti-Stokes sideband ratio with the same heterodyne chain, and check that it gives the known $n$; a mismatch would show the sideband asymmetry is corrupted by the detector or an unmodeled noise floor, making the reported $n = 0.04$ a measurement artifact.

Watch

Extended reading notes

Core claim

The paper reports that the $\alpha$ librational mode of an optically levitated anisotropic silica nanoparticle—angular oscillation of the particle's long axis in the tweezer focal plane at $\Omega_\alpha/(2\pi) = 1.08$ MHz—can be cooled from room temperature to a mean phonon occupation of $n = 0.04(1)$, corresponding to a state purity of $P = 92\%$, via coherent scattering into a high-finesse Fabry-Perot cavity in the resolved-sideband regime. With an active phase-noise eater suppressing laser phase noise by roughly 20 dB, the remaining heating is attributed to radiation-torque shot noise, i.e., quantum backaction, and the measured occupation approaches the quantum backaction limit. The authors claim that this purity exceeds that of the cryogenic clamped opto- and electromechanical oscillators cited in the introduction, including gigahertz-frequency systems.

Load-bearing premise

The inferred phonon number $n = 0.04$ rests on the assumption that the Stokes and anti-Stokes sideband areas measured by the free-space heterodyne detector faithfully reflect the librational state, with no distortion from classical laser phase noise or from the detector transfer function; the paper states that these artifacts are ruled out only in the Supplemental Material.

Editorial extensions

If this is right

Room-temperature levitated optomechanics can now reach state purities that match or exceed cryogenic clamped opto- and electromechanical systems, removing the cryostat as a prerequisite for high-purity quantum state preparation.
With phase noise suppressed, the librational occupation is limited by quantum backaction (radiation-torque shot noise), so further gains must come from reducing measurement backaction, for example through squeezed light.
The 1.08 MHz librational ground state is a starting point for preparing non-classical rotational states, such as squeezed librational motion via modulation of the confining potential or via the cavity's unstable dynamics.
The megahertz frequency and high state purity open a route to resonantly couple levitated nanoparticles to trapped atomic ions, enabling hybrid quantum systems at room temperature.

Reading between the lines

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

If the inferred purity survives independent calibration, the same combination of coherent-scattering cavity cooling and active phase-noise cancellation should extend to other mechanical modes of levitated particles, including center-of-mass modes, potentially allowing multi-mode ground-state preparation at room temperature.
Because the free-space heterodyne thermometry does not require knowledge of the cavity detuning, it could serve as a cross-check for cavity-output thermometry in other levitated experiments where classical laser noise may fake sideband asymmetry.
The paper's model implies a quantitative prediction: at full phase-noise cancellation, the minimum occupation at the cavity antinode should equal the quantum backaction limit; tuning the cavity linewidth or tweezer power would test whether the backaction rate extracted from fits matches an independently measured photon number.

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.

Desk Editor's Note

read the letter

Quick take: this is a real result, likely to be cited as the first room-temperature levitated oscillator with purity above 90%, exceeding cryogenic clamped systems. The experimental work is careful: they use free-space heterodyne detection to avoid cavity transfer artifacts, they actively suppress laser phase noise, and they validate the cooling model against position and gain scans. The sideband thermometry is standard and well executed. That part genuinely impresses.

The main soft spot is exactly where the reader put the finger: the headline n=0.04(1) is a single-point homodyne measurement cross-calibrated by sideband thermometry, and the detector transfer-function check lives in the Supplemental Material. The main text reports fit standard deviations only. A systematic error of order +0.03 quanta would drop purity to ~88%, which is parity with the best cryogenic systems instead of ahead of them. That is not a fatal flaw — every sideband thermometry experiment carries this kind of calibration burden, and the authors explicitly state they ruled out the transfer function — but it is the right thing for a referee to verify. I would not desk-reject over it; I would send to review with instructions to read the supplement carefully.

The backaction-limit curve is the only mildly circular step: it uses a heating rate extracted from the same data. But that curve is context, not the headline claim. The citation pattern is fine; the comparison values (47% prior levitated, 85–88% cryogenic) match the cited papers.

Who is this for: anyone working on levitodynamics, cavity optomechanics, and quantum state preparation of massive oscillators. It is a benchmark paper for the room-temperature program. I would bring it to the reading group and would cite it if I worked in the area.

Recommendation: accept for peer review. The result is important enough that referees should spend the effort; the supplement is where the battle will be won or lost.

Referee Report

3 major / 4 minor

Summary. The paper reports cavity cooling of the 1.08-MHz librational mode of an optically levitated anisotropic silica nanoparticle at room temperature to a phonon occupation of n = 0.04(1), inferred from Raman sideband thermometry on a free-space balanced heterodyne detector, with a final low-occupation point obtained using a homodyne detector cross-calibrated by sideband thermometry. The authors claim this corresponds to a state purity of 92%, exceeding the purity of the most performant cryogenic opto- and electromechanical systems cited in the introduction. The manuscript supports the claim with a cavity-detuning scan, a position-dependence study, and a phase-noise cancellation (noise-eater) study, together with a theoretical model that includes radiation-torque shot noise and laser phase noise.

Significance. If the calibration and systematic-error concerns are resolved, this result is a milestone: it would be the first demonstration of ground-state cooling of a levitated librator at room temperature and would place room-temperature levitated optomechanics ahead of cryogenic clamped oscillators in state purity. The use of free-space sideband thermometry to avoid cavity transfer artifacts is a sound and well-motivated methodological choice, and the active phase-noise cancellation is an important technical contribution. The consistency checks against a quantitative model of phase noise and radiation-torque shot noise are valuable. The main weakness is that the headline number, n = 0.04(1), rests on detection-chain assumptions that are only deferred to the Supplemental Material and on an uncertainty budget that appears to be purely statistical.

major comments (3)

[Sideband thermometry and cavity detuning scan; Figs. 2 and 3] The central claim n = 0.04(1) is inferred from the anti-Stokes/Stokes sideband area ratio. Because the Stokes and anti-Stokes sidebands are measured at different radiofrequencies (1.65 MHz and 3.81 MHz in the heterodyne signal), any frequency-dependent detector gain directly biases n. In addition, the lowest-occupation point is obtained with a homodyne detector that is cross-calibrated by sideband thermometry, so the calibration must transfer reliably across detector settings and operating points. The main text reports only fit standard deviations and states that the detector transfer function is ruled out in the Supplemental Material. Please provide in the main text (or in a way that can be assessed) a quantitative detector transfer measurement covering the two sideband frequencies, a description of the homodyne calibration chain, and a systematic uncertainty budget for n. Without this, an error of order 0.03 quanta would reduce the purity from 92% to 88%, placing the result at parity with the cited cryogenic system of Ref. [16] rather than ahead of it.
[Position dependence of cooling performance; Fig. 3(a)] The minimum occupation n = 0.04(1) appears to be extracted from a single configuration (kyeq ≈ π/2, g = 1). The manuscript should state how many independent measurements and particles contribute to this value, whether the quoted uncertainty is purely statistical, and whether the homodyne calibration was validated at the same gain and operating point as the minimum. If the calibration was performed at a different operating point or at a larger occupation, the linearity of the detection chain between those conditions needs to be demonstrated, since this is load-bearing for the reported purity.
[Sideband thermometry and cavity detuning scan; Fig. 2(b)] The sideband ratio aaS/aS = n/(n + 1) assumes a thermal mechanical state and negligible asymmetric background in the two sideband regions. The Lorentzian fits in Fig. 2(b) include background levels, but the main text does not state how background subtraction was performed or whether a background asymmetry could shift n by 0.01–0.03 quanta at the lowest occupations. This is important because the sideband areas become small at the optimal cooling point, and the comparison with cryogenic systems depends on the accuracy of n at the 0.03 level.

minor comments (4)

[Sideband thermometry and cavity detuning scan] The sentence that the detector transfer function is 'ruled out' in the Supplemental Material is important for the central claim; please either include a brief version of the transfer measurement in the main text or provide a quantitative bound with an uncertainty.
[Conclusions] The conclusion states that phase-noise cancellation reaches 'up to ~20 dB', but this value does not appear to be supported by data in the main text; please add a reference to a figure or provide the measurement in the main text.
[Position dependence of cooling performance; Fig. 3(a,c,d)] The black dashed 'quantum back-action limit' curves are computed using Gamma_BA/(2π) = 0.5(1) kHz extracted from fits to the same dataset. These curves should be labeled as model predictions based on the fitted Gamma_BA rather than as independent measurements, or the uncertainty in Gamma_BA should be propagated as a band.
[Position dependence of cooling performance; Fig. 3(b)] A one-sentence description of how the homodyne signal is converted to units of alpha_zpf would improve readability; currently this is only described in the Supplemental Material.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity: n=0.04 is measured from sideband asymmetry; only the quantum-backaction limit line is fit-based and interpretive.

fitted input called prediction [Fig. 3(a), Section 'Position dependence of cooling performance']
"From these fits, we extract the shot noise heating rate (i.e., the heating rate in total absence of phase noise) ΓBA/(2π) = 0.5(1) kHz. We use this value to calculate the backaction-limited occupation that can be provided by our system, shown as the dashed black line in Figure 3(a). The proximity of the shot-noise limit to the data taken at cancellation gain g = 1 (blue triangles) suggests that at this level of laser phase noise (S˙ϕ˙ϕ(Ωα) = 0.01 Hz2/Hz [32]) the measured occupations are predominantly limited by quantum back-action."

The dashed 'quantum back-action limit' curve is not an independent prediction: ΓBA/(2π)=0.5(1) kHz is extracted from simultaneous theory fits to the same occupation-number data (blue areas in Fig. 3(a)), and the dashed line is then calculated from that fitted ΓBA. Hence the reported proximity of the g=1 data to the back-action limit is partly enforced by the fit rather than demonstrated by an out-of-sample measurement. This is a mild interpretive circularity only: the headline value n=0.04(1) is obtained from the directly measured sideband ratio aaS/aS=n/(n+1), not from this fitted curve.

full rationale

The central claim, cooling a levitated librator to n=0.04(1) and 92% purity, is derived from Raman sideband thermometry using the standard relation aaS/aS=n/(n+1), applied to Stokes and anti-Stokes sidebands detected in free space before the cavity. This is a direct measurement, not a quantity contained in the theoretical cooling model. The homodyne detector used for the final low-occupation point is explicitly 'cross-calibrated by sideband thermometry,' which transfers a measured sideband ratio into a displacement scale; this is a calibration chain, not a circular derivation. The only mild circular step is the quantum-backaction limit line, which is computed from a heating rate extracted by fitting the same data set; that affects the interpretation that the system is back-action limited, but does not feed back into the reported purity. The detector transfer-function check is deferred to the Supplemental Material, which is a validation gap rather than a circularity. Self-citations to the authors' theoretical framework are normal and are used for model interpretation, not to define the measured occupation. The headline result is therefore statistically self-contained, and the paper merits a low circularity score.

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

The central claim rests on a measured sideband ratio plus a standard thermometry formula; no new entities are introduced. The main unverified inputs are the experimental calibrations and the completeness of the heating model, most of which are deferred to the Supplemental Material.

free parameters (3)

Radiation torque shot-noise heating rate Gamma_BA = 2*pi*0.5(1) kHz
Extracted from simultaneous theory fits to position scans in Fig. 3(a); used to draw the quantum backaction limit and to support the claim that the measured occupation is backaction-limited.
Laser phase noise spectral density S_phidot(Omega_alpha) = 0.01 Hz^2/Hz
Inferred from model fits and supplementary characterization; quantifies the noise level after cancellation and enters the theory curves in Figs. 2 and 3.
Libration-cavity optomechanical coupling rate
Used in the theory model for occupation versus detuning and position; its value and uncertainty are stated only in the Supplemental Material, not in the main text.

assumptions (3)

standard math The sideband area ratio a_as/a_S equals n/(n+1) for a harmonic oscillator in a thermal state.
Used in sideband thermometry to convert measured Stokes and anti-Stokes sideband areas into phonon occupation; standard quantum optics result.
domain assumption The free-space heterodyne detector measures the librational Stokes and anti-Stokes sidebands without distortion from the cavity transfer function or classical laser phase noise.
The authors state this and say it is ruled out in the Supplemental Material; the main text does not show the verification.
domain assumption The anisotropic nanoparticle's highest-frequency libration mode is a well-isolated harmonic oscillator, with decoherence dominated by gas collisions, radiation torque shot noise, and laser phase noise.
The model for Gamma_BA and the occupation versus position in Fig. 3 assumes this list of heating mechanisms is complete.

how reviews work

0 comments

Cite this review

Pith. "Pith review of High-purity quantum optomechanics at room temperature." pith.science (2026). https://pith.science/paper/4BUF5VQ3

@misc{pith2026241214117,
  author       = {Pith},
  title        = {Pith review of: High-purity quantum optomechanics at room temperature},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4BUF5VQ3}},
  note         = {Machine review of arXiv:2412.14117}
}

read the original abstract

Exploiting quantum effects of mechanical motion, such as backaction evading measurements or squeezing, requires preparation of the oscillator in a high-purity state. The largest state purities in optomechanics to date have relied on cryogenic cooling, combined with coupling to electromagnetic resonators driven with a coherent radiation field. In this work, we cool the mega-hertz-frequency librational mode of an optically levitated silica nanoparticle from room temperature to its quantum ground state. Cooling is realized by coherent scattering into a Fabry-Perot cavity. We use sideband thermometry to infer a phonon population of 0.04 quanta under optimal conditions, corresponding to a state purity of 92%. The purity reached by our room-temperature experiment exceeds the performance offered by mechanically clamped oscillators in a cryogenic environment. Our work establishes a platform for high-purity quantum optomechanics at room temperature.

Figures

Figures reproduced from arXiv: 2412.14117 by the authors.

**Figure 2.** (b) shows heterodyne spectra normalized to the detection shot-noise level S sn centered around the Stokes (left column) and anti-Stokes (right column) libration peaks, and for increasing values of the cavity detuning ∆ (top to bottom). For better comparison, the spectra have been shifted along the frequency axis to align the Stokes and anti-Stokes peaks, respectively. The original spectra are shown in the Suppleme… view at source ↗

**Figure 3.** (a) shows as blue squares the occupation n obtained with phase-noise cancellation gain g = 0.2. The occupation reaches a minimum value of n = 0.25 at a position kyeq ≈ 0.2π, closer to the cavity anti-node with respect to the situation without phase-noise cancellation. For gain g = 1, shown as blue triangles in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

Trap-to-trap free falls with an optically levitated nanoparticle
quant-ph 2025-07 conditional novelty 7.0 of 10

An optically levitated silica nanoparticle was released, fell freely for up to 0.25 ms under gravity, was recaptured by a second optical tweezer, and showed an approximately 190-fold growth in position uncertainty.
Cooling of an optically levitated nanoparticle via measurement-free coherent feedback
quant-ph 2025-06 conditional novelty 6.0 of 10

Coherent, measurement-free optical feedback cools a levitated nanoparticle to about 344 phonons, with phase noise identified as the main barrier to ground-state cooling.
Optical centrifuge for nanoparticles
physics.optics 2025-06 conditional novelty 6.0 of 10

A chirped rotating polarization in an optical tweezer can, according to theory and simulation, accelerate levitated anisotropic nanoparticles to rotation frequencies above 100 MHz.
Roto-translational optomechanics
quant-ph 2025-07 accept novelty 3.0 of 10

A comprehensive review of the coupled rotational and translational motion of levitated nanoparticles, with a classical-to-quantum theoretical framework and a survey of experiments and applications.

Reference graph

Works this paper leans on

59 extracted references · 52 canonical work pages · cited by 4 Pith papers

[16]

Youssefi, S

A. Youssefi, S. Kono, M. Chegnizadeh, and T. J. Kippenberg, A squeezed mechanical oscillator with millisecond quantum decoherence, Nat. Phys. 19, 1697 (2023)

work page 2023
[1]

Aspelmeyer, T

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

2014
[2]

Lecocq, J

F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Quantum nondemolition measurement of a nonclassical state of a massive object, Phys. Rev. X 5, 041037 (2015)

2015
[3]

Shomroni, L

I. Shomroni, L. Qiu, D. Malz, A. Nunnenkamp, and T. J. Kip- penberg, Optical backaction-evading measurement of a mechan- ical oscillator, Nat. Commun. 10, 10.1038/s41467-019-10024-3 (2019)

work page doi:10.1038/s41467-019-10024-3 2019
[4]

Barzanjeh, A

S. Barzanjeh, A. Xuereb, S. Gr¨oblacher, M. Paternostro, C. A. Regal, and E. M. Weig, Optomechanics for quantum technolo- gies, Nat. Phys. 18, 15–24 (2021)

work page 2021
[5]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, Bidirectional and efficient conversion between microwave and optical light, Nat. Phys. 10, 321–326 (2014)

work page 2014
[6]

Arndt and K

M. Arndt and K. Hornberger, Testing the limits of quantum mechanical superpositions, Nat. Phys. 10, 271 (2014)

2014
[7]

Croquette, S

M. Croquette, S. Del´eglise, T. Kawasaki, K. Komori, M. Kurib- ayashi, A. Lartaux-V ollard, N. Matsumoto, Y . Michimura, M. Andia, N. Aritomi, R. Braive, T. Briant, S. Briaudeau, S. B. Cata ˜no-Lopez, S. Chua, J. Degallaix, M. Fujimoto, K. Gerashchenko, F. Glotin, P. Gruning, K. Harada, A. Hei- dmann, D. Hofman, P.-E. Jacquet, T. Jacqmin, O. Kozlova, N. L...

work page 2023

Show all 59 references

[8]

Rickles and C

D. Rickles and C. M. DeWitt,The Role of Gravitation in Physics: Report from the 1957 Chapel Hill Conference (Max-Planck- Gesellschaft zur F¨orderung der Wissenschaften, 2011)

1957
[9]

Belenchia, R

A. Belenchia, R. M. Wald, F. Giacomini, E. Castro-Ruiz, i. c. v. Brukner, and M. Aspelmeyer, Quantum superposition of massive objects and the quantization of gravity, Phys. Rev. D98, 126009 (2018)

2018
[10]

J. Guo, R. Norte, and S. Gr¨oblacher, Feedback cooling of a room temperature mechanical oscillator close to its motional ground state, Phys. Rev. Lett. 123, 223602 (2019)

2019
[11]

Tendick, H

L. Tendick, H. Kampermann, and D. Bruß, Quantifying nec- essary quantum resources for nonlocality, Phys. Rev. Res. 4, L012002 (2022)

2022
[12]

Roda-Llordes, A

M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Gro- chowski, and O. Romero-Isart, Macroscopic quantum superposi- tions via dynamics in a wide double-well potential, Phys. Rev. Lett. 132, 023601 (2024)

2024
[13]

M. G. A. Paris, F. Illuminati, A. Serafini, and S. De Siena, Purity of gaussian states: Measurement schemes and time evolution in noisy channels, Phys. Rev. A 68, 012314 (2003)

2003
[14]

Riedinger, S

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V . Anant, M. Aspelmeyer, and S. Gr ¨oblacher, Non- classical correlations between single photons and phonons from a mechanical oscillator, Nature 530, 313 (2016)

2016
[15]

Y . Chu, P. Kharel, W. H. Renninger, L. D. Burkhart, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Quantum acoustics with superconducting qubits, Science 358, 199 (2017)

2017
[17]

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gr ¨oblacher, M. Aspelmeyer, and O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state, Nature 478, 89 (2011)

2011
[18]

R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, Laser cooling of a micromechanical membrane to the quantum backaction limit, Phys. Rev. Lett. 116, 063601 (2016)

2016
[19]

Rossi, D

M. Rossi, D. Mason, J. Chen, Y . Tsaturyan, and A. Schliesser, 6 Measurement-based quantum control of mechanical motion, Na- ture 563, 53–58 (2018)

2018
[20]

Tebbenjohanns, M

F. Tebbenjohanns, M. L. Mattana, M. Rossi, M. Frimmer, and L. Novotny, Quantum control of a nanoparticle optically levi- tated in cryogenic free space, Nature 595, 378 (2021)

2021
[21]

L. Qiu, I. Shomroni, P. Seidler, and T. J. Kippenberg, Laser cooling of a nanomechanical oscillator to its zero-point energy, Phys. Rev. Lett. 124, 173601 (2020)

2020
[22]

Gonzalez-Ballestero, M

C. Gonzalez-Ballestero, M. Aspelmeyer, L. Novotny, R. Quidant, and O. Romero-Isart, Levitodynamics: Levitation and control of microscopic objects in vacuum, Science 374, 168 (2021)

2021
[23]

Magrini, P

L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, A. Kugi, and M. Aspelmeyer, Real-time optimal quantum control of mechanical motion at room temperature, Nature 595, 373 (2021)

2021
[24]

Deli ´c, M

U. Deli ´c, M. Reisenbauer, K. Dare, D. Grass, V . Vuleti ´c, N. Kiesel, and M. Aspelmeyer, Cooling of a levitated nanopar- ticle to the motional quantum ground state, Science 367, 892 (2020)

2020
[25]

G. S. MacCabe, H. Ren, J. Luo, J. D. Cohen, H. Zhou, A. Sipahigil, M. Mirhosseini, and O. Painter, Nano-acoustic res- onator with ultralong phonon lifetime, Science 370, 840 (2020)

2020
[26]

Beccari, D

A. Beccari, D. A. Visani, S. A. Fedorov, M. J. Bereyhi, V . Boureau, N. J. Engelsen, and T. J. Kippenberg, Strained crys- talline nanomechanical resonators with quality factors above 10 billion, Nat. Phys. 18, 436 (2022)

2022
[27]

Huang, A

G. Huang, A. Beccari, N. J. Engelsen, and T. J. Kippenberg, Room-temperature quantum optomechanics using an ultralow noise cavity, Nature 626, 512–516 (2024)

2024
[28]

Sch¨afer, H

J. Sch¨afer, H. Rudolph, K. Hornberger, and B. A. Stickler, Cool- ing nanorotors by elliptic coherent scattering, Phys. Rev. Lett. 126, 163603 (2021)

2021
[30]

J. Bang, T. Seberson, P. Ju, J. Ahn, Z. Xu, X. Gao, F. Robicheaux, and T. Li, Five-dimensional cooling and nonlinear dynamics of an optically levitated nanodumbbell, Phys. Rev. Res. 2, 043054 (2020)

2020
[31]

B. A. Stickler, K. Hornberger, and M. S. Kim, Quantum rotations of nanoparticles, Nat. Rev. Phys. 3, 589 (2021)

2021
[32]

[52– 61]

See Supplemental Material for more details about the model, ex- perimental setup, particle shape, data fitting, including Ref. [52– 61]
[33]

T. M. Hoang, Y . Ma, J. Ahn, J. Bang, F. Robicheaux, Z.-Q. Yin, and T. Li, Torsional optomechanics of a levitated nonspherical nanoparticle, Phys. Rev. Lett. 117, 123604 (2016)

2016
[34]

J. Gao, F. van der Laan, J. A. Zieli´nska, A. Militaru, L. Novotny, and M. Frimmer, Feedback cooling a levitated nanoparticle’s li- bration to below 100 phonons, Phys. Rev. Res.6, 033009 (2024)

2024
[35]

Parniak, I

M. Parniak, I. Galinskiy, T. Zwettler, and E. S. Polzik, High- frequency broadband laser phase noise cancellation using a delay line, Opt. Express 29, 6935 (2021)

2021
[36]

Pontin, H

A. Pontin, H. Fu, M. Toro ˇs, T. S. Monteiro, and P. F. Barker, Simultaneous cavity cooling of all six degrees of freedom of a levitated nanoparticle, Nat. Phys. 19, 1003 (2023)

2023
[37]

Kamba, R

M. Kamba, R. Shimizu, and K. Aikawa, Nanoscale feedback control of six degrees of freedom of a near-sphere, Nat. Comm. 14, 7943 (2023)

2023
[38]

Schliesser, R

A. Schliesser, R. Rivi`ere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Resolved-sideband cooling of a micromechanical oscillator, Nat. Phys. 4, 415 (2008)

2008
[40]

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010)

2010
[41]

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, Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle, Nat. Phys. 19, 1009 (2023)

2023
[42]

A. M. Jayich, J. C. Sankey, K. Børkje, D. Lee, C. Yang, M. Un- derwood, L. Childress, A. Petrenko, S. M. Girvin, and J. G. E. Harris, Cryogenic optomechanics with a Si3N4 membrane and classical laser noise, New J. Phys. 14, 115018 (2012)

2012
[43]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, S. Gr¨oblacher, H. Miao, Y . Chen, M. Aspelmeyer, and O. Painter, Laser noise in cavity- optomechanical cooling and thermometry, New J. Phys. 15, 035007 (2013)

2013
[44]

Meyer, A

N. Meyer, A. d. l. R. Sommer, P. Mestres, J. Gieseler, V . Jain, L. Novotny, and R. Quidant, Resolved-sideband cooling of a levitated nanoparticle in the presence of laser phase noise, Phys. Rev. Lett. 123, 153601 (2019)

2019
[45]

van der Laan, F

F. van der Laan, F. Tebbenjohanns, R. Reimann, J. Vijayan, L. Novotny, and M. Frimmer, Sub-kelvin feedback cooling and heating dynamics of an optically levitated librator, Phys. Rev. Lett. 127, 123605 (2021)

2021
[46]

Rossi, A

M. Rossi, A. Militaru, N. C. Zambon, A. Riera-Campeny, O. Romero-Isart, M. Frimmer, and L. Novotny, Quantum delo- calization of a levitated nanoparticle, arXiv:2408.01264 (2024)

2024 arXiv
[47]

B. A. Stickler, B. Papendell, S. Kuhn, B. Schrinski, J. Millen, M. Arndt, and K. Hornberger, Probing macroscopic quantum superpositions with nanorotors, New J. Phys. 20, 122001 (2018)

2018
[48]

Kustura, C

K. Kustura, C. Gonzalez-Ballestero, A. d. l. R. Sommer, N. Meyer, R. Quidant, and O. Romero-Isart, Mechanical squeez- ing via unstable dynamics in a microcavity, Phys. Rev. Lett.128, 143601 (2022)

2022
[49]

Y . Ma, K. E. Khosla, B. A. Stickler, and M. S. Kim, Quantum persistent tennis racket dynamics of nanorotors, Phys. Rev. Lett. 125, 053604 (2020)

2020
[50]

D. S. Bykov, L. Dania, F. Goschin, and T. E. Northup, A nanopar- ticle stored with an atomic ion in a linear paul trap (2024), arXiv:2403.02034 [quant-ph]

2024
[51]

Najera-Santos, R

B.-L. Najera-Santos, R. Rousseau, K. Gerashchenko, H. Patange, A. Riva, M. Villiers, T. Briant, P.-F. Cohadon, A. Heidmann, J. Palomo, M. Rosticher, H. le Sueur, A. Sarlette, W. C. Smith, Z. Leghtas, E. Flurin, T. Jacqmin, and S. Del ´eglise, High- sensitivity ac-charge detect...

2024
[52]

Gonzalez-Ballestero, J

C. Gonzalez-Ballestero, J. Zieli ´nska, M. Rossi, A. Militaru, M. Frimmer, L. Novotny, P. Maurer, and O. Romero-Isart, Suppressing recoil heating in levitated optomechanics using squeezed light, PRX Quantum 4, 030331 (2023)

2023
[53]

Gonzalez-Ballestero, P

C. Gonzalez-Ballestero, P. Maurer, D. Windey, L. Novotny, R. Reimann, and O. Romero-Isart, Theory for cavity cooling of levitated nanoparticles via coherent scattering: Master equation approach, Phys. Rev. A 100, 013805 (2019)

2019
[54]

Wilson-Rae, N

I. Wilson-Rae, N. Nooshi, J. Dobrindt, T. J. Kippenberg, and W. Zwerger, Cavity-assisted backaction cooling of mechanical resonators, New Journal of Physics 10, 095007 (2008)

2008
[55]

Van Kampen, A cumulant expansion for stochastic linear differential equations

N. Van Kampen, A cumulant expansion for stochastic linear differential equations. i, Physica 74, 215 (1974)

1974
[56]

Van Kampen, A cumulant expansion for stochastic linear differential equations

N. Van Kampen, A cumulant expansion for stochastic linear differential equations. ii, Physica 74, 239 (1974)

1974
[57]

P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, Phase- 7 noise induced limitations on cooling and coherent evolution in optomechanical systems, Phys. Rev. A 80, 063819 (2009)

2009
[58]

Deli´c, M

U. Deli´c, M. Reisenbauer, D. Grass, N. Kiesel, V . Vuleti´c, and M. Aspelmeyer, Cavity cooling of a levitated nanosphere by coherent scattering, Phys. Rev. Lett. 122, 123602 (2019)

2019
[59]

Windey, C

D. Windey, C. Gonzalez-Ballestero, P. Maurer, L. Novotny, O. Romero-Isart, and R. Reimann, Cavity-based 3d cooling of a levitated nanoparticle via coherent scattering, Phys. Rev. Lett. 122, 123601 (2019)

2019
[60]

Tebbenjohanns, M

F. Tebbenjohanns, M. Frimmer, V . Jain, D. Windey, and L. Novotny, Motional sideband asymmetry of a nanoparticle optically levitated in free space, Phys. Rev. Lett. 124, 013603 (2020)

2020
[61]

Gonzalez-Ballestero, Tutorial: projector approach to open quantum systems, arXiv:2305.19704 (2023)

C. Gonzalez-Ballestero, Tutorial: projector approach to open quantum systems, arXiv:2305.19704 (2023)

2023 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [16]

Youssefi, S

A. Youssefi, S. Kono, M. Chegnizadeh, and T. J. Kippenberg, A squeezed mechanical oscillator with millisecond quantum decoherence, Nat. Phys. 19, 1697 (2023)

work page 2023

[2] [1]

Aspelmeyer, T

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

2014

[3] [2]

Lecocq, J

F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Quantum nondemolition measurement of a nonclassical state of a massive object, Phys. Rev. X 5, 041037 (2015)

2015

[4] [3]

Shomroni, L

I. Shomroni, L. Qiu, D. Malz, A. Nunnenkamp, and T. J. Kip- penberg, Optical backaction-evading measurement of a mechan- ical oscillator, Nat. Commun. 10, 10.1038/s41467-019-10024-3 (2019)

work page doi:10.1038/s41467-019-10024-3 2019

[5] [4]

Barzanjeh, A

S. Barzanjeh, A. Xuereb, S. Gr¨oblacher, M. Paternostro, C. A. Regal, and E. M. Weig, Optomechanics for quantum technolo- gies, Nat. Phys. 18, 15–24 (2021)

work page 2021

[6] [5]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, Bidirectional and efficient conversion between microwave and optical light, Nat. Phys. 10, 321–326 (2014)

work page 2014

[7] [6]

Arndt and K

M. Arndt and K. Hornberger, Testing the limits of quantum mechanical superpositions, Nat. Phys. 10, 271 (2014)

2014

[8] [7]

Croquette, S

M. Croquette, S. Del´eglise, T. Kawasaki, K. Komori, M. Kurib- ayashi, A. Lartaux-V ollard, N. Matsumoto, Y . Michimura, M. Andia, N. Aritomi, R. Braive, T. Briant, S. Briaudeau, S. B. Cata ˜no-Lopez, S. Chua, J. Degallaix, M. Fujimoto, K. Gerashchenko, F. Glotin, P. Gruning, K. Harada, A. Hei- dmann, D. Hofman, P.-E. Jacquet, T. Jacqmin, O. Kozlova, N. L...

work page 2023