Spontaneous Raman scattering from metastable states of Ba$^+$

Isaac L. Chuang; Jasmine Sinanan-Singh; John Chiaverini; Timothy J. Burke; Xiaoyang Shi

REVIEW 2 major objections 4 minor 30 references

Spontaneous Raman scattering from metastable states of Ba$^+$

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper reports that spontaneous Raman scattering from a metastable state of 137Ba+ follows the four-process model [16], so Raman gates detuned by tens of terahertz can reach error rates near 10^-4 with no fundamental scattering floor.

desk verdict Clean SRS leakage measurements in a metastable Ba+ qubit that favor Moore over Ozeri, but the headline 10^-4 gate-error numbers lean on unmeasured within-manifold scattering. read the letter →

arxiv 2505.22466 v1 pith:VUTXW374 submitted 2025-05-28 quant-ph physics.atom-ph

Timothy J. Burke , Xiaoyang Shi , Jasmine Sinanan-Singh , Isaac L. Chuang , John Chiaverini This is my paper

classification quant-phphysics.atom-ph

keywords spontaneousRamanscatteringmetastablequbitstrapped-ionquantumcomputingbarium-137stimulatedtransitionsgateerrorratesACStarkshiftatomictransitiondata

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

Spontaneous Raman scattering is the fundamental error source for stimulated-Raman quantum gates in trapped ions, and the authors set out to test whether that error has a true lower bound. They measure the scattering rate out of a metastable $|{}^5D_{5/2},F=1,m_F=0\rangle$ state of $^{137}$Ba$^+$ at 617 nm, 674 nm, and 461 nm, and compare the rates to two models. The data agree with the four-process model [16] and deviate from the earlier single-process model [15] at the large detunings where the predictions diverge. If correct, the result means far-detuned lasers can suppress Raman scattering errors below $10^{-4}$ per two-qubit gate, eliminating a supposed fundamental limit.

What carries the argument

The load-bearing object is the four-process scattering rate formula of [16], Eq. (1): a sum over intermediate $k$ and scattered-photon polarization $q$ of $\Lambda$, $V$, and two ladder amplitudes, each weighted by its own detuning denominator and an energy-conserving Heaviside factor. The comparison harness is the differential AC Stark shift of Eq. (A.1), which converts measured laser intensity into a common scale and lets the experiment test the model without a separate intensity calibration. The ladder terms were not tested here because the energy-conservation condition $(E_i-E_f)>\hbar\omega_\ell$ was not met for the chosen states.

What would settle it

A direct check would calibrate the 674 nm intensity by an independent method, such as a power meter and measured beam waist, and compare the extracted scattering rate per unit intensity with the Stark-shift-based value; a common multiplicative shift would expose the Stark-shift assumption. The untested ladder terms could be probed by choosing initial and final states with $(E_i-E_f)>\hbar\omega_\ell$ and a sufficiently red-detuned laser, where the two ladder channels are energy-conserving.

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Extended reading notes

Core claim

The central discovery is that spontaneous scattering from a metastable qubit level in $^{137}$Ba$^+$ behaves as the four-process formula Eq. (1) of [16] predicts, rather than as the simpler model [15] predicts. The experiment prepares $|0\rangle = |{}^5D_{5/2},F=1,m_F=0\rangle$, applies scattering light at three wavelengths, and extracts the decay rate into $6S_{1/2}$ and $5D_{3/2}$ by comparing the measured lifetime with and without the scattering beam. Laser intensity is calibrated through the differential AC Stark shift, so the data are plotted as scattering rate per unit Stark shift and compared directly with the theoretical curves. At 674 nm and 461 nm the measured slopes track the four-process model and fall below the older prediction, supporting the conclusion that the scattering rate can be reduced without a finite floor by increasing red or blue detuning.

Load-bearing premise

The measurement assumes the laser intensity is correctly inferred from the differential AC Stark shift, which is computed by summing dipole matrix elements from the atomic-data reference [18]; a systematic error in those matrix elements or in the Stark-shift formula would shift every extracted scattering rate by the same factor.

Editorial extensions

If this is right

Far-detuned Raman operations inside the metastable $D_{5/2}$ manifold can reach single-qubit spontaneous-scattering errors below $10^{-5}$ per gate.
Two-qubit entangling gates driven tens of terahertz from resonance can approach error rates near $10^{-4}$, limited by other decoherence sources rather than by scattering.
The measurements discriminate between the two scattering models, favoring the four-process description at large detunings and finding no evidence for a finite detuning floor.
The ratio of scattering rate to differential AC Stark shift provides a calibration-free way to compare theory and experiment for other metastable species.

Reading between the lines

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

If the four-process model holds at even larger detunings, gate engineering can trade speed against scattering error continuously, and the practical limit for Raman gates becomes available laser power and gate-time decoherence rather than a scattering floor.
The ladder-scattering channels in Eq. (1) have not been experimentally isolated; a measurement from a higher-energy metastable sublevel with a red-detuned beam could validate or falsify that part of the model.
The same comparison of scattering rate to AC Stark shift could be applied to metastable qubits in other species, such as Ca+ or Sr+, to test whether the four-process model is universal across different intermediate-state structures.
The results strengthen the case for dual-type encodings that use metastable states for operations and ground states for storage, since metastable-manifold Raman gates can be made scattering-clean without disturbing ground-state coherence.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is the first experimental SRS measurement on a metastable-state qubit, and the core data are solid. Measured leakage rates out of |0> = |5D5/2,F=1,mF=0> into 6S1/2 and 5D3/2 at 674 and 461 nm sit on the Moore et al. curve and clearly below the Ozeri-style prediction. The lifetime-vs-Stark-shift extraction is careful, the polarization is characterized for 674 and 617 nm, and the paper is honest that ladder terms are not tested. That part deserves a serious referee.

The soft spot is the gate-error extrapolation. What is measured is only scattering out of the D5/2 manifold; the experiment does not detect scattering between D5/2 sublevels, which is precisely the channel where an Ozeri-like lower bound would show up in the far-detuned limit. Table II folds that missing channel in by scaling the measured rates with the very model under test. The paper flags this in the Fig. 4 caption and the Table II note, so it is transparent, but the abstract and conclusion phrase the 10^-4 result as if the measurement supports it directly. The support is indirect and depends on untested parts of Moore's theory.

Minor caveats: the 461 nm polarization is assumed equal to 617 nm, with no quoted uncertainty on that equality, and the Ozeri-extension in the appendix is a simplified version—fine for comparison, but don't mistake it for the full model. None of this undermines the measured leakage rates.

Who should read it: trapped-ion experimentalists working on metastable or dual-type qubits, especially OMG-protocol people, and theorists interested in spontaneous scattering limits. It deserves peer review. My recommendation: accept with revisions that tighten the abstract/conclusion to distinguish measured leakage from modeled total scattering, and ideally add one sentence describing what is direct evidence versus model extrapolation.

Referee Report

2 major / 4 minor

Summary. This manuscript reports measurements of spontaneous Raman scattering out of the metastable |5D5/2,F=1,mF=0> state of 137Ba+ at 617 nm (near resonance), 674 nm (red-detuned), and 461 nm (blue-detuned). The scattering rate per unit differential AC Stark shift is extracted from the shortening of the D5/2 lifetime under illumination, and the results are compared with the Ozeri et al. and Moore et al. models. The authors report better agreement with Moore et al. and use this agreement to argue that metastable-state two-qubit Raman gates with errors near 10^-4 are achievable at tens of terahertz of detuning.

Significance. The experimental method is sound and the data set is valuable: three wavelengths, red and blue detuning, direct lifetime-based rate extraction, and a comparison with two published models using the differential AC Stark shift as an intensity-independent x-axis. If the claim is restricted to scattering into 6S1/2 and 5D3/2, the data indeed favor the Moore model over Ozeri at large detuning, in line with the prior ground-state measurement in 133Ba+. However, the headline gate-error projection requires the unmeasured within-D5/2 scattering channels, so the significance is conditional. The manuscript is transparent about this limitation in Sec. IV, but the abstract and conclusion do not carry the same caveat.

major comments (2)

[Fig. 3 caption; Sec. IV] The measurement and the model comparison in Fig. 3 are restricted to final states in 6S1/2 and 5D3/2, as the caption explicitly states. This validates only the leakage contribution to SRS, not the total scattering error, which also includes Rayleigh and Raman processes ending in the 5D5/2 manifold. The Ozeri-Moore disagreement at large detuning concerns the total scattering error, and the within-D5/2 channels are precisely where an Ozeri-style lower bound would appear. The paper acknowledges this in Sec. IV, noting that 'scattering back into D5/2 (excluding |0>) would need to be included,' and Fig. 4 and Table II include this channel only through model-dependent scaling. Therefore the abstract's statement that the measurements suggest metastable-level two-qubit gates with error rate approximately 10^-4 are possible is not directly supported by the data. The authors should either measure or bound repopulation of the D5/2 manifold, or revise the central claim so that it explicitly applies only to leakage out of the qubit manifold.
[Table II; Sec. IV] The 'Scaled experiment' column in Table II is not an experimental result: it is obtained by multiplying the measured leakage rate by factors that account for the |1> state population and for scattering back into D5/2, using the very model under test. No formula or uncertainty for this scaling is given. As a result, the two-qubit error numbers in Table II cannot serve as evidence discriminating between the Ozeri and Moore models. The conclusions should be rephrased so that the gate-error projection is explicitly identified as a model-based extrapolation rather than a directly measured quantity.

minor comments (4)

[Sec. III] The 461-nm polarization is assumed equal to the 617-nm polarization based on a polarizing beam splitter measurement, but no uncertainty is quoted for the polarization difference; since the scattering rate depends on polarization, a quantitative bound on any residual difference would strengthen the 461-nm point.
[Fig. 3] The slopes of the linear fits in Fig. 3 are not reported numerically; providing them, with uncertainties, would make the model comparison quantitative and reproducible.
[Sec. IV] There is a typo in 'scattering back into D5/2 (excluding |0>) would need to be be included,' and Ref. [19] contains 'and and NIST'; these should be corrected.
[Conclusion] The concluding claim that the SRS-induced error can be reduced below 10^-5 per single-qubit gate should carry the same caveat as the two-qubit projection: it relies on the model-dependent D5/2 back-scattering correction and is not a directly measured quantity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the measured scattering comparison is independent of the models tested, and model-scaled gate-error extrapolations are transparently labeled.

full rationale

The paper's central measurement is a decay-rate comparison, not a fit-then-predict cycle. The SRS rate out of |0> = |5D5/2,F=1,mF=0> into 6S1/2 and 5D3/2 is obtained from time-resolved shelving/detection data; the theoretical curves in Fig. 3 come from prior models [15,16] with reduced matrix elements and lifetimes from [18] and energies from [19]. No parameter of either model is fitted to the measured scattering rates. The AC Stark shift is used only to determine laser intensity, and because both the measured rate and the differential Stark shift scale with E^2, the plotted ratio (scatter rate per Stark shift) is intensity-independent and provides a non-trivial test of the theoretical ratio. The paper explicitly limits the comparison to leakage channels in the Fig. 3 caption, so the measured quantity is matched to the computed quantity rather than being defined as the full theoretical prediction. The only places where the model under test is used beyond the raw measured channels are Fig. 4's extension to gate error and Table II's scaling for scatter back into the 5D5/2 manifold; both are clearly labeled as scalings/extrapolations, and the paper states that scattering back into D5/2 (excluding |0>) would need to be included. That is a stated limitation, not a circular reduction. Self-citations such as the omg blueprint [6] are contextual and are not load-bearing for the scattering measurement; no uniqueness theorem or ansatz is imported from the authors' own prior work to force the conclusion. The untested ladder terms and unmeasured D5/2-to-D5/2 channels are explicitly acknowledged scope limitations, so they do not make the derivation circular. The central claim therefore has independent empirical content and is not equivalent to its inputs by construction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new entities. It relies on atomic data from references and prior theoretical models. The only fitted parameters are the beam polarization angles, which are calibrated experimentally and not central to the physics claim. The central measurement is a direct rate, not a fit parameter.

free parameters (2)

polarization angle for 674 nm beam = 0.045 ± 0.001 rad
Determined by least-squares fit to measured Rabi frequencies of quadrupole transitions in 88Sr+.
polarization angle for 617 nm beam = 0.105 ± 0.006 rad
Determined by least-squares fit to Raman Rabi frequencies in 137Ba+.

assumptions (3)

domain assumption The laser intensity is calibrated using the AC Stark shift formula (eq. A.1) with dipole matrix elements from the Portal for High-Precision Atomic Data [18].
The accuracy of the intensity calibration depends on the accuracy of the atomic data and the sum over E1 transitions.
domain assumption The theoretical models (Eq. 1 and Eq. A.7) correctly describe the scattering processes with the given detuning definitions and dipole couplings.
The paper assumes the Moore et al. and Ozeri et al. models are valid, and tests them against experiment. The models themselves are prior theoretical work.
domain assumption The 461 nm beam polarization equals the 617 nm beam polarization.
The paper validates this with a polarizing beam splitter and window birefringence measurement, but no uncertainty is quoted for the polarization difference.

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Cite this review

Pith. "Pith review of Spontaneous Raman scattering from metastable states of Ba$^+$." pith.science (2026). https://pith.science/paper/VUTXW374

@misc{pith2026250522466,
  author       = {Pith},
  title        = {Pith review of: Spontaneous Raman scattering from metastable states of Ba$^+$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VUTXW374}},
  note         = {Machine review of arXiv:2505.22466}
}

abstract

Quantum logic gates performed via two-photon stimulated-Raman transitions in ions and atoms are fundamentally limited by spontaneous scattering errors. Recent theoretical treatment of these scattering processes has predicted no lower bound on the error rate of such gates when implemented with far-detuned lasers, while also providing an extension to metastable qubits. To validate this theoretical model, we provide experimental measurements of Raman scattering rates due to near-, and far-detuned lasers for initial states in the metastable D$_{5/2}$ level of $^{137}$Ba$^+$. The measured spontaneous Raman scattering rate is consistent with the theoretical prediction and suggests that metastable-level two-qubit gates with an error rate $\approx10^{-4}$ are possible with laser excitation detuned by tens of terahertz or more.

Figures

Figures reproduced from arXiv: 2505.22466 by the authors.

**Figure 2.** FIG. 2. Relevant scattering processes and experimental beam ge [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Experimental measurement of SRS rate into 6 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Representative gate error due to SRS during a single qubit, [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

AC Stark Shift We use the differential Stark shift,∆d,s, between two levels, |s⟩ = |Fs, ms⟩ and |d⟩ = |Fd, md⟩ in the S1/2 and D5/2 respec- tively, to determine the amplitude of the laser electric field. The AC Stark shift is calculated by [26, 27]: δi = E2 ℓ 4¯h2 ∑ k ωik |⟨i| r · ˆεℓ |k⟩| ω2 ik − ω2 ℓ ∆d,s = δd − δs (A.1) where the laser is described by ...

work page

[2] [2]

For 674 nm light, we use the quadrupole transitions in 88Sr+ between S1/2 and D5/2

Polarization Measurements We determine the polarization ˆεℓ and direction ˆk of each laser beam by measuring the Rabi frequency of various tran- sitions. For 674 nm light, we use the quadrupole transitions in 88Sr+ between S1/2 and D5/2. For this single beam, we de- fine ˆk = (sin φ ,0,cos φ ), parameterized by its angleφ from the quantization axis provid...

work page

[3] [3]

Scattering rate for metastable states We extend the ground state scattering model of Ozeri et al. [15] by assuming a constant density of states (the scat- tered photon energy is constant), including only the Λ scat- tering process, and only coupling to the nearest manifold (the metastable qubits we consider in Ba+ are housed in the 5D5/2 manifold and only...

work page

[4] [4]

Levine, D

H. Levine, D. Bluvstein, A. Keesling, T. T. Wang, S. Ebadi, G. Semeghini, A. Omran, M. Greiner, V . Vuleti ´c, and M. D. Lukin, Dispersive optical systems for scalable raman driving of hyperfine qubits, Phys. Rev. A 105, 032618 (2022)

work page 2022

[5] [5]

C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, High-fidelity quantum logic gates using trapped-ion hy- 6 perfine qubits, Phys. Rev. Lett. 117, 060504 (2016)

work page 2016

[6] [6]

J. P. Gaebler, T. R. Tan, Y . Lin, Y . Wan, R. Bowler, A. C. Keith, S. Glancy, K. Coakley, E. Knill, D. Leibfried, and D. J. Wineland, High-fidelity universal gate set for 9Be+ ion qubits, Phys. Rev. Lett. 117, 060505 (2016)

work page 2016

[7] [7]

A. J. Kerman, V . Vuleti´c, C. Chin, and S. Chu, Beyond optical molasses: 3d raman sideband cooling of atomic cesium to high phase-space density, Phys. Rev. Lett.84, 439 (2000)

work page 2000

[8] [8]

Berto, E

P. Berto, E. R. Andresen, and H. Rigneault, Background-free stimulated raman spectroscopy and microscopy, Phys. Rev. Lett. 112, 053905 (2014)

work page 2014