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REVIEW 4 major objections 7 minor 163 references

All-electrical Coherent Control of a Single Rare-earth Spin Qubit

T0 review · 4 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read By coupling a single erbium 4f spin to a titanium atom and driving the pair with a radio-frequency electric field, this paper demonstrates all-electrical coherent control of a shielded rare-earth spin at Rabi frequencies up to 190 MHz, an…

desk verdict Solid experimental demonstration of all-electrical coherent control of a single surface Er spin at 190 MHz, with a plausible but underdetermined exchange-wobbling mechanism. read the letter →

arxiv 2608.07929 v1 pith:IIOWQ4LT submitted 2026-08-08 cond-mat.mes-hall quant-ph

Yaowu Liu , Dasom Choi , Stefano Reale , Jeongmin Oh , Seorhin Choi , Lei Fang , We-hyo Soe , Arzhang Ardavan
show 3 more authors
Andreas J. Heinrich Soo-hyon Phark Fabio Donati
This is my paper · ORCID
classification cond-mat.mes-hallquant-ph
keywords rare-earthspinqubitall-electricalcontrolanisotropicexchangeelectronresonanceSTMerbiumRabioscillationssurfacescannedprobequantum
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports all-electrical coherent control of a single erbium 4f electron spin by coupling it to a titanium atom on a MgO film and driving the pair with a radio-frequency electric field. The authors claim that the RF field does not act directly on the shielded 4f electrons; instead it modulates the anisotropic exchange interaction between Er and Ti, effectively wobbling the coupled magnetic moments and producing a transverse field strong enough to drive the Er spin at up to 190 MHz. That is roughly an order of magnitude faster than previous rare-earth spin qubit control. If correct, the result establishes anisotropic exchange as a general, site-engineerable resource for electrically controlling otherwise well-shielded rare-earth spins, a step toward ultrafast local quantum gates and spin-photon interfaces.

What carries the argument

The load-bearing object is the anisotropic exchange tensor $\mathbf{J}$ and its RF-induced rotational modulation. The paper writes the driving term as $H_1 = \delta\alpha\, \mathbf{S}_{\mathrm{Ti}}[\mathbf{J}, G]\mathbf{S}_{\mathrm{Er}}$, where $\delta\alpha(t) = \delta\alpha_0 \cos(\omega_{\mathrm{RF}} t)$ is an infinitesimal wobbling angle of both magnetic moments about the external field and $G$ is the generator of rotations about $\mathbf{B}_{\mathrm{ext}}$. Because the commutator vanishes for isotropic $\mathbf{J}$, the drive exists only because the Er-Ti exchange is anisotropic, and the resulting transverse field is further amplified by the large out-of-plane Er g-factor $g_{zz}^{\mathrm{Er}} = 9.59$. This rotational mode is chosen as the energetically favorable trajectory because it preserves the dominant Zeeman energy, and it is formalized as a Lie-derivative change of $\mathbf{J}$ along the RF trajectory.

What would settle it

Measure the Er Rabi frequency as a function of RF power and magnetic-field direction for an Er-Ti pair engineered to have a nearly isotropic exchange tensor (for example the Er(O)-Ti geometry), since the model predicts a Rabi rate about 30 times smaller than in Er(B)-Ti; additionally, if Rabi oscillations appear when the in-plane field is aligned along $\phi = 0^\circ$ or $90^\circ$, where the rotational mechanism predicts zero drive, the wobbling picture would be refuted.

Watch

Extended reading notes

Core claim

The central claim is that a nearby Ti mediator spin lets an RF electric field drive a single Er 4f spin through rotational modulation of the Er-Ti exchange tensor. With three-dimensional magnetic-field control, the authors map the resonance and Rabi frequencies and fit a spin Hamiltonian with a strongly anisotropic Er g-tensor ($g^{\mathrm{Er}}_{xx} = 1.05$, $g^{\mathrm{Er}}_{yy} = 2.22$, $g^{\mathrm{Er}}_{zz} = 9.59$) and exchange tensor ($J^{\mathrm{exc}}_{xx} = 79.6$ MHz, $J^{\mathrm{exc}}_{yy} = 543.7$ MHz, $J^{\mathrm{exc}}_{zz} = 1272.5$ MHz). They show that diagonal modulations of the exchange coupling cannot reproduce the measured ESR angular maps, whereas a rotational wobbling trajectory, in which the RF field rotates the magnetic-moment frames about the external field while leaving the Zeeman energy unchanged, reproduces both the spectra and the angular dependence of the Rabi frequencies. The Er transition shows Rabi oscillations at 190 MHz, about ten times the previous rare-earth record, while the Ti transition and the double-quantum transition stay near 19 MHz. The authors conclude that anisotropic exchange is the general mechanism enabling electrical access to shielded 4f spins.

Load-bearing premise

The load-bearing premise is that the RF electric field acts mainly as a rigid rotation of the Er and Ti magnetic-moment frames about the external field, with the wobble amplitude set by hand to $\delta\alpha_0 = 0.1\pi$ in all simulations, rather than by measured bond-length or orbital-deformation terms.

Editorial extensions

If this is right

  • The demonstrated 190 MHz Rabi rate is an order of magnitude above the previous rare-earth record and puts coherent Er rotations on a nanosecond timescale, well below the measured coherence time of about 113 ns.
  • The mechanism is general: any coupled spin pair with anisotropic exchange and contrasting g-tensor anisotropies should exhibit electrically driven coherent rotation, not just Er-Ti on MgO.
  • Because the drive is electric rather than magnetic, it can be applied locally and at high speed without requiring a resonant magnetic structure.
  • The angular maps identify field orientations where the Er transition is driven strongly and orientations where it vanishes, providing a practical operating recipe for future devices.
  • Coherent control of the double-quantum transition, demonstrated here for the first time for surface atoms, offers a route to two-spin rotations relevant for entanglement protocols.

Reading between the lines

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

  • Inference: if the wobbling mechanism is correct, the orientation of the spin-pair bond becomes a design parameter, so rotating the Er-Ti axis relative to the field should tune the Rabi rate; this could be tested with the (3,0), (3.5,0.5), and (2.5,-0.5) pairs already studied.
  • Inference: the model fixes the wobbling amplitude to $\delta\alpha_0 = 0.1\pi$ by hand, so a decisive independent check would be to extract this amplitude from the RF-power dependence of Rabi frequencies rather than from a global fit.
  • Inference: replacing Ti with a different transition-metal partner such as Ho or Sm could both improve coherence and create a tunable series of anisotropic-exchange mediators, extending the paper's central strategy beyond the single Er-Ti pair.
  • Inference: the same rotational-modulation picture implies that near-isotropic exchange pairs, like the previously studied Er(O)-Ti system, should show almost no electrical Rabi drive, which the paper predicts to be about 30 times weaker than in Er(B)-Ti.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 7 minor

Summary. The manuscript reports ESR-STM experiments on individual Er-Ti pairs on MgO/Ag(100) and claims all-electrical coherent control of a single rare-earth 4f electron spin. The authors observe five ESR transitions of the exchange-coupled Er(B)-Ti pair, identify the Er-dominated transition (f3), and drive coherent Rabi oscillations at up to 190 MHz, an order of magnitude above previous rare-earth spin qubit results. The Rabi frequency scales linearly with RF voltage and, for f3, is independent of tunnel conductance, which supports a non-tip-field driving mechanism. Three pair geometries are compared, showing a non-monotonic dependence of the Er Rabi rate on pair separation. From angular ESR maps under three-dimensional field control, the authors extract the Er g-tensor (g_xx = 1.05, g_yy = 2.22, g_zz = 9.59) and an anisotropic exchange tensor (J_xx = 79.6, J_yy = 543.7, J_zz = 1272.5 MHz). The proposed driving mechanism is an RF-induced rotational wobble of both magnetic-moment frames around the external field, which converts the anisotropic exchange into an effective transverse field; the model is implemented with a commutator term δα μ_Ti[J_M, G_B] μ_Er, and its angular predictions are compared with the experimental maps. Multiplet calculations (4f11 5d2 configuration) with three fitted parameters reproduce the principal g-values, and spin-echo and recovery measurements yield T2 ≈ 113 ns and T1 ≈ 57 ns.

Significance. The experimental core is strong and clearly presented: clean Rabi oscillations at 190 MHz, linear V_RF scaling, conductance independence of the Er Rabi rate (Fig. 2e), a three-pair geometry series, and full (θ, φ) angular maps. If the proposed mechanism is correct, the anisotropic-exchange transducer is a genuinely transferable design resource for electrically driving shielded rare-earth spins, and the demonstrated rate is a real ten-fold advance. The theoretical framework is also elegant: the commutator form vanishes for isotropic J (Eq. S28), and the model yields falsifiable structural predictions, notably the vanishing of the drive at φ = 0° and 90° and a predicted ~30-fold suppression for the near-isotropic Er(O)-Ti pair. The principal weakness is that the validation of the specific drive hypothesis is partly circular and underdetermined: normalized Rabi data enter the spin-Hamiltonian fit that the model later reproduces; the absolute Rabi scale is set by the unconstrained amplitude δα0 = 0.1π; and the equal-rotation ansatz of Eq. (S20) is not distinguished from Ti-only rotation or direct g-tensor modulation.

major comments (4)
  1. [Supp. III; Figs. 5(c,d), S13(c)] Supplementary Section III states that the fit of g_Er, J_exc, and B_tip includes 'both the transition energies and the normalized Rabi frequencies,' with Fig. S13(c) identified as the normalization curve. Because the normalized Rabi frequencies entering the fit are computed from a driving operator, and the only driving operator developed in the supplement is the rotational-modulation Hamiltonian of Section IX (Eq. S27), the model's subsequent reproduction of the normalized Rabi angular dependence in Fig. 5(c,d) and Fig. S13(c) is, on the natural reading, partly guaranteed by the fitting procedure rather than an independent test. The authors should either refit the spin Hamiltonian using only the transition energies of Figs. 4(a,b) and report the predicted (not fitted) normalized Rabi curves, or explicitly identify which data were withheld from the fit. Without this, Section V's statement that off-diagonal rotational modulation 'successfully reproduces' the experimental trends overstates the independent validation content.
  2. [Sec. V, Eq. (2); Supp. IX Eq. (S21)] In the drive term of Eq. (2) and Eq. (S21), δα(t) = δα0 cos(ωRF t) with δα0 = 0.1π adopted in all simulations (Figs. S13, S14, S19, S20). The angular maps used for model validation are normalized (Fig. S13(c) divides by the f3 Rabi frequency at θ = 90°), so they are invariant to δα0; the absolute 190 MHz rate is matched by hand rather than predicted. The paper should state this limitation explicitly and give an order-of-magnitude estimate of δα0 from the RF field at the junction and the calculated orbital response (e.g., the 5d occupation computed in Supp. VIII), or identify which future measurement would calibrate the transduction coefficient. As written, the Discussion's claim that the mechanism 'transduces electrical excitations into an effective coherent rotation' attributes to the model quantitative content it does not yet have.
  3. [Supp. IX Eq. (S20); Fig. 5(a)] Equation (S20) assumes R_Ti(t) = R_Er(t) = R_B[δα(t)], i.e., both local spin frames rotate rigidly about B_ext by the same angle, while the physically plausible alternatives are not computed: a Ti-only rotation (A_Er = 0 in Eq. S13), an Er-only rotation, and direct modulation of the Er g-tensor through H_drive = -μ_B S_Er · δg_Er(t) · B_ext. Given that the RF field is localized under the tip positioned on Ti, and that the paper's own schematic (Fig. 5a) describes the drive as the wobbling of the Ti moment alone, the equal-rotation ansatz is not the obvious default. The authors should justify it from the field geometry or estimate the relative RF amplitudes at the two sites, and should compare the angular predictions of equal rotation, Ti-only rotation, and the δg_Er channel against the datasets of Figs. 4 and 5 and Fig. S13 to show which mechanism the data can actually discriminate. As it stands, 'common rotational wobble' is one plausible choice among several, and the general-resource claim of the abstract rests on that untested choice.
  4. [Supp. VIII; Fig. 4(c)] Supplementary Section VIII fits three free parameters (α = 1.155, q_red = 0.5932, Δ = 6.6467 eV), together with an imposed 10-eV 5d crystal-field splitting, to reproduce the three principal values of the Er g-tensor, so the agreement in Fig. 4(c) is a fit rather than a prediction. The main text's phrasing in Section IV ('the calculated principal values of g-tensor ... qualitatively agree with the experimental results') should be revised to state that the multiplet calculation was tuned to the experimental g-values. The non-fitted outputs — in particular the ground-doublet decomposition with 79.8% |m_J = ±1/2⟩ weight in Table S1 and the hard-axis direction — are the legitimate predictive content of the calculation and should be presented as such, with the caveat that they are not yet directly measured.
minor comments (7)
  1. [Abstract; Sec. VI] The measured Rabi frequency is 190 MHz (0.19 GHz), but the abstract and Discussion describe the result as 'near-gigahertz'; this overstates the demonstrated rate by roughly a factor of five and should be rephrased (e.g., 'hundreds of MHz').
  2. [Sec. V] Section V cites 'the fits in Section II.B' and 'Rabi frequencies shown in Section II.A'; these internal references do not match the manuscript structure (the relevant content is in Section III and in Methods), suggesting leftover cross-references from an earlier draft.
  3. [Supp. III; Supp. X] The fitted value of B_tip is never reported, and the tip-drive amplitude 0.17 S_Ti,x introduced in Supp. X is an additional adjustable parameter; both should be stated explicitly wherever the Fig. 5(b,d) agreements are presented.
  4. [Methods] No data availability statement is included; given the number of fitted parameters and simulations, depositing the raw angular ESR and Rabi datasets and the simulation scripts would substantially improve reproducibility.
  5. [Abstract; Sec. III] The abstract's 'ten-fold improvement over the present record for rare-earth spin qubits' is broader than the main-text comparison to 'the previously reported record for Er-based qubits in solid-state platforms' (ref. 41); the abstract claim should be checked against the actual scope of the prior record.
  6. [Acknowledgment; Methods] Typos: 'Chirstopher P. Lutz' in the Acknowledgment and 'A WG 5400' in Methods; the text would also benefit from stating that S_Ti,x in Supp. X is defined in the effective spin-1/2 basis.
  7. [Sec. V; Fig. 5(c)] The φ-dependence of the Rabi maps in Fig. 5(c) is simulated; the experimental Rabi data are all at φ = 52° (Fig. S13(c)) plus the vanishing points at φ = 0° and 90° (Fig. S16). The text should mark clearly which parts of the angular maps are experimental and which are predictions.

Circularity Check

2 steps flagged · score 6.0 of 10

Partial circularity: normalized Rabi angular maps are fitted parameters presented as reproduced, and the absolute scale rests on an assumed wobbling angle; the rotational commutator mechanism itself retains independent operator content.

  1. fitted input called prediction [Supplementary Section SIII (Fitting ESR spectrum), Fig. S13c; main text Sec. V, Eq. (2), Fig. 5c]
    "The experimental data are fitted using this Hamiltonian, with both the transition energies and the normalized Rabi frequencies included in the fitting procedure. Here, the Rabi frequencies are normalized by the Rabi frequency of the f3 transition at θ=90° and ϕ=52°, as shown in Fig. S13c."

    The same normalized Rabi angular curves that are later presented as reproduced by the rotational modulation model (Fig. S13c solid lines, and the f3/f5 angular maps in Fig. 5c) were explicit fitting targets used to determine g_Er and J_exc. Reproducing those curves with the subsequently chosen commutator drive is therefore partly enforced by construction rather than an independent test. The absolute 190 MHz scale is also not predicted, because the wobbling amplitude δα0 = 0.1π is assumed in all simulations; only the shape and the operator form [J, G] carry independent content.

  2. fitted input called prediction [Supplementary Section VIII (Multiplet calculations); main text Sec. IV, Fig. 4c]
    "The reduced charge (q red) and the radial rescaling parameter (α) were treated as free parameters to fit the experimental g-tensor. ... The fitting procedure was performed using Bayesian optimization as implemented in MATLAB. The error function was defined as the squared difference between calculated and experimental principal values of the Er g-tensor."

    The multiplet calculation is optimized directly to the three experimental principal g-values using three free parameters (q_red, α, and the on-site energy Δ). The subsequently displayed 'qualitative agreement' of the calculated g-tensor in Fig. 4c is therefore a report of the fit, not an independent confirmation. It does not independently validate the g_Er used in the drive mechanism, although it is not load-bearing for the main coherent-control demonstration.

full rationale

The experimental core of the paper—190 MHz Rabi oscillations of the Er f3 transition, linear scaling with V_RF, and the contrast with isolated Ti—is solid and is not itself circular. The rotational drive model also has genuine non-vacuous content: it uses a specific commutator operator δα S_Ti [J, G] S_Er, and the paper explicitly tests diagonal J-modulation terms and shows they fail to reproduce the observed ESR trends. Those comparisons are independent evidence in favor of an off-diagonal rotational term. However, the claimed validation of the angular dependence is partially circular: Supplementary Section SIII states that the fitting procedure included the normalized Rabi frequencies as fit targets, and Fig. S13c then presents those same normalized Rabi curves as simulated reproductions. Thus a substantial part of the 'agreement' is enforced by construction. In addition, the absolute Rabi scale is set by hand through δα0 = 0.1π in every simulation, so the near-gigahertz value is demonstrated experimentally but not derived from the model. The multiplet calculation is similarly a three-parameter fit to the experimental g-tensor, not an independent check. No load-bearing self-citation chain is present: Ref. 12 is used as a consistency check for the Er(O)-Ti estimate, and the central mechanism is developed in this paper rather than imported from prior work. Overall the demonstration is real, but the mechanistic validation is partially circular, giving a score of 6.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a fitted effective spin Hamiltonian (3 g_Er values, 3 J_exc values, B_tip), a hand-set wobbling amplitude, and a multiplet model with three fitted parameters (q_red, alpha, Delta). None of these is independently predicted; the angular dependence of the Rabi maps and the Er(O)-Ti contrast provide the main non-fitted evidence.

free parameters (7)
  • g_Er tensor components = xx=1.05±0.02, yy=2.22±0.02, zz=9.59±0.04
    Fitted to the angular ESR transition map in Fig. 4 with B_tip free; central to the anisotropy and the large out-of-plane g_zz that amplifies the drive.
  • J_exc tensor components = xx=79.6±5.5 MHz, yy=543.7±6.3 MHz, zz=1272.5±7.8 MHz
    Fitted to angular ESR splittings between f1/f2 and f3/f4; the anisotropy of J is the engine of the proposed driving mechanism.
  • B_tip = not stated
    Taken as a free parameter in the Hamiltonian fit, with the assumption that it acts only on Ti and follows B_ext.
  • δα0 = 0.1π
    Wobbling angle assumed for all rotational-modulation simulations; no microscopic calculation fixes its value.
  • q_red = 0.5932
    Reduced charge in the multiplet calculation, fitted to reproduce the experimental g-tensor.
  • alpha = 1.155
    Radial rescaling of the 4f orbitals in the multiplet calculation, fitted to the g-tensor.
  • Delta = 6.6467 eV
    On-site energy for the 5d2 configuration in the multiplet calculation, fitted to yield a 5d occupation of 0.5344 electrons.
assumptions (5)
  • domain assumption The Er ground-state doublet maps to an effective spin S=1/2 with an anisotropic g-tensor.
    The paper assumes the lowest Kramers doublet is an isolated two-level system; multiplet calculations partially justify this, but the spin Hamiltonian is an effective construction.
  • domain assumption Only diagonal components of g_Er and J are non-zero by pair symmetry.
    The O-O bridge site symmetry is used to set off-diagonal tensor components to zero, restricting the model before fitting.
  • ad hoc to paper The RF drive follows the rotational trajectory that leaves the dominant Zeeman energy unchanged.
    This energy-minimizing wobble is posited, not derived from the RF electric field or from a microscopic orbital response calculation.
  • domain assumption Tip-induced magnetic field acts only on Ti and is parallel to B_ext.
    Standard in ESR-STM treatments; used to separate tip and exchange contributions to the f1 and f2 transitions.
  • ad hoc to paper Multiplet calculation with 4f11 5d2 configuration, a 10 eV crystal-field splitting, and configuration interaction.
    The 5d2 configuration and large splitting are introduced to reproduce the measured g-tensor; this is a fitting construction rather than a first-principles prediction.

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Pith. "Pith review of All-electrical Coherent Control of a Single Rare-earth Spin Qubit." pith.science (2026). https://pith.science/paper/IIOWQ4LT

@misc{pith2026260807929,
  author       = {Pith},
  title        = {Pith review of: All-electrical Coherent Control of a Single Rare-earth Spin Qubit},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IIOWQ4LT}},
  note         = {Machine review of arXiv:2608.07929}
}
read the original abstract

Electrical control of single spin qubits is a major frontier for nanoscale, high-speed, and scalable quantum devices. Yet, extending it to highly shielded rare-earth 4f electrons remains an experimental challenge across solid-state platforms. Here we demonstrate all-electrical coherent control of a single Er electron spin, which is exchange-coupled to a nearby Ti atom. Scanning tunneling microscopy-based electron spin resonance with three-dimensional magnetic-field control enables comprehensive mapping of the resonance and Rabi frequencies, revealing pronounced anisotropies in both the Er g-tensor and the Er-Ti exchange interaction. The electrical modulation of the anisotropic Er-Ti coupling results in an efficient drive of the Er spin, allowing us to achieve near-gigahertz Rabi frequencies - a ten-fold improvement over the present record for rare-earth spin qubits. By establishing anisotropic exchange as a general resource for electrically accessing shielded rare-earth spins, our results open a new route to ultrafast and local control of rare-earth spins in solid-state quantum devices.

Figures

Figures reproduced from arXiv: 2608.07929 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p021_5.png]

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