Pith. sign in

REVIEW 4 major objections 5 minor 118 references

Single-atom sensor for low-frequency electric field

T0 review · 4 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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

Pith's one-line read A single injection-locked trapped ion, acting as a phonon laser, recovers the frequency, phase, and amplitude of a 30–300 kHz electric-field signal in one measurement, at 404 µV/(m·√Hz) sensitivity and a 61.5 µV/m detection limit.

desk verdict A genuinely new single-ion beat-readout method with a self-calibrated absolute scale; the qualitative result holds, but the headline V/m numbers need an independent calibration before they are quoted. read the letter →

arxiv 2607.17583 v1 pith:OP2EOHEE submitted 2026-07-20 quant-ph physics.app-ph

Quan Yuan , Shuang-Qing Dai , Tai-Hao Cui , Pei-Dong Li , Yuan-Zhang Dong , Zhuo-Zhu Wu , Ji Li , Fei Zhou
show 3 more authors
Jian-Qi Zhang Liang Chen Mang Feng
This is my paper · ORCID
classification quant-phphysics.app-ph
keywords single-ionsensorphononlaserinjectionlockingbeatfrequencylow-frequencyelectricfieldtrappedionelectrometryphasemeasurement
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 claims that a single trapped ion, operated as an injection-locked phonon laser, can simultaneously measure the frequency, phase, and amplitude of a low-frequency electric-field signal (30–300 kHz) in a single measurement, without sideband cooling. The ion, held in a surface-electrode trap at its secular frequency near 238 kHz, is phase-locked to an injected voltage; an unknown signal applied to the same electrode beats against the locked oscillation, imprinting its parameters as slow sinusoidal modulations of the phonon laser's phase and amplitude. The authors report a sensitivity of 403.8 µV/(m·√Hz) and a detection limit of 61.5 µV/m, with noise robustness attributed to injection locking. If correct, this provides a compact alternative to electrically large antennas for low-frequency field sensing, with potential applications in subsurface communication, precision metrology, and biomedical monitoring.

What carries the argument

The central object is the injection-locked single-ion phonon laser: a single ⁴⁰Ca⁺ ion oscillating at its secular frequency (238.42 kHz) in a surface-electrode trap, dressed by two detuned laser beams that provide gain and Doppler cooling, and phase-locked to an injected oscillating voltage S_i. The unknown signal S_t applied to the same electrode creates a small force term; the beat between S_t and the locked oscillation appears as slow sinusoidal modulations in the phonon laser's phase Φ and amplitude A, described by Eqs. (2) and (3). The response factors R_p = e/(2mω_i Δ A_0) and R_A = e/(2mω_i Δ) set the mapping from applied voltage to measured phase and amplitude modulation.

What would settle it

Apply a well-characterized low-frequency electric-field signal whose amplitude at the ion is independently calibrated (e.g., by measuring the ion's displacement via sideband spectroscopy or by using a second ion as a reference) and compare the recovered amplitude with the quoted linear calibration; significant deviation would falsify the single-scalar-response model. Alternatively, sweep the input frequency across the claimed 30–300 kHz range and check whether the sensitivity stays constant; strong frequency dependence would invalidate the single-k assumption.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the response formulas Φ ≈ −R_p k V_t sin(Δ t + φ_t) and A ≈ A_0 + R_A k V_t cos(Δ t + φ_t) hold for a single-ion phonon laser, allowing the input signal's amplitude, frequency, and phase to be recovered by fitting the beat-induced oscillations of the phase, with the amplitude used to resolve sign ambiguities. The authors demonstrate this experimentally for beat frequencies from 0.2 mHz to 2 Hz, extract a linear calibration ∂E_fit/∂V_t = 136.8 mrad/mV, and from it compute the sensitivity and detection limit. The approach requires only Doppler cooling, operates near the trap secular frequency (adjustable from 90 kHz to 300 kHz), and shows

Load-bearing premise

The conversion of applied electrode voltage to the electric field at the ion is treated as a single scalar constant k = 1.3 m⁻¹, back-calculated from the same fitted slope that defines the amplitude sensitivity; if the electrode response varies with frequency or position, or if the calibration is inaccurate, the quoted sensitivity and detection limit shift.

Editorial extensions

If this is right

  • A single measurement yields all three signal parameters (frequency, phase, amplitude), whereas prior approaches often required multiple scans or modulation.
  • No sideband cooling is required; only Doppler cooling, making the technique practical in existing trapped-ion systems.
  • The reported sensitivity (403.8 µV/(m·√Hz)) and detection limit (61.5 µV/m) are comparable to previous trapped-ion force sensors, and the method is robust to noise much stronger than the signal.
  • The operating frequency range can be extended from tens of kHz to MHz by choosing different trap geometries and secular frequencies.
  • The phase sensitivity opens avenues for high-resolution mass spectrometry and detection of biochemical oscillations.

Reading between the lines

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

  • Because the phase modulation scales as 1/Δ (through R_p), operating at smaller beat detunings with longer integration times could push the detection limit below 61.5 µV/m, at the cost of measurement time.
  • The demonstrated phase sensitivity (~0.4 rad/√Hz) suggests the locked-phonon-laser readout could be adapted for phase-modulated signal sensing in noisy environments, a testable extension beyond the paper's amplitude-focused calibration.
  • The scalar response calibration k = 1.3 m⁻¹ is geometry-specific; if the true field at the ion is frequency-dependent (due to electrode impedance or shielding), the quoted absolute sensitivity would need re-calibration per frequency, which could be tested with an independent field source.
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 reports a single 40Ca+ ion in a surface-electrode trap operated as an injection-locked phonon laser, used as a beat-frequency sensor for low-frequency electric fields (30–300 kHz). A weak electrode signal St is superimposed on the injection-locking drive; the resulting phase and amplitude modulation of the phonon laser is measured via photon scattering, and fits to Eqs. (2)–(3) yield the frequency, phase, and amplitude of the input. The authors report a frequency resolution of 3.4 mHz/√Hz, an amplitude sensitivity of 403.8 µV/(m·√Hz), a phase sensitivity of 0.4(0.3) rad/√Hz, and a detection limit of 61.5 µV/m, along with robustness against applied Gaussian noise.

Significance. If the absolute calibration can be made trustworthy, this would be a compact and relatively simple single-atom LFEF sensor that extracts frequency, phase, and amplitude simultaneously without sideband cooling. The direct observation of beat modulation at 0.2 mHz–2 Hz, the clean sinusoidal fits in Fig. 2, the linear calibration in Fig. 3(a), the one-to-one phase mapping in Fig. 3(b), and the noise-robustness data in Fig. 4 are genuine experimental strengths. The frequency and phase readout are robust and model-independent to a good degree. However, the two headline numbers in V/m units depend entirely on a self-calibrated electrode response parameter, and the stated detection limit is an x-intercept rather than a statistical LOD; these issues must be fixed before the central quantitative claims can be accepted.

major comments (4)
  1. [Eq. (2)-(3) and calibration paragraph (p. 4)] The absolute-unit conversion E_t = kV_t uses k = 1.3 m^-1, which is back-computed from the same measured slope ∂E_fit/∂V_t = 136.8 mrad/mV that defines the amplitude sensitivity in V/m. This is self-calibration: any error in the model Eq. (2) (e.g., a missing numerical factor, an inaccurate A0, or an invalid small-argument expansion) is absorbed into k and shifts both the quoted sensitivity and detection limit. Please provide an independent calibration of k (trap simulation, a known reference field, or at least a cross-check with a second electrode geometry), and a systematic uncertainty budget that includes frequency dependence over 30–300 kHz and spatial variation over the 25.5 µm oscillation amplitude.
  2. [Detection limit paragraph (p. 4-5)] The 'minimum detectable strength' is obtained as the x-intercept of the calibration line (Vt = 46.2 µV, corresponding to 61.5 µV/m). An x-intercept of a linear fit is not a statistical limit of detection. Please report a proper LOD from repeated zero-signal measurements (e.g., 3σ of E_fit at Vt = 0, or the standard error of prediction at zero concentration) with the integration time stated. The current number does not connect to the reported σ_a = 9.5 mrad or to the noise statistics.
  3. [Eqs. (2)-(3) and reference [50]] The response model is central: Eq. (2) determines the calibration slope, the phase extraction, and the amplitude sensitivity. The derivation is referred to the 'supplementary materials' (ref. [50]), which is not present in the submission. Since the manuscript cannot be checked without this derivation, either include the full derivation in the paper or cite a published article where it appears. Also state quantitatively the conditions Vt << Vi and |Δ| << ω_i, and how A0 is measured.
  4. [Amplitude sensitivity definition (p. 4)] The amplitude sensitivity η_a = σ_a√t_tot / (∂E_fit/∂E_t) is computed by dividing the voltage-referred slope by the same back-calculated k. Thus the reported 403.8 µV/(m·√Hz) is a consistency check of the model rather than an independently measured quantity. Please report the raw voltage-referred sensitivity (e.g., in mV/√Hz) together with the calibration uncertainty, and separate the model-dependent conversion to V/m.
minor comments (5)
  1. [Eq. (1)] The notation 'ke' in Eq. (1) is ambiguous: is it k·e or a single symbol? If it is e·k, clarify that e is the elementary charge and k is the electrode response parameter.
  2. [Table I] The column 'FE (Hz)' appears to be Δ_fit - Δ, but the sign convention is not explained. Also state the integration time for each row explicitly in the table or in the caption.
  3. [Phase sensitivity notation] The notation '0.4(0.3) rad/√Hz' should be defined; it appears to mean 0.4 rad/√Hz for one condition and 0.3 for another, but the text is ambiguous.
  4. [Fig. 3(a)] The caption says error bars are statistical standard errors, but none are visible in the figure as printed. Please ensure error bars are shown or explain their absence.
  5. [Noise robustness section (p. 5)] The statement 'contrary to expectations' is vague. Specify the expected degradation mechanism and why phase stability is expected under injection locking.

Circularity Check

1 steps flagged · score 2.0 of 10

Mild self-calibration of the absolute E-field conversion: k is back-calculated from the same fitted slope used to quote the amplitude sensitivity and detection limit, so the V/m numbers are model-dependent but not forced identities.

  1. fitted input called prediction [Sensitivity/limitations section, around Eq. (2), Fig. 3(a), and the detection-limit sentence]
    "The LFEF signal applied to the trapped ion can be denoted as E_t = k V_t with a response parameter k... η_a = σ_a√t_tot/(∂E_fit/∂E_t)... In our experiment, the response parameter k is calculated as 1.3 m^-1 with the fitted slope of ∂E_fit/∂V_t = 136.8 mrad/mV... the fitted line does not pass through the origin but approaches zero at Vt = 46.2 µV, indicating the minimum detectable strength of the LFEF in our system is 61.5 µV/m."

    The absolute-field calibration constant k is not independently measured; it is back-calculated from the same fitted calibration slope ∂E_fit/∂V_t that defines the amplitude response. The amplitude sensitivity η_a is then evaluated using ∂E_fit/∂E_t = (∂E_fit/∂V_t)/k, and the detection limit is quoted as k × 46.2 µV. Thus the absolute V/m figures are rescalings of the same fitted line through a factor derived from that line. The mV-level measurements, fitting errors, and linearity checks are genuine experimental data, so this is self-calibration rather than a fully forced identity; but the absolute-field sensitivity and detection limit cannot independently validate the calibration.

full rationale

The paper's central measurements are direct: the beat-induced phase/amplitude oscillations are observed, the frequency extraction is a one-to-one reconstruction with reported fitting errors, and the phase calibration uses an independent control of the input phase. The principal load-bearing theoretical input is Eq. (2) (and Eq. (3)), but its derivation is deferred to the paper's own supplementary materials (ref. 50), which are absent from the submission; this is a missing-support issue rather than a demonstrated circularity. The mild circularity is in the absolute-field calibration: k is calculated from the same fitted slope that is used to state the sensitivity and detection limit in V/m, so those absolute numbers are not independently calibrated. The quoted 403.8 µV/(m·Hz^(1/2)) and 61.5 µV/m therefore inherit any error in Eq. (2) or in the assumption E_t = k V_t. Because the beat signals themselves are directly observed and the relative mV-scale sensor response is honestly fitted, the derivation does not reduce to its inputs by construction; hence the score is low.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim is an experimental demonstration, so the main cost is not a new physical entity but a set of calibrated operating parameters and a response model. The absolute E-field numbers are self-calibrated via k, which is back-computed from the same fitted line that defines the sensitivity; no independent electrode-geometry calibration is shown.

free parameters (6)
  • Electrode response parameter k = 1.3 m^-1
    Back-calculated from the measured calibration slope ∂E_fit/∂V_t = 136.8 mrad/mV using Eq. (2); converts applied voltage to absolute E-field for sensitivity and detection limit.
  • Injection-locking amplitude V_i = 7.5 mV
    Chosen operating point that determines the locked phonon-laser amplitude and response; not independently optimized.
  • Saturation ratio r = s_b/s_r = 0.58
    Hand-picked laser power ratio that sets A0 and the phonon-laser gain; affects the response factors R_p and R_A.
  • Average phonon-laser amplitude A0 = 25.5 µm
    Measured; enters R_p = e/(2mω_iΔA0) and R_A, so the voltage-to-radian conversion depends on it.
  • Calibration slope ∂E_fit/∂V_t = 136.8 mrad/mV
    Linear fit over V_t from 0.42 to 2.92 mV; used to define amplitude sensitivity and converted detection strength.
  • Zero-signal voltage intercept = 46.2 µV
    Extrapolated x-intercept of the calibration line; quoted as 61.5 µV/m minimum detectable field without a statistical noise-floor threshold.
assumptions (4)
  • domain assumption The ion motion is governed by Eq. (1), mZ¨ = -mω_z²Z + F_c + F_g + F(t), with external force F(t) = ke(S_i + S_t).
    This forced-oscillator model underlies all response formulas; scattering forces are modeled as in prior phonon-laser work but not rederived.
  • ad hoc to paper For V_t ≪ V_i and |Δ| ≪ ω_i, the phase and amplitude responses reduce to Eqs. (2)-(3) with R_p = e/(2mω_iΔA0) and R_A = e/(2mω_iΔ).
    The paper's measurement interpretation rests entirely on this ansatz; the derivation is delegated to ref. 50 (supplementary), which is not included.
  • domain assumption The applied electric field at the ion is E_t = k V_t with a single scalar response parameter k determined by electrode materials and geometry.
    The absolute sensitivity and detection limit depend on k, which is not independently measured; k is recovered from the same data used for calibration.
  • domain assumption Injection locking pins the phonon-laser frequency and phase so that the beat-induced phase modulation is the dominant readout and remains stable under added noise.
    This is taken from ref. 49 and is central to the noise-robustness claim.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Single-atom sensor for low-frequency electric field." pith.science (2026). https://pith.science/paper/OP2EOHEE

@misc{pith2026260717583,
  author       = {Pith},
  title        = {Pith review of: Single-atom sensor for low-frequency electric field},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OP2EOHEE}},
  note         = {Machine review of arXiv:2607.17583}
}
read the original abstract

Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 kHz to 300 kHz is crucial for advancing both fundamental science and practical applications, owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint that efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor acted by an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with the sensitivity of 404 uV/(m * Hz1/2) and the detection limit of 61.5 uV/m. Besides, this approach also shows remarkable robustness against noise. Our study helps realizing practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.

Figures

Figures reproduced from arXiv: 2607.17583 by the authors.

Figure 1
Figure 1. FIG. 1. Principle of the beat frequency measurement by [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Beat frequency measurement of sinusoidal input [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Evaluation of the accuracy of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The influence of different noise amplitudes on [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

118 extracted references · 33 canonical work pages

  1. [50]

    de Leon and Kohei M

    Nathalie P. de Leon and Kohei M. Itoh and Dohun Kim and Karan K. Mehta and Tracy E. Northup and Hanhee Paik and B. S. Palmer and N. Samarth and Sorawis Sangtawesin and D. W. Steuerman , title =. Science , volume =. 2021 , doi =

    2021

  2. [1]

    Compact quantum VLF/ELF sources for submarine to air communication , year=

    Latypov, Damir , booktitle=. Compact quantum VLF/ELF sources for submarine to air communication , year=

  3. [2]

    Physical review letters , volume=

    Improved bounds on ultralight scalar dark matter in the radio-frequency range , author=. Physical review letters , volume=. 2022 , publisher=

    2022

  4. [3]

    Science , volume=

    Optical frequency combs: Coherently uniting the electromagnetic spectrum , author=. Science , volume=. 2020 , publisher=

    2020

  5. [4]

    2013 , publisher=

    An introduction to signal detection and estimation , author=. 2013 , publisher=

    2013

  6. [5]

    2023 IEEE 16th International Conference on Electronic Measurement & Instruments (ICEMI) , pages=

    Review of weak signals detection methods , author=. 2023 IEEE 16th International Conference on Electronic Measurement & Instruments (ICEMI) , pages=. 2023 , organization=

    2023

  7. [6]

    , publisher =

    Paschotta, R. , publisher =. Optical Heterodyne Detection , abstract =. 2009 , month =. doi:10.61835/79k" title="This link will reload the current page. , urldate =

    work page doi:10.61835/79k 2009

  8. [7]

    Nature Photonics , volume=

    Digitally synthesized beat frequency multiplexing for sub-millisecond fluorescence microscopy , author=. Nature Photonics , volume=. 2013 , publisher=

    2013

Show all 118 references
  1. [8]

    Natural Hazards and Earth System Sciences , volume=

    Review of unprecedented ULF electromagnetic anomalous emissions possibly related to the Wenchuan M S= 8.0 earthquake, on 12 May 2008 , author=. Natural Hazards and Earth System Sciences , volume=. 2013 , publisher=

    2008

  2. [9]

    science , volume=

    Neuronal oscillations in cortical networks , author=. science , volume=. 2004 , publisher=

    2004

  3. [10]

    , booktitle=

    Yoon, Suk-Un and Cheng, Liang and Ghazanfari, Ehsan and Wang, Zi and Zhang, Xiaotong and Pamukcu, Sibel and Suleiman, Muhannad T. , booktitle=. Subsurface monitoring using low frequency wireless signal networks , year=

  4. [11]

    Chu, L. J. , title =. Journal of Applied Physics , volume =. 1948 , month =

    1948

  5. [12]

    French and John C

    Michael J. French and John C. Angus and Alan G. Walton , title =. Science , volume =. 1969 , doi =

    1969

  6. [13]

    Laser frequency stabilization by means of optical self-heterodyne beat-frequency control , author =. Opt. Lett. , keywords =. 1998 , doi =

    1998

  7. [14]

    P. Zem\'. Use of the beat frequency between two modes for frequency stabilization of internal-mirror lasers , volume =. Appl. Opt. , keywords =. 1994 , doi =

    1994

  8. [15]

    2013 , issn =

    Study on fiber ring laser in sensing application with beat frequency demodulation , journal =. 2013 , issn =. doi:https://doi.org/10.1016/j.optlastec.2012.07.014 , author =

    2013 doi

  9. [16]

    2014 , title =

    Burghoff, David and Kao, Tsung-Yu and Han, Ningren and Chan, Chun Wang Ivan and Cai, Xiaowei and Yang, Yang and Hayton, Darren J and Gao, Jian-Rong and Reno, John L and Hu, Qing , journal =. 2014 , title =. doi:10.1038/nphoton.2014.85 , abstract =

    2014 doi

  10. [17]

    2023 , issn =

    Simultaneous measurement of vibration and temperature based on FBG and DBR fiber laser beat frequency digital sensing system , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.yofte.2022.103155 , author =

    2023

  11. [18]

    1972 , issn =

    Application of laser beat frequency spectroscopy to the detection and characterization of an oncogenic RNA virus , journal =. 1972 , issn =. doi:https://doi.org/10.1016/0006-291X(72)90958-8 , author =

    1972 doi

  12. [19]

    Highly sensitive liquid-level sensor based on dual-wavelength double-ring fiber laser assisted by beat frequency interrogation , volume =

    Yi Dai and Qizhen Sun and Sisi Tan and Jianghai Wo and Jiejun Zhang and Deming Liu , journal =. Highly sensitive liquid-level sensor based on dual-wavelength double-ring fiber laser assisted by beat frequency interrogation , volume =. 2012 , doi =

    2012

  13. [20]

    Beat frequency trimming of dual-polarization fiber grating lasers for multiplexed sensor applications , volume =

    Yang Zhang and Yan-Nan Tan and Tuan Guo and Bai-Ou Guan , journal =. Beat frequency trimming of dual-polarization fiber grating lasers for multiplexed sensor applications , volume =. 2011 , doi =

    2011

  14. [21]

    Wearable Optical Fiber Beat Frequency Digital Sensing System for Real-Time Non-Invasive Multiple Human Physiological Parameters Monitoring , year=

    Guo, Yu and Tong, Xingxing and Shen, Yanxia and Wu, Haodong , journal=. Wearable Optical Fiber Beat Frequency Digital Sensing System for Real-Time Non-Invasive Multiple Human Physiological Parameters Monitoring , year=

  15. [22]

    Applied Physics B , volume=

    Laser phase and frequency stabilization using an optical resonator , author=. Applied Physics B , volume=. 1983 , publisher=

    1983

  16. [23]

    Optical atomic clocks , author =. Rev. Mod. Phys. , volume =. 2015 , month =

    2015

  17. [24]

    , journal=

    Allan, D.W. , journal=. Statistics of atomic frequency standards , year=

  18. [25]

    Nature Physics , volume=

    Atomic superheterodyne receiver based on microwave-dressed Rydberg spectroscopy , author=. Nature Physics , volume=. 2020 , publisher=

    2020

  19. [26]

    Photonics , VOLUME =

    Cai, Minghao and Xu, Zishan and You, Shuhang and Liu, Hongping , TITLE =. Photonics , VOLUME =. 2022 , NUMBER =

    2022

  20. [27]

    2020 , title =

    Jing, Mingyong and Hu, Ying and Ma, Jie and Zhang, Hao and Zhang, Linjie and Xiao, Liantuan and Jia, Suotang , journal =. 2020 , title =. doi:10.1038/s41567-020-0918-5 , abstract =

    2020 doi

  21. [28]

    Rydberg-Atom-Based Electrometry Using a Self-Heterodyne Frequency-Comb Readout and Preparation Scheme , author =. Phys. Rev. Appl. , volume =. 2023 , month =

    2023

  22. [29]

    R. F. Lucy and K. Lang and C. J. Peters and K. Duval , journal =. Optical Superheterodyne Receiver , volume =. 1967 , doi =

    1967

  23. [30]

    2013 , title =

    Diebold, Eric D and Buckley, Brandon W and Gossett, Daniel R and Jalali, Bahram , journal =. 2013 , title =. doi:10.1038/nphoton.2013.245 , abstract =

    2013 doi

  24. [31]

    A Low-Power Process-Scalable Super-Heterodyne Receiver With Integrated High- Q Filters , year=

    Mirzaei, Ahmad and Darabi, Hooman and Murphy, David , journal=. A Low-Power Process-Scalable Super-Heterodyne Receiver With Integrated High- Q Filters , year=

  25. [32]

    An Interference Mitigation Technique for FMCW Radar Using Beat-Frequencies Interpolation in the STFT Domain , year=

    Neemat, Sharef and Krasnov, Oleg and Yarovoy, Alexander , journal=. An Interference Mitigation Technique for FMCW Radar Using Beat-Frequencies Interpolation in the STFT Domain , year=

  26. [33]

    An Efficient Frequency and Phase Estimation Algorithm With CRB Performance for FMCW Radar Applications , year=

    Scherr, Steffen and Ayhan, Serdal and Fischbach, Benjamin and Bhutani, Akanksha and Pauli, Mario and Zwick, Thomas , journal=. An Efficient Frequency and Phase Estimation Algorithm With CRB Performance for FMCW Radar Applications , year=

  27. [34]

    Scientific reports , volume=

    Micro-Doppler measurement of insect wing-beat frequencies with W-band coherent radar , author=. Scientific reports , volume=. 2017 , publisher=

    2017

  28. [35]

    Cohen , journal =

    Steven C. Cohen , journal =. Heterodyne detection: phase front alignment, beam spot size, and detector uniformity , volume =. 1975 , doi =

    1975

  29. [36]

    2009 , publisher=

    Laser heterodyning , author=. 2009 , publisher=

    2009

  30. [37]

    Kompfner , title =

    R. Kompfner , title =. Science , volume =. 1965 , doi =

    1965

  31. [38]

    Dual-comb spectroscopy , volume =

    Ian Coddington and Nathan Newbury and William Swann , journal =. Dual-comb spectroscopy , volume =. 2016 , doi =

    2016

  32. [39]

    2016 , title =

    Millot, Guy and Pitois, Stéphane and Yan, Ming and Hovhannisyan, Tatevik and Bendahmane, Abdelkrim and Hänsch, Theodor W and Picqué, Nathalie , journal =. 2016 , title =. doi:10.1038/nphoton.2015.250 , abstract =

    2016 doi

  33. [40]

    2010 , title =

    Bernhardt, Birgitta and Ozawa, Akira and Jacquet, Patrick and Jacquey, Marion and Kobayashi, Yohei and Udem, Thomas and Holzwarth, Ronald and Guelachvili, Guy and Hänsch, Theodor W and Picqué, Nathalie , journal =. 2010 , title =. doi:10.1038/nphoton.2009.217 , abstract =

    2010 doi

  34. [41]

    and Reddy, Karthik and Zhong, Zhaohui and Fan, Xudong , title=

    Kulkarni, Girish S. and Reddy, Karthik and Zhong, Zhaohui and Fan, Xudong , title=. Nature Communications , year=

  35. [42]

    Science Advances , volume =

    Agata Cygan and Szymon Wójtewicz and Hubert Jóźwiak and Grzegorz Kowzan and Nikodem Stolarczyk and Katarzyna Bielska and Piotr Wcisło and Roman Ciuryło and Daniel Lisak , title =. Science Advances , volume =. 2025 , doi =

    2025

  36. [43]

    Nature Communications , year=

    Liang, Yizhi and Fu, Wubing and Li, Qiang and Chen, Xiaolong and Sun, Huojiao and Wang, Lidai and Jin, Long and Huang, Wei and Guan, Bai-Ou , title=. Nature Communications , year=

  37. [44]

    Herman and Mathieu Walsh and Molly Kate Kreider and Noah Lordi and Eugene J

    Daniel I. Herman and Mathieu Walsh and Molly Kate Kreider and Noah Lordi and Eugene J. Tsao and Alexander J. Lind and Matthew Heyrich and Joshua Combes and Jérôme Genest and Scott A. Diddams , title =. Science , volume =. 2025 , doi =

    2025

  38. [45]

    Fiber Bragg Gratings for Medical Applications and Future Challenges: A Review , year=

    Lo Presti, Daniela and Massaroni, Carlo and Jorge Leitão, Cátia Sofia and De Fátima Domingues, Maria and Sypabekova, Marzhan and Barrera, David and Floris, Ignazio and Massari, Luca and Oddo, Calogero Maria and Sales, Salvador and Iordachita, Iulian Ioan and Tosi, Daniele and ...

  39. [46]

    and Meltz, G

    Hill, K.O. and Meltz, G. , journal=. Fiber Bragg grating technology fundamentals and overview , year=

  40. [47]

    Review of Scientific Instruments , volume =

    Othonos, Andreas , title =. Review of Scientific Instruments , volume =. 1997 , month =

    1997

  41. [48]

    Ion-trap measurements of electric-field noise near surfaces , author =. Rev. Mod. Phys. , volume =. 2015 , month =

    2015

  42. [49]

    Quantum sensing , author =. Rev. Mod. Phys. , volume =. 2017 , month =

    2017

  43. [51]

    Time and Frequency Resolution of Alternating Electric Signals via Single-Atom Sensor , author =. Phys. Rev. Appl. , volume =. 2023 , month =

    2023

  44. [52]

    2017 , month = jul, journal =

    Quantum Sensing , author =. 2017 , month = jul, journal =. doi:10.1103/RevModPhys.89.035002 , copyright =

    2017 doi

  45. [53]

    Anderson, David Alexander and Sapiro, Rachel Elizabeth and Raithel, Georg , year =. An. IEEE Transactions on Antennas and Propagation , volume =. doi:10.1109/TAP.2020.2987112 , abstract =

    2020

  46. [54]

    and Gong, Qihuang and Wang, Xingjun and Xiao, Yun-Feng , title=

    Jin, Ming and Tang, Shui-Jing and Chen, Jin-Hui and Yu, Xiao-Chong and Shu, Haowen and Tao, Yuansheng and Chen, Antony K. and Gong, Qihuang and Wang, Xingjun and Xiao, Yun-Feng , title=. Nature Communications , year=

  47. [55]

    Berkeland, D. J. and Miller, J. D. and Bergquist, J. C. and Itano, W. M. and Wineland, D. J. , year =. Minimization of Ion Micromotion in a. Journal of Applied Physics , volume =. doi:10.1063/1.367318 , abstract =

    doi

  48. [56]

    2018 , month = may, journal =

    High-Fidelity Entanglement between a Trapped Ion and a Telecom Photon via Quantum Frequency Conversion , author =. 2018 , month = may, journal =. doi:10.1038/s41467-018-04341-2 , abstract =

    2018 doi

  49. [57]

    and Linde, Bogumi

    Borkowski, Maciej and Skrodzka, Ewa B. and Linde, Bogumi. 2014 , month = jul, journal =

    2014

  50. [58]

    2017 , month = may, journal =

    Quantum Sensing with Arbitrary Frequency Resolution , author =. 2017 , month = may, journal =. doi:10.1126/science.aam7009 , abstract =

    2017 doi

  51. [59]

    2013 , month = mar, journal =

    Arbitrary Waveform Generator for Quantum Information Processing with Trapped Ions , author =. 2013 , month = mar, journal =. doi:10.1063/1.4795552 , abstract =

    2013 doi

  52. [60]

    Braakman, F. R. and Cadeddu, D. and T. Nonlinear Motion and Mechanical Mixing in As-Grown. 2014 , month = oct, journal =. doi:10.1063/1.4900928 , abstract =

    2014 doi

  53. [61]

    1972 , month = aug, journal =

    A Simple Reference Generator for Lock-in Amplifiers , author =. 1972 , month = aug, journal =. doi:10.1088/0022-3735/5/8/006 , abstract =

    1972 doi

  54. [62]

    Bushev, P. and H. Shot-. 2013 , month = mar, journal =. doi:10.1103/PhysRevLett.110.133602 , copyright =

    2013 doi

  55. [63]

    2024 , month = jun, journal =

    Quantum Double Lock-in Amplifier , author =. 2024 , month = jun, journal =

    2024

  56. [64]

    2011 , month = dec, journal =

    Audio Mixing in a Tri-Port Nano-Electro-Mechanical Device , author =. 2011 , month = dec, journal =. doi:10.1063/1.3665958 , abstract =

    2011 doi

  57. [65]

    and Wolffenbuttel, R.F

    De Graaf, G. and Wolffenbuttel, R.F. , year =. Lock-in Amplifier Techniques for Low-Frequency Modulated Sensor Applications , booktitle =. doi:10.1109/I2MTC.2012.6229510 , abstract =

    2012

  58. [66]

    and Rist

    De Lange, G. and Rist. Single-. 2011 , month = feb, journal =. doi:10.1103/PhysRevLett.106.080802 , copyright =

    2011 doi

  59. [67]

    1977 , month = mar, journal =

    Inexpensive Linear Displacement Transducer Using a Low Power Lock-in Amplifier , author =. 1977 , month = mar, journal =. doi:10.1063/1.1135018 , abstract =

    1977 doi

  60. [68]

    2000 , month = nov, journal =

    Mechanical Mixing in Nonlinear Nanomechanical Resonators , author =. 2000 , month = nov, journal =. doi:10.1063/1.1324721 , abstract =

    2000 doi

  61. [69]

    2002 , month = aug, journal =

    Silicon-on-Insulator Based Nanoresonators for Mechanical Mixing at Radio Frequencies , author =. 2002 , month = aug, journal =. doi:10.1109/TUFFC.2002.1026023 , abstract =

    2002 arXiv

  62. [70]

    and Scherer, David R

    Fancher, Charles T. and Scherer, David R. and John, Marc C. St. and Marlow, Bonnie L. Schmittberger , year =. Rydberg. IEEE Transactions on Quantum Engineering , volume =. doi:10.1109/TQE.2021.3065227 , abstract =

    2021

  63. [71]

    Phononic

    Ganesan, Adarsh and Do, Cuong and Seshia, Ashwin , year =. Phononic. Physical Review Letters , volume =. doi:10.1103/PhysRevLett.118.033903 , copyright =

    doi

  64. [72]

    2019 , month = jul, journal =

    Mixed Dynamical Decoupling , author =. 2019 , month = jul, journal =. doi:10.1088/2058-9565/ab2afd , abstract =

    2019 doi

  65. [73]

    and Simons, Matthew T

    Gordon, Joshua A. and Simons, Matthew T. and Haddab, Abdulaziz H. and Holloway, Christopher L. , year =. Weak Electric-Field Detection with Sub-1. AIP Advances , volume =. doi:10.1063/1.5095633 , abstract =

    doi

  66. [74]

    and Gordon, Joshua A and Anderson, David A and Raithel, Georg and Voran, Steven , year =

    Holloway, Christopher and Simons, Mathew and Haddab, Abdulaziz H. and Gordon, Joshua A and Anderson, David A and Raithel, Georg and Voran, Steven , year =. A. IEEE Antennas and Propagation Magazine , volume =. doi:10.1109/MAP.2020.2976914 , copyright =

    2020

  67. [75]

    Injection

    Kn. Injection. 2010 , month = jul, journal =. doi:10.1103/PhysRevLett.105.013004 , copyright =

    2010 doi

  68. [76]

    2007 , month = oct, journal =

    Direct Mechanical Mixing in a Nanoelectromechanical Diode , author =. 2007 , month = oct, journal =. doi:10.1063/1.2789812 , abstract =

    2007 doi

  69. [77]

    Kishore, Kaushal and Akbar, S. A. , year =. Evolution of. IEEE Sensors Journal , volume =. doi:10.1109/JSEN.2020.2993309 , abstract =

    2020

  70. [78]

    2011 , month = may, journal =

    Single-Ion Quantum Lock-in Amplifier , author =. 2011 , month = may, journal =. doi:10.1038/nature10010 , copyright =

    2011 doi

  71. [79]

    Atomic Mixer Based on Phase Control without Ac

    Liang, Zhi and Geng, Xu-xing and Yang, Guo-qing and Jin, Kai and Liang, Shang-qing and Wu, Shao-ping and Huang, Guang-ming and Li, Gao-xiang , year =. Atomic Mixer Based on Phase Control without Ac. Physical Review A , volume =

  72. [80]

    Liu, Zhichao and Wei, Yaqi and Chen, Liang and Li, Ji and Dai, Shuangqing and Zhou, Fei and Feng, Mang , year =. Phonon-. Physical Review Applied , volume =

  73. [81]

    Lyu, Hongming and Wu, Huaqiang and Liu, Jinbiao and Lu, Qi and Zhang, Jinyu and Wu, Xiaoming and Li, Junfeng and Ma, Teng and Niu, Jiebin and Ren, Wencai and Cheng, Huiming and Yu, Zhiping and Qian, He , year =. Double-. Nano Letters , volume =. doi:10.1021/acs.nanolett.5b0250...

    doi

  74. [82]

    1982 , month = apr, journal =

    Advances in Lock-in Amplifiers , author =. 1982 , month = apr, journal =. doi:10.1088/0022-3735/15/4/001 , abstract =

    1982 doi

  75. [83]

    2021 , month = may, journal =

    Heterodyne Sensing of Microwaves with a Quantum Sensor , author =. 2021 , month = may, journal =. doi:10.1038/s41467-021-22714-y , abstract =

    2021 doi

  76. [84]

    and Kunz, Paul D

    Meyer, David H. and Kunz, Paul D. and Cox, Kevin C. , year =. Waveguide-. Physical Review Applied , volume =

  77. [85]

    2009 , month = sep, journal =

    A Phonon Laser , author =. 2009 , month = sep, journal =. doi:10.1038/nphys1367 , copyright =

    2009 doi

  78. [86]

    1985 , month = mar, journal =

    Low-Frequency Digital Lock-in Amplifier , author =. 1985 , month = mar, journal =. doi:10.1063/1.1138324 , abstract =

    1985 doi

  79. [87]

    and Prajapati, Nikunjkumar and Senic, Damir and Simons, Matthew T

    Robinson, Amy K. and Prajapati, Nikunjkumar and Senic, Damir and Simons, Matthew T. and Holloway, Christopher L. , year =. Determining the Angle-of-Arrival of a Radio-Frequency Source with a. Applied Physics Letters , volume =. doi:10.1063/5.0045601 , abstract =

    doi

  80. [88]

    2017 , month = may, journal =

    Submillihertz Magnetic Spectroscopy Performed with a Nanoscale Quantum Sensor , author =. 2017 , month = may, journal =. doi:10.1126/science.aam5532 , abstract =

    2017 doi

  81. [89]

    1994 , month = feb, journal =

    Frequency-Domain Description of a Lock-in Amplifier , author =. 1994 , month = feb, journal =. doi:10.1119/1.17629 , abstract =

    1994 doi

  82. [90]

    Quantum Lock-in Force Sensing Using Optical Clock

    Shaniv, Ravid and Ozeri, Roee , year =. Quantum Lock-in Force Sensing Using Optical Clock. Nature Communications , volume =. doi:10.1038/ncomms14157 , abstract =

    doi

  83. [91]

    2021 , month = apr, journal =

    Quantum Lock-in Detection of a Vector Light Shift , author =. 2021 , month = apr, journal =

    2021

  84. [92]

    and Haddab, Abdulaziz H

    Simons, Matthew T. and Haddab, Abdulaziz H. and Gordon, Joshua A. and Novotny, David and Holloway, Christopher L. , year =. Embedding a. IEEE Access , volume =. doi:10.1109/ACCESS.2019.2949017 , abstract =

    2019

  85. [93]

    and Haddab, Abdulaziz H

    Simons, Matthew T. and Haddab, Abdulaziz H. and Gordon, Joshua A. and Holloway, Christopher L. , year =. A. Applied Physics Letters , volume =. doi:10.1063/1.5088821 , abstract =

    doi

  86. [94]

    and Alsid, Scott T

    Wang, Guoqing and Liu, Yi-Xiang and Schloss, Jennifer M. and Alsid, Scott T. and Braje, Danielle A. and Cappellaro, Paola , year =. Sensing of. Physical Review X , volume =

  87. [95]

    Detection of

    Wei, Ya-Qi and Wang, Ying-Zheng and Liu, Zhi-Chao and Cui, Tai-Hao and Chen, Liang and Li, Ji and Dai, Shuang-Qin and Zhou, Fei and Feng, Mang , year =. Detection of. Science China Physics, Mechanics & Astronomy , volume =

  88. [96]

    Coherent

    Weinzetl, Christian and G. Coherent. 2019 , month = feb, journal =

    2019

  89. [97]

    2023 , month = nov, number =

    Quantum Vector Signal Analyzer , author =. 2023 , month = nov, number =. arXiv , keywords =:2311.12263 , primaryclass =

    2023 arXiv

  90. [98]

    IEEE Access , volume =

    Zhang, Cheng and Liu, Huan and Ge, Jian and Dong, Haobin , year =. IEEE Access , volume =. doi:10.1109/ACCESS.2020.3006070 , abstract =

    2020

  91. [99]

    and Isoya, Junichi and Jelezko, Fedor and Onoda, Shinobu and Sumiya, Hitoshi and Cappellaro, Paola and Knowles, Helena S

    Zhou, Hengyun and Choi, Joonhee and Choi, Soonwon and Landig, Renate and Douglas, Alexander M. and Isoya, Junichi and Jelezko, Fedor and Onoda, Shinobu and Sumiya, Hitoshi and Cappellaro, Paola and Knowles, Helena S. and Park, Hongkun and Lukin, Mikhail D. , year =. Quantum. P...

  92. [100]

    Multi-Round

    Zhu, Yingyue and Zhang, Zewen and Sundar, Bhuvanesh and Green, Alaina M and Huerta Alderete, C and Nguyen, Nhung H and Hazzard, Kaden R A and Linke, Norbert M , year =. Multi-Round. Quantum Science and Technology , volume =. doi:10.1088/2058-9565/ac91ef , abstract =

    doi

  93. [101]

    Zhuang, Min and Huang, Jiahao and Lee, Chaohong , year =. Many-. PRX Quantum , volume =

  94. [102]

    2024 , month = feb, journal =

    Quantum Lock-in Measurement of Weak Alternating Signals , author =. 2024 , month = feb, journal =. doi:10.1007/s44214-024-00051-7 , abstract =

    2024 doi

  95. [103]

    Allcock, D. T. C. and Guidoni, L. and Harty, T. P. and Ballance, C. J. and Blain, M. G. and Steane, A. M. and Lucas, D. M. , year =. Reduction of Heating Rate in a Microfabricated Ion Trap by Pulsed-Laser Cleaning , shorttitle =. New Journal of Physics , volume =. doi:10.1088/...

    doi

  96. [104]

    2016 , journal =

    Active Stabilization of Ion Trap Radiofrequency Potentials , author =. 2016 , journal =

    2016

  97. [105]

    2023 , month = mar, journal =

    Nonlinear Multi-Frequency Phonon Lasers with Active Levitated Optomechanics , author =. 2023 , month = mar, journal =. doi:10.1038/s41567-022-01857-9 , abstract =

    2023 doi

  98. [106]

    2019 , month = jun, journal =

    An Optical Tweezer Phonon Laser , author =. 2019 , month = jun, journal =

    2019

  99. [107]

    2020 , month = jan, journal =

    A Coherent Nanomechanical Oscillator Driven by Single-Electron Tunnelling , author =. 2020 , month = jan, journal =

    2020

  100. [108]

    2022 , month = dec, journal =

    Dissipative Coupling-Induced Phonon Lasing , author =. 2022 , month = dec, journal =. doi:10.1073/pnas.2207543119 , abstract =

    2022 doi

  101. [109]

    2012 , month = apr, journal =

    Bio-Effects and Safety of Low-Intensity, Low-Frequency Ultrasonic Exposure , author =. 2012 , month = apr, journal =. doi:10.1016/j.pbiomolbio.2012.01.004 , abstract =

    2012 doi

  102. [110]

    Chen, Fang-Hsu and Cheng, Chun-Yen and Chou, Szu-Wei and Yang, Cheng-Han and Lu, I-Chung and Yeh, Ming-Long , year =. High-. Analytical Chemistry , volume =. doi:10.1021/acs.analchem.4c02775 , abstract =

    doi

  103. [111]

    2018 , month = apr, journal =

    Design Principles for Enhancing Phase Sensitivity and Suppressing Phase Fluctuations Simultaneously in Biochemical Oscillatory Systems , author =. 2018 , month = apr, journal =. doi:10.1038/s41467-018-03826-4 , abstract =

    2018 doi

  104. [112]

    Review of

    Gaj. Review of. 2016 , month = sep, journal =. doi:10.3390/ijerph13090875 , abstract =

    2016 doi

  105. [113]

    and Schwettmann, Arne and K

    Sedlacek, Jonathon A. and Schwettmann, Arne and K. Microwave Electrometry with. 2012 , month = nov, journal =. doi:10.1038/nphys2423 , copyright =

    2012 doi

  106. [114]

    2024 , month = sep, journal =

    Stochastic Resonance via Single-Ion Phonon Laser , author =. 2024 , month = sep, journal =. doi:10.1063/5.0222517 , abstract =

    2024 doi

  107. [115]

    Qu, Zihan and Lai, Mengqin , year =. A. IEEE Access , volume =. doi:10.1109/ACCESS.2024.3353623 , abstract =

    2024

  108. [116]

    Ultralong Transients Enhance Sensitivity and Resolution in

    Desligni. Ultralong Transients Enhance Sensitivity and Resolution in. 2024 , month = apr, journal =

    2024

  109. [117]

    Engineering of microfabricated ion traps and integration of advanced on-chip features , journal=

    Romaszko, Zak David and Hong, Seokjun and Siegele, Martin and Puddy, Reuben Kahan and Lebrun-Gallagher, Foni Rapha. Engineering of microfabricated ion traps and integration of advanced on-chip features , journal=. 2020 , month=

    2020

  110. [118]

    3D-printed micro ion trap technology for quantum information applications , journal=

    Xu, Shuqi and Xia, Xiaoxing and Yu, Qian and Parakh, Abhinav and Khan, Sumanta and Megidish, Eli and You, Bingran and Hemmerling, Boerge and Jayich, Andrew and Beck, Kristin and Biener, Juergen and H. 3D-printed micro ion trap technology for quantum information applications , ...

    2025

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.