Pith. sign in

REVIEW 2 major objections 6 minor 35 references

A resonant laser pulse sequence prepares metrologically useful motional Fock mixtures in a trapped ion without ground-state cooling, and two routine calibrations keep errors low up to strong coupling.

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 · grok-4.5

2026-07-31 18:16 UTC pith:MC7R7J2A

load-bearing objection Clean strong-drive extension of their own SPT protocol; headline η≈0.5 numbers need a truncation check before you trust the last few percent. the 2 major comments →

arxiv 2607.24318 v1 pith:MC7R7J2A submitted 2026-07-27 quant-ph

Fast Generation of Metrologically Relevant Fock State Mixtures

Gonzalo Reina Rivero , Marcel Morillas-Rozas , Alberto L\'opez-Garc\'ia , Javier Cerrillo This is my paper
classification quant-ph
keywords trapped ionsquantum sensingFock state mixturesselective population trappingdisplacement metrologyLamb-Dicke parameterBloch-Siegert shiftatomic physics
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 aims to show that non-thermal mixtures of a trapped ion’s motional Fock states—states that beat the standard quantum limit in displacement sensing—can be prepared far faster than earlier weak-drive methods, straight from a thermal distribution and without ground-state cooling. The authors work in a polaron frame that is exact in the Lamb–Dicke parameter and find a resonant operating point (zero detuning, Rabi frequency equal to the trap frequency) where selective population trapping still works under strong driving. They identify the residual error at large coupling as one coherent process, the counter-rotating blue-sideband term dropped by the rotating-wave approximation, and suppress it with a percent-level pulse-duration refocus and a small Bloch–Siegert detuning. Full-sequence simulations keep preparation error at or below about 10% up to η≈0.5 and recover up to 9 dB of displacement Fisher information lost by the uncorrected protocol. A sympathetic reader cares because this would be a practical, cooling-free route to faster motional resources for force and displacement metrology.

Core claim

At zero detuning and Rabi frequency matching the trap frequency, selective population trapping of motional Fock states survives strong driving. Residual infidelity at large Lamb–Dicke parameter η traces to the counter-rotating blue-sideband term neglected in the rotating-wave approximation; percent-level refocusing of the pulse duration plus a small compensating Bloch–Siegert detuning keep preparation error at or below the 10% level up to η≈0.5 and restore displacement-sensing Fisher information, recovering up to 9 dB relative to the nominal sequence.

What carries the argument

The polaron-frame description of the ion–laser interaction, exact in η, which at the resonant point Ω=ν yields an effective Jaynes–Cummings generator for the trapping dynamics; the leading coherent error is the counter-rotating blue-sideband term, suppressed by a global pulse-length factor f and a static Bloch–Siegert detuning δ.

Load-bearing premise

That one counter-rotating blue-sideband process is the only coherent leakage channel at large coupling, so a single global pulse-length tweak and a small static detuning restore trapping for the full multi-cycle sequence with realistic reset and recoil.

What would settle it

Implement the full multi-cycle sequence on a trapped ion at η around 0.4–0.5 with the calibrated pulse-length factor and detuning; if the measured motional populations stay far from the ideal trapped mixture (trace distance well above ~0.1) or the displacement Fisher information fails to recover relative to the uncorrected protocol, the central claim is false.

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

If this is right

  • Motional Fock mixtures for displacement metrology can be prepared orders of magnitude faster by driving at Ω=ν instead of in the weak-drive limit.
  • Ground-state cooling is not required before preparing these metrologically useful states from a thermal distribution.
  • Conventional amplitude pulse shaping is counterproductive at resonance; time-dependent detuning is the appropriate shaping degree of freedom.
  • Routine ion-trap calibrations of pulse duration and detuning extend usable Lamb–Dicke parameters up to about η≈0.5 while restoring sensing gain.

Where Pith is reading between the lines

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

  • The speed-up could make Fock-mixture probes competitive with squeezed-state methods in settings where phase control relative to the signal is difficult.
  • If motional heating and laser-amplitude noise do not spoil the refocusing, the protocol may apply directly in surface-electrode traps used for electric-field noise sensing.
  • Optimized multi-Fock or adaptive readout could close more of the remaining gap between refined preparation and the ideal-trap Fisher information at η=0.5.

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

2 major / 6 minor

Summary. The manuscript proposes a resonant implementation of the authors' earlier Selective Population Trapping (SPT) protocol for preparing non-thermal Fock-state mixtures of a trapped ion's motion. Using a polaron-frame transformation that is exact in the Lamb–Dicke parameter η, the authors identify an operating point (∆=0, Ω=ν) at which a resonant Jaynes–Cummings interaction — and hence the trapping mechanism — survives strong driving, giving a preparation speed-up of 10²–10³ over the weak-driving protocol. The residual infidelity at large η is attributed to the counter-rotating blue-sideband term discarded by the single RWA of the derivation; this diagnosis is corroborated by an ablation test in which removing that term by hand restores trapping to machine precision. Two routine calibrations — a percent-level pulse-duration refocusing factor f and a Bloch–Siegert compensating detuning δ — are shown in full Lindblad simulations (with recoil) to keep the trace distance to the ideal trapped distribution at or below ~10% up to η≈0.5 and to restore 4–9 dB of displacement-sensing Fisher information relative to the uncorrected sequence. A useful negative result shows that smooth amplitude shaping is counterproductive at the resonant point, while time-dependent detuning is the compatible shaping degree of freedom.

Significance. If the quantitative claims hold, this is a practical contribution: it removes both the weak-driving and Lamb–Dicke restrictions of the original SPT scheme without requiring ground-state cooling, using only calibrations (pulse length and detuning scans) that are standard in ion-trap laboratories. Particular strengths deserve emphasis: (i) the polaron derivation is non-perturbative in η, with a single, explicitly identified approximation whose leading correction is then diagnosed and suppressed — a clean logical structure; (ii) the "sole leakage channel" claim is supported by a controlled numerical ablation rather than asserted; (iii) the full-sequence simulations use the lab-frame Hamiltonian with a Lindblad reset including photon recoil, not the effective model being validated; (iv) the (f,δ) calibration landscape is experimentally falsifiable via a routine two-parameter scan; and (v) simulation code is publicly available on GitHub. The main vulnerability is that every headline number at strong coupling rests on tight motional truncations with no reported convergence study, at exactly the point where the discarded thermal tail and basis-boundary effects are the same size as the rep

major comments (2)
  1. [§3.1, Figs. 5 and 7; §3, simulation parameters] All quantitative headline results — preparation error ≤10% up to η≈0.5 (Fig. 5A) and the 4–9 dB Fisher-information recovery (Fig. 7) — come from simulations with motional truncations N=14 (default), N=16 (Fig. 5), and N=24 (the n̄=5 metrological benchmark), and no convergence study in N is reported anywhere. Three specific pressures make this load-bearing rather than cosmetic: (a) at the benchmark point n̄=5, N=24, the discarded thermal tail is P(n>24)=(5/6)^25≈1%, directly comparable to the few-percent trace distances reported; (b) the trap-state ladder n=n0m² places n=16 at the very edge of the N=16 space used for Fig. 5, and the n=25 trap state falls entirely outside the N=24 benchmark space, so the ~1% of initial population that the ideal protocol would funnel into the m=5 manifold has no consistent target, and the ideal distribution ptr(m) of Eq. (14) is itself modified by the trunc
  2. [§3.1, paragraph following the identification of the counter-rotating term] The mechanistic justification for the refocusing correction states that Ωg(n)=√((2ν)²+η²ν²(n+1)) 'depends only weakly on n', so that a single global factor f 'collectively refocuses the excursions of all relevant trap states'. Quantitatively this is stretched exactly where the correction is most needed: at η=0.5, Ωg(n)/ν ranges from ≈2.12 (n=1) to ≈2.55 (n=9), a ~20% spread, and with τ=2π/(ην) the refocusing phases Ωg(n)τ differ by O(π) across the populated trap manifold — so no single f can satisfy Ωg(n)fτ ∈ 2πZ simultaneously, and the excursions at large n are also the largest (matrix element ∝√(n+1)). The numerical calibration landscape (Fig. 5B) does show that optima exist and that f stays within ~5% of unity on the nearest branch, so the scheme empirically works; but the analytic narrative as written overstates why. The authors should either quantify the residual defocusing across t
minor comments (6)
  1. [Figs. 3–4] Fig. 4B is labelled 'old protocol (Ω=0.001)' while Fig. 3 compares against Ω=ν/100 and ν/1000; please state the drive strength used for the legacy-protocol curve in Fig. 4B unambiguously, and state the motional truncation used for Figs. 2–4 (the N=16/24 values are only given for Fig. 5 onward).
  2. [§3, below Eq. (14)] The phrase 'trace distance to the ideal trapped distribution' is used throughout, but it is never stated whether this is the trace distance between the full final motional density matrix and a target state built from ptr(m) of Eq. (14), or a classical distance between populations. Please define it operationally in §3.
  3. [§3, pulse sequence steps (ii) and (v)] The choice Γ=1000ν for the reset and ΩY=100ν for the Y pulse should be briefly justified: the Y pulse is simulated with the full Eq. (12) including D(iη), but at ΩY/ν=100 its own strong-driving corrections could inject errors not present in the effective description; a sentence confirming convergence in ΩY (or noting that results are insensitive to it) would help. Similarly, comment on how the results depend on Γ.
  4. [§4 or §1] A brief experimental-context remark would strengthen the paper: η up to 0.5 with Ω≃ν and a fast reset is a demanding combination; indicating which platforms/transitions could reach the strong-η end (e.g. microwave-dressed or Sagiv/deep-Lamb–Dicke-violating regimes) would help readers place the benchmark.
  5. [throughout] Typographical: 'R W A' appears with spurious internal spacing throughout; 'Keywords:trapped ions' is missing a space; the floor brackets in Eq. (14) and the axis label 'detuning [ ]' in Fig. 5B render incorrectly; several figures (e.g. Fig. 2) have small shared axis labels that are hard to read.
  6. [Appendix B, Data Availability] The public GitHub repository is commendable; consider archiving the exact version used (e.g. a Zenodo DOI) so the record is stable, and including the scripts that generate Figs. 5B and 7 specifically, since these carry the headline claims.

Circularity Check

1 steps flagged

Mild calibration circularity only: f and δ are chosen by minimizing the same trace distance later reported as the preparation-error claim; the resonant JC derivation and Fisher-information recovery remain independent.

specific steps
  1. fitted input called prediction [§3.1, Fig. 5A–B and abstract claim on preparation error]
    "a small rescaling of the pulse duration, τ→f τ with f within a few percent of unity, collectively refocuses the excursions of all relevant trap states. The residual effect is a coherent level shift... compensated by adding a small static detuning δ to the X pulse. ... Figure 5A) ... Refocusing the pulse duration alone reduces the trace distance to the ideal trapped distribution by up to an order of magnitude ... keeping the preparation error at the few-percent level up to η=0.45 and reducing it from 0.41 to 0.10 at η=0.5. ... Figure 5B) shows the corresponding two-parameter calibration landsca"

    The reported preparation-error floors (trace distance ≤0.10 at η≈0.5, few-percent up to η≈0.45) are the objective values of the same two-parameter (f,δ) minimization that defines the refined protocol. For the trace-distance metric alone, the improvement is therefore partly by construction of the calibration scan rather than an out-of-sample prediction. (Fisher-information recovery in Fig. 7 is a separate metric and is not circular in the same way.)

full rationale

The load-bearing theoretical step—the resonant effective JC Hamiltonian H_JC at ∆=0, Ω=ν—is obtained from the lab-frame Hamiltonian by an exact polaron transform, a π/2 spin rotation, and a single RWA; it does not presuppose the trapping fidelity or the metrological figures of merit. The ideal trapped distribution ptr(m) and the mean trapping-rate formula are imported from the authors’ prior SPT paper [19], which is ordinary methodological self-citation and is not used as a uniqueness theorem that forces the new resonant operating point. Speed-up versus weak driving and robustness versus η are measured in fresh full-sequence QuTiP simulations. The only mild circularity is that the two refinement parameters (pulse-length factor f and Bloch–Siegert detuning δ) are calibrated by minimizing the trace distance to the ideal trap, after which the paper reports that same minimized trace distance as ‘preparation error ≤10% up to η≈0.5’. That particular number is therefore partly by construction of the scan. The Fisher-information recovery (up to 9 dB) is evaluated on a distinct observable not used in the (f,δ) fit, and the physical diagnosis that the counter-rotating blue sideband is the sole coherent leakage channel is independently checked by hand-removal of that term. Overall circularity is therefore low and non-central.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claims rest on standard trapped-ion quantum optics plus one modeling chain (lab-frame Hamiltonian → exact polaron → RWA at Ω=ν) and on numerical optimization of two pulse knobs. No new physical entities are postulated. Free parameters are the calibration knobs f and δ and ordinary simulation choices (truncation, cycle count, n0).

free parameters (4)
  • pulse-length factor f = within ~5–14% of 1, η-dependent
    Rescales the nominal Rabi-cycle duration τ to refocus blue-sideband excursions; optimized per η against trace distance (e.g. f=0.96 or 1.14 at η=0.4).
  • Bloch–Siegert compensating detuning δ = order 0 to −0.47ν at η=0.4
    Static detuning added to the X pulse to cancel the residual level shift ~η²ν/8; optimized jointly with f.
  • target trap manifold n0 = n0=1 (default)
    Chooses which Fock levels are trapped (τ∝1/√n0); fixed to n0=1 for most runs, n=4 readout for metrology.
  • motional truncation N and cycle count = N=14–24; 30–40 cycles
    Hilbert-space cutoff and number of SPT iterations used in numerics; affect reported residual error at large η.
axioms (5)
  • domain assumption Lab-frame ion–laser Hamiltonian after optical RWA (Eq. 1) is an adequate starting point for the driven two-level ion plus harmonic motion.
    Standard trapped-ion quantum optics; invoked from §2 onward.
  • standard math Polaron unitary UP exactly removes the displacement operators from the coupling, yielding Eq. 3 for arbitrary η.
    Unitary conjugation identity; used to justify non-perturbative treatment beyond Lamb–Dicke.
  • domain assumption A single RWA at Ω=ν retains only the JC term (Eq. 5) as the generator of trapping dynamics; counter-rotating corrections are treatable as a coherent error to be refocused.
    Core approximation of §2–3.1; accuracy controlled by η√(n+1)/4.
  • domain assumption Dissipative spin reset is well modeled by the Lindblad equation with angular-averaged recoil displacement (Eqs. 8–9).
    Used for all full-sequence simulations; idealized recoil-free reset is checked only as a control.
  • ad hoc to paper Ideal trapped distribution ptr(m) defined from the initial thermal state (Eq. 14) is the correct fidelity target for metrology.
    Inherited from prior SPT work [19]; defines the trace-distance benchmark throughout §3.

pith-pipeline@v1.2.0-grok45-kimik3 · 17890 in / 3335 out tokens · 61637 ms · 2026-07-31T18:16:15.261855+00:00 · methodology

0 comments
read the original abstract

We propose a fast laser pulse sequence for the generation of non-thermal Fock state mixtures of the motion of a trapped ion, targeted at displacement metrology beyond the standard quantum limit. Using a polaron-frame description of the ion-laser interaction, we identify a resonant operating point-zero detuning and a Rabi frequency matching the trap frequency-at which selective population trapping survives strong driving, enabling preparation speeds beyond the weak-driving limit of previous protocols without requiring ground-state cooling. We trace the residual infidelity at large Lamb-Dicke parameter $\eta$ to a single coherent process, the counter-rotating blue-sideband term neglected in the rotating-wave approximation, and show that it is suppressed by two routine calibrations: a percent-level refocusing of the pulse duration and a small compensating Bloch-Siegert detuning. Numerical simulations of the full sequence show that this refinement keeps the preparation error at or below the $10\%$ level up to $\eta\approx0.5$ and restores the displacement-sensing Fisher information that the uncorrected protocol loses at strong coupling, recovering up to 9 dB relative to the nominal sequence.

Figures

Figures reproduced from arXiv: 2607.24318 by Alberto L\'opez-Garc\'ia, Gonzalo Reina Rivero, Javier Cerrillo, Marcel Morillas-Rozas.

Figure 1
Figure 1. Figure 1: Pulse sequence diagram To realize the effective dynamics of Eq. (5) we implement, within each cycle, the composite pulse sequence illustrated in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Final trapped-state populations for in￾creasing values of η after 30 cycles of the pulse sequence [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Preparation speed at η = 0.05. Trace distance to the ideal trapped distribution versus elapsed preparation time tν for the resonant se￾quence (Ω = ν) and the weak-driving SPT protocol (Ω = ν/100 and ν/1000); markers denote succes￾sive cycles. The resonant sequence saturates within about 10 cycles (dotted line), whereas reducing Ω shifts the curves rigidly towards longer times, re￾flecting the linear trappi… view at source ↗
Figure 5
Figure 5. Figure 5: Blue-sideband refocusing and Bloch– Siegert detuning on the full pulse sequence. A) Trace distance to the ideal trapped distribution ver￾sus η for the nominal pulse duration τ , the refocused duration fτ , and the refocused duration combined with a compensating detuning δ. B) Calibration landscape at η = 0.4: trace distance as a function of the pulse-length factor f and the detuning δ, with the nominal ope… view at source ↗
Figure 8
Figure 8. Figure 8: Pulse shaping at the resonant operat￾ing point. A) Trace distance to the ideal trapped distribution for area-matched smooth amplitude en￾velopes (Hann, Blackman, cosine-ramped flat-top) compared with the square pulse and with refocusing plus detuning. B) Time-dependent detuning profiles δ(t) (with amplitude optimized at each η and f = 1) compared with the nominal protocol. Finally, we address whether smoot… 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

35 extracted references · 10 canonical work pages

  1. [1]

    Quantum Computations with Cold Trapped Ions

    J. I. Cirac and P. Zoller. “Quantum Computations with Cold Trapped Ions”. In:Physical Review Letters74.20 (May 1995), pp. 4091–4094.doi: 10 . 1103 / PhysRevLett . 74 . 4091. (Visited on 02/11/2026)

    1995

  2. [2]

    Quantum Computation with Ions in Thermal Motion

    Anders Sørensen and Klaus Mølmer. “Quantum Computation with Ions in Thermal Motion”. In: Physical Review Letters82.9 (Mar. 1999), pp. 1971–1974.doi: 10.1103/PhysRevLett.82.1971 . (Visited on 02/11/2026)

    doi:10.1103/physrevlett.82.1971 1999

  3. [3]

    Quantum Information Processing and Metrology with Trapped Ions

    D. J. Wineland and D. Leibfried. “Quantum Information Processing and Metrology with Trapped Ions”. In:Laser Physics Letters8.3 (Jan. 2011), p. 175.issn: 1612-202X.doi: 10.1002/lapl. 201010125. (Visited on 02/11/2026)

    work page doi:10.1002/lapl 2011

  4. [4]

    Optical Atomic Clocks

    Andrew D. Ludlow et al. “Optical Atomic Clocks”. In:Reviews of Modern Physics87.2 (June 2015), pp. 637–701.doi:10.1103/RevModPhys.87.637. (Visited on 02/17/2026)

    doi:10.1103/revmodphys.87.637 2015

  5. [5]

    Motional Fock States for Quantum-Enhanced Amplitude and Phase Measure- ments with Trapped Ions

    Fabian Wolf et al. “Motional Fock States for Quantum-Enhanced Amplitude and Phase Measure- ments with Trapped Ions”. In:Nature Communications10.1 (July 2019), p. 2929.issn: 2041-1723. doi:10.1038/s41467-019-10576-4. (Visited on 11/28/2025)

    doi:10.1038/s41467-019-10576-4 2019

  6. [6]

    Quantum Sensing of the Phase-Space-Displacement Parameters Using a Single Trapped Ion

    Peter A. Ivanov and Nikolay V. Vitanov. “Quantum Sensing of the Phase-Space-Displacement Parameters Using a Single Trapped Ion”. In:Physical Review A97.3 (Mar. 2018), p. 032308.doi: 10.1103/PhysRevA.97.032308. (Visited on 02/17/2026)

    work page doi:10.1103/physreva.97.032308 2018

  7. [7]

    Quantum Lock-in Force Sensing Using Optical Clock Doppler Velocimetry

    Ravid Shaniv and Roee Ozeri. “Quantum Lock-in Force Sensing Using Optical Clock Doppler Velocimetry”. In:Nature Communications8.1 (Feb. 2017), p. 14157.issn: 2041-1723.doi: 10.1038/ ncomms14157. (Visited on 02/21/2026)

    2017

  8. [8]

    https://www.nature.com/articles/nnano.2010.165

    Ultrasensitive Detection of Force and Displacement Using Trapped Ions — Nature Nanotechnology. https://www.nature.com/articles/nnano.2010.165. (Visited on 02/21/2026)

    2010

  9. [9]

    High-Precision Force Sensing Using a Single Trapped Ion

    Peter A. Ivanov, Nikolay V. Vitanov, and Kilian Singer. “High-Precision Force Sensing Using a Single Trapped Ion”. In:Scientific Reports6.1 (June 2016), p. 28078.issn: 2045-2322.doi: 10.1038/srep28078. (Visited on 02/21/2026). 8

    doi:10.1038/srep28078 2016

  10. [10]

    https://www.nature.com/articles/ncomms14157

    Quantum Lock-in Force Sensing Using Optical Clock Doppler Velocimetry — Nature Communications. https://www.nature.com/articles/ncomms14157. (Visited on 02/21/2026)

    2026

  11. [11]

    An Optical Atomic Clock Based on a Highly Charged Ion

    Steven A. King et al. “An Optical Atomic Clock Based on a Highly Charged Ion”. In:Nature 611.7934 (Nov. 2022), pp. 43–47.issn: 0028-0836, 1476-4687.doi: 10.1038/s41586-022-05245-4 . arXiv:2205.13053 [physics]. (Visited on 02/17/2026)

    Pith/arXiv arXiv 2022

  12. [12]

    A Cryogenic Radio-Frequency Ion Trap for Quantum Logic Spectroscopy of Highly Charged Ions

    Tobias Leopold et al. “A Cryogenic Radio-Frequency Ion Trap for Quantum Logic Spectroscopy of Highly Charged Ions”. In:Review of Scientific Instruments90.7 (July 2019), p. 073201.issn: 0034-6748, 1089-7623.doi: 10 . 1063 / 1 . 5100594. arXiv: 1901 . 03082 [physics]. (Visited on 02/17/2026)

    2019

  13. [13]

    Measurement of Electric-Field Noise from Interchangeable Samples with a Trapped-Ion Sensor

    Kyle S. McKay et al. “Measurement of Electric-Field Noise from Interchangeable Samples with a Trapped-Ion Sensor”. In:Physical Review A104.5 (Nov. 2021), p. 052610.doi: 10.1103/PhysRevA. 104.052610. (Visited on 02/17/2026)

    doi:10.1103/physreva 2021

  14. [14]

    Distance Scaling of Electric-Field Noise in a Surface-Electrode Ion Trap

    J. A. Sedlacek et al. “Distance Scaling of Electric-Field Noise in a Surface-Electrode Ion Trap”. In: Physical Review A97.2 (Feb. 2018), p. 020302.doi: 10.1103/PhysRevA.97.020302. (Visited on 02/17/2026)

    work page doi:10.1103/physreva.97.020302 2018

  15. [15]

    Applications of Charge Detection Mass Spectrometry in Molecular Biology and Biotechnology

    Martin F. Jarrold. “Applications of Charge Detection Mass Spectrometry in Molecular Biology and Biotechnology”. In:Chemical reviews122.8 (Apr. 2022), pp. 7415–7441.issn: 0009-2665.doi: 10.1021/acs.chemrev.1c00377. (Visited on 02/17/2026)

    work page doi:10.1021/acs.chemrev.1c00377 2022

  16. [16]

    “Dark” Squeezed States of the Motion of a Trapped Ion

    J. I. Cirac et al. ““Dark” Squeezed States of the Motion of a Trapped Ion”. In:Physical Review Letters70.5 (Feb. 1993), pp. 556–559.doi: 10.1103/PhysRevLett.70.556. (Visited on 02/21/2026)

    work page doi:10.1103/physrevlett.70.556 1993

  17. [17]

    Quantum-Limited Cooling and Detection of Radio-Frequency Oscillations by Laser-Cooled Ions

    D. J. Heinzen and D. J. Wineland. “Quantum-Limited Cooling and Detection of Radio-Frequency Oscillations by Laser-Cooled Ions”. In:Physical Review A42.5 (Sept. 1990), pp. 2977–2994.doi: 10.1103/PhysRevA.42.2977. (Visited on 02/21/2026)

    work page doi:10.1103/physreva.42.2977 1990

  18. [18]

    Quantum-Enhanced Sensing of Displacements and Electric Fields with Large Trapped-Ion Crystals

    Kevin A. Gilmore et al. “Quantum-Enhanced Sensing of Displacements and Electric Fields with Large Trapped-Ion Crystals”. In:Science373.6555 (Aug. 2021), pp. 673–678.issn: 0036-8075, 1095- 9203.doi:10.1126/science.abi5226. arXiv:2103.08690 [quant-ph]. (Visited on 02/17/2026)

    Pith/arXiv arXiv 2021

  19. [19]

    Production of Fock Mixtures in Trapped Ions for Motional Metrology

    Antonis Delakouras, Daniel Rodr ´ ıguez, and Javier Cerrillo. “Production of Fock Mixtures in Trapped Ions for Motional Metrology”. In:Quantum Science and Technology9.1 (Oct. 2023), p. 015006. issn: 2058-9565.doi:10.1088/2058-9565/ad01d7. (Visited on 10/31/2025)

    work page doi:10.1088/2058-9565/ad01d7 2023

  20. [20]

    Neill Lambert et al.QuTiP 5: The Quantum Toolbox in Python. Oct. 2025.doi: 10.48550/arXiv. 2412.04705. arXiv:2412.04705 [quant-ph]. (Visited on 02/26/2026)

    Pith/arXiv arXiv doi:10.48550/arxiv.2412.04705 2025

  21. [21]

    Exploring the Quantum: Atoms, Cavities, and Photons

    Jonathan P. Dowling. “Exploring the Quantum: Atoms, Cavities, and Photons.” In:American Journal of Physics82.1 (Jan. 2014), pp. 86–87.issn: 0002-9505.doi: 10.1119/1.4827830. (Visited on 02/21/2026)

    work page doi:10.1119/1.4827830 2014

  22. [22]

    On the Generators of Quantum Dynamical Semigroups

    G. Lindblad. “On the Generators of Quantum Dynamical Semigroups”. In:Communications in Mathematical Physics48.2 (June 1976), pp. 119–130.issn: 1432-0916.doi: 10.1007/BF01608499. (Visited on 02/21/2026)

    doi:10.1007/bf01608499 1976

  23. [23]

    Vibrational Bloch-Siegert Effect in Trapped Ions

    I. Lizuain, J. G. Muga, and J. Eschner. “Vibrational Bloch-Siegert Effect in Trapped Ions”. In: Physical Review A77.5 (May 2008), p. 053817.issn: 1050-2947, 1094-1622.doi: 10.1103/PhysRevA. 77.053817. arXiv:0801.1642 [quant-ph]. (Visited on 02/17/2026)

    Pith/arXiv arXiv 2008

  24. [24]

    Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

    Dingshun Lv et al. “Quantum Simulation of the Quantum Rabi Model in a Trapped Ion”. In: Physical Review X8.2 (Apr. 2018), p. 021027.doi: 10.1103/PhysRevX.8.021027 . (Visited on 07/13/2026)

    doi:10.1103/physrevx.8.021027 2018

  25. [25]

    Magnetic Resonance for Nonrotating Fields

    F. Bloch. “Magnetic Resonance for Nonrotating Fields”. In:Physical Review57.6 (1940), pp. 522– 527.doi:10.1103/PhysRev.57.522

    doi:10.1103/physrev.57.522 1940

  26. [26]

    Entanglement and Quantum Computation with Ions in Thermal Motion

    Anders Sørensen and Klaus Mølmer. “Entanglement and Quantum Computation with Ions in Thermal Motion”. In:Physical Review A62.2 (July 2000), p. 022311.doi: 10.1103/PhysRevA.62. 022311. (Visited on 07/12/2026)

    doi:10.1103/physreva.62 2000

  27. [27]

    Experimental Demonstration of a Robust, High-Fidelity Geometric Two Ion-Qubit Phase Gate

    D. Leibfried et al. “Experimental Demonstration of a Robust, High-Fidelity Geometric Two Ion-Qubit Phase Gate”. In:Nature422.6930 (Mar. 2003), pp. 412–415.issn: 1476-4687.doi: 10.1038/nature01492. (Visited on 07/12/2026). 9

    doi:10.1038/nature01492 2003

  28. [28]

    Robust 2-Qubit Gates in a Linear Ion Crystal Using a Frequency-Modulated Driving Force

    Pak Hong Leung et al. “Robust 2-Qubit Gates in a Linear Ion Crystal Using a Frequency-Modulated Driving Force”. In:Physical Review Letters120.2 (Jan. 2018), p. 020501.doi: 10.1103/PhysRevLett. 120.020501. (Visited on 07/13/2026)

    doi:10.1103/physrevlett 2018

  29. [29]

    High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits

    C. J. Ballance et al. “High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits”. In:Physical Review Letters117.6 (Aug. 2016), p. 060504.doi: 10.1103/PhysRevLett.117.060504. (Visited on 07/13/2026)

    doi:10.1103/physrevlett.117.060504 2016

  30. [30]

    High-Fidelity Universal Gate Set for$ {ˆ{9}\mathrm{Be}}ˆ{+}$Ion Qubits

    J. P. Gaebler et al. “High-Fidelity Universal Gate Set for$ {ˆ{9}\mathrm{Be}}ˆ{+}$Ion Qubits”. In:Physical Review Letters117.6 (Aug. 2016), p. 060505.doi: 10.1103/PhysRevLett.117.060505. (Visited on 07/13/2026)

    doi:10.1103/physrevlett.117.060505 2016

  31. [31]

    High-Fidelity Bell-State Preparation with$ˆ {40}{\mathrm{Ca}}ˆ{+}$ Optical Qubits

    Craig R. Clark et al. “High-Fidelity Bell-State Preparation with$ˆ {40}{\mathrm{Ca}}ˆ{+}$ Optical Qubits”. In:Physical Review Letters127.13 (Sept. 2021), p. 130505.doi: 10 . 1103 / PhysRevLett.127.130505. (Visited on 07/13/2026)

    2021

  32. [32]

    Precision Measurement and Compensation of Optical Stark Shifts for an Ion-Trap Quantum Processor

    H. H¨ affner et al. “Precision Measurement and Compensation of Optical Stark Shifts for an Ion-Trap Quantum Processor”. In:Physical Review Letters90.14 (Apr. 2003), p. 143602.doi: 10.1103/ PhysRevLett.90.143602. (Visited on 07/13/2026)

    2003

  33. [33]

    Accurate and Agile Digital Control of Optical Phase, Amplitude and Frequency for Coherent Atomic Manipulation of Atomic Systems

    Joseph Thom et al. “Accurate and Agile Digital Control of Optical Phase, Amplitude and Frequency for Coherent Atomic Manipulation of Atomic Systems”. In:Optics Express21.16 (Aug. 2013), pp. 18712–18723.issn: 1094-4087.doi:10.1364/OE.21.018712. (Visited on 07/13/2026)

    work page doi:10.1364/oe.21.018712 2013

  34. [34]

    Breaking the Entangling Gate Speed Limit for Trapped-Ion Qubits Using a Phase-Stable Standing Wave

    S. Saner et al. “Breaking the Entangling Gate Speed Limit for Trapped-Ion Qubits Using a Phase-Stable Standing Wave”. In:Physical Review Letters131.22 (Dec. 2023), p. 220601.doi: 10.1103/PhysRevLett.131.220601. (Visited on 07/13/2026)

    work page doi:10.1103/physrevlett.131.220601 2023

  35. [35]

    Robust and Resource-Efficient Microwave Near-Field Entangling$ˆ{9}{\mathrm{Be}}ˆ{+}$ Gate

    G. Zarantonello et al. “Robust and Resource-Efficient Microwave Near-Field Entangling$ˆ{9}{\mathrm{Be}}ˆ{+}$ Gate”. In:Physical Review Letters123.26 (Dec. 2019), p. 260503.doi: 10.1103/PhysRevLett.123. 260503. (Visited on 07/13/2026). 10 A. Funding Authors acknowledge support from grant CNS2023-144994 funded by MICIU/AEI/10.13039/501100011033 and by “ERDF...

    doi:10.1103/physrevlett.123 2019