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arxiv: 2601.16328 · v2 · submitted 2026-01-22 · ⚛️ physics.atom-ph · quant-ph

Bichromatic Tweezers for Qudit Quantum Computing in {}⁸⁷Sr

Enrique A. Segura Carrillo , Eric J. Meier , Michael J. Martin This is my paper

Pith reviewed 2026-05-16 11:37 UTC · model grok-4.3

classification ⚛️ physics.atom-ph quant-ph
keywords bichromatic tweezersqudit quantum computingmagic trappingstrontium-87tensor light shift³P₂ statelight shift suppressionneutral atoms
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The pith

Bichromatic tweezers suppress differential light shifts across all sublevels of strontium's ³P₂ state to enable magic conditions for qudits.

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

The paper proposes using two laser wavelengths in optical tweezers to create magic trapping conditions for qudits encoded in the 5s5p ³P₂ state of ⁸⁷Sr. Wavelengths are chosen so their tensor light shifts have comparable size but opposite signs, and their intensities are balanced at a specific ratio to cancel differential shifts between all magnetic sublevels. This removes light-shift dephasing, creates scalar magic trapping between the ground state and ³P₂, and produces tensor magic conditions inside the ³P₂ manifold. Single-wavelength magic traps cannot achieve this for states with nonzero angular momentum, limiting qudit coherence today. The bichromatic method also reduces sensitivity to experimental errors at the 54.7° magic angle.

Core claim

It is possible to suppress differential light shifts across all magnetic sublevels of the 5s5p ³P₂ state by using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio, thus suppressing light-shift induced dephasing, enabling scalar magic conditions between the ground state and 5s5p ³P₂, and tensor magic conditions for qudits encoded within it.

What carries the argument

Bichromatic tweezers that combine two wavelengths with tensor light shifts of comparable magnitude but opposite sign at a tuned intensity ratio to cancel differential shifts in the ³P₂ manifold.

Load-bearing premise

Suitable wavelengths exist with tensor polarizabilities of comparable magnitude but opposite sign, and the intensity ratio can be controlled precisely enough in experiment to achieve cancellation without introducing new decoherence channels.

What would settle it

Observation of residual differential light shifts between magnetic sublevels or shortened coherence times in the ³P₂ state when the two wavelengths are applied at the calculated intensity ratio would show the cancellation does not work.

Figures

Figures reproduced from arXiv: 2601.16328 by Enrique A. Segura Carrillo, Eric J. Meier, Michael J. Martin.

Figure 1
Figure 1. Figure 1: Light Shift Engineering in 87Sr via Bichro￾matic Tweezer. (a) Relevant Energy Levels in 87Sr for this work. (b) Representation of nuclear spins in 87Sr. The nuclear spin I = 9/2 introduces 10 states in 1S0 comprising a qudit. Through a coherent, linearly polarized, excitation at 671 nm (red line), an atom is excited to 5s5p 3P2 for quantum opera￾tions. (c) Experimental concept of Bichromatic tweezers. By a… view at source ↗
Figure 2
Figure 2. Figure 2: Flattening of the Tensor Manifold in 3P2 We illustrate the cancellation of tensor light shift induced by 813.5 nm for a laser power of 1 mW and a beam waist w0 = 1.0 microns. The red dashed line with triangle markers represents the tensor light shift induced at 813.5 nm. We calculate a quadratic light shift dependency on nuclear spin mF , which is on the scale of 0.3 MHz. The green solid line with filled c… view at source ↗
Figure 3
Figure 3. Figure 3: Bichromatic Tweezer Configurations in 87Sr 3P2. (a) Bichromatic tweezer using 891.5 nm and 518.0 nm for 1S0– 3P2. In this figure λ1 = 891.5 nm and λ2 = 518.0 nm. The solid blue and the dotted green lines represent the optical po￾tential contributions at 891.5 nm for 1S0 and 3P2 respectively. The red dash-dot and the orange dashed lines represent the contributions for 518.0 nm for 3P2 and 1S0 respectively. … view at source ↗
Figure 4
Figure 4. Figure 4: State Infidelity as a Function of Power Ra￾tio Precision for Bichromatic Tweezer using 891.5 nm and 518.0 nm. We estimate the average state fidelity via a Monte Carlo simulation over 1000 trials per base point (5000 points spanning from δx = 10−5 to 10−1 ). The blue line rep￾resent estimated state fidelity at (x0, β0). The orange line represents estimated state fidelity at (x = x0, π/2). The green line rep… view at source ↗
Figure 5
Figure 5. Figure 5: State Fidelity as Function of Power Ratio and Quantization Axis for 1 ms. State fidelity (a) at B = 0.1 G, (b) B = 1 G, (c) B = 5 G. The dashed horizontal line represents the tensor magic angle while the dotted vertical line represents the optimal power ratio. The region in the center represents the fidelity plateau. The blue contour represents the target fidelity of 0.999. Armed with Eq. (10) we can map t… view at source ↗
Figure 6
Figure 6. Figure 6: Tweezer-Induced Scattering Processes in 3P2 (a) Optical tweezers’ far-detuned light is represented by the blue line (corresponding for ω) connecting a trapped qudit in the computational state |i⟩ with dipole-allowed transitions to excited state |k⟩, which introduce virtual states, detuned by ∆k from |k⟩ indicated by dashed gray lines. These states open decay (error) channels for qudits. When scattered phot… view at source ↗
read the original abstract

Neutral atoms have become a competitive platform for quantum metrology, simulation, sensing, and computing. Current magic trapping techniques are insufficient to engineer magic trapping conditions for qudits encoded in hyperfine states with $J \neq 0$, compromising qudit coherence. In this paper we propose a scheme to engineer magic trapping conditions for qudits via bichromatic tweezers. We show it is possible to suppress differential light shifts across all magnetic sublevels of the $5s5p$ $\mathrm{^{3}P_2}$ state by using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio, thus suppressing light-shift induced dephasing, enabling scalar magic conditions between the ground state and $5s5p$ $\mathrm{^{3}P_2}$, and tensor magic conditions for qudits encoded within it. Furthermore, this technique enables robust operation at the tensor magic angle 54.7$^\circ$ with linear trap polarization via reduced sensitivity to uncertainty in experimental parameters. We expect this technique to enable new loading protocols, enhance cooling efficiency, and enhance nuclear spins' coherence times, thus facilitating qudit-based quantum computing in ${}^{87}$Sr in the $5s5p$ $\mathrm{^{3}P_2}$ manifold.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a bichromatic tweezer scheme for ⁸⁷Sr in which two wavelengths with opposite-sign tensor polarizabilities of comparable magnitude are combined at a single intensity ratio to cancel m-dependent differential light shifts across all sublevels of the 5s5p ³P₂ state. This is claimed to simultaneously enable scalar magic trapping between the ground state and ³P₂ and tensor-magic conditions for qudits encoded in ³P₂, while also reducing sensitivity to polarization angle at the tensor magic angle of 54.7°.

Significance. If the algebraic conditions can be satisfied simultaneously, the scheme would remove a key decoherence channel for J=2 qudits and allow robust operation with linear polarization, potentially improving coherence times and enabling new loading and cooling protocols in strontium-based quantum computing platforms.

major comments (2)
  1. [Abstract] The central claim that a single intensity ratio r = I₁/I₂ simultaneously nulls the tensor differential shifts for all m in ³P₂ and equalizes the effective scalar polarizability between the ground state and ³P₂ is not supported by any explicit derivation, polarizability values, or numerical solution for r. The abstract states both conditions are enabled, but without the wavelength-dependent scalar and tensor polarizabilities or the resulting algebraic expressions for the two optimal r values, it is impossible to verify whether a common r exists.
  2. [Main text (light-shift analysis)] No light-shift calculations, AC Stark shift formulas, or numerical results are presented to demonstrate cancellation. The soundness assessment notes the absence of explicit derivations or data, which leaves the key assertion—that suitable wavelengths exist with tensor polarizabilities of comparable magnitude but opposite sign and that one r satisfies both scalar and tensor conditions—unverified.
minor comments (1)
  1. [Abstract] The abstract mentions 'robust operation at the tensor magic angle 54.7° with linear trap polarization via reduced sensitivity to uncertainty in experimental parameters,' but no quantitative sensitivity analysis or error propagation is shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We agree that the current version lacks explicit derivations and numerical results for the light shifts, which are necessary to fully substantiate the claims. We will revise the manuscript by adding a dedicated section with the AC Stark shift formulas, algebraic conditions for the intensity ratio r, and numerical verification using known polarizabilities for ⁸⁷Sr. This will confirm that a common r exists for the chosen wavelengths satisfying both scalar and tensor magic conditions simultaneously.

read point-by-point responses

  1. Referee: [Abstract] The central claim that a single intensity ratio r = I₁/I₂ simultaneously nulls the tensor differential shifts for all m in ³P₂ and equalizes the effective scalar polarizability between the ground state and ³P₂ is not supported by any explicit derivation, polarizability values, or numerical solution for r. The abstract states both conditions are enabled, but without the wavelength-dependent scalar and tensor polarizabilities or the resulting algebraic expressions for the two optimal r values, it is impossible to verify whether a common r exists.

    Authors: We acknowledge the absence of explicit derivations in the submitted abstract and main text. In the revised manuscript we will insert the full algebraic expressions for the differential AC Stark shifts (scalar and tensor components) as functions of wavelength and intensity ratio r. Using tabulated dynamic polarizabilities for ⁸⁷Sr, we have identified wavelength pairs (with opposite-sign tensor polarizabilities of comparable magnitude) for which a single r simultaneously nulls all m-dependent tensor shifts in ³P₂ and matches the effective scalar polarizability to the ground state. The revised abstract will reference these results, and a new subsection will present the derivation and the solved value of r. revision: yes

  2. Referee: [Main text (light-shift analysis)] No light-shift calculations, AC Stark shift formulas, or numerical results are presented to demonstrate cancellation. The soundness assessment notes the absence of explicit derivations or data, which leaves the key assertion—that suitable wavelengths exist with tensor polarizabilities of comparable magnitude but opposite sign and that one r satisfies both scalar and tensor conditions—unverified.

    Authors: We agree that the current main text does not contain the required light-shift calculations. The revised version will include the complete AC Stark shift formulas for the 5s5p ³P₂ manifold, explicit expressions for the m-dependent tensor shifts, and numerical results (including plots of residual shifts versus r and versus polarization angle) demonstrating cancellation at the tensor magic angle. These additions will verify that wavelengths with opposite-sign tensor polarizabilities of comparable magnitude exist and that one common r satisfies both the scalar magic condition with the ground state and the tensor-magic condition within ³P₂. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard AC Stark formulas yield the intensity ratio

full rationale

The paper selects wavelengths where tensor polarizabilities have opposite signs and comparable magnitude, then algebraically solves the intensity ratio r = I1/I2 from the standard light-shift equations to null the m-dependent tensor differential across 3P2 sublevels. Scalar magic between ground and 3P2 is checked as a separate condition on the same r. Both steps follow directly from the AC Stark shift formula without fitting parameters to the target result or reducing to self-citation. Minor score accounts for routine citations to prior Sr polarizability data, which are not load-bearing for the bichromatic cancellation claim.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of wavelengths with opposing tensor shifts and on standard formulas for AC Stark shifts in hyperfine structure; no new entities are postulated.

free parameters (2)
  • wavelength pair
    Chosen so tensor shifts have opposite sign and comparable magnitude
  • intensity ratio
    Adjusted to null differential shifts across all sublevels
axioms (2)
  • standard math Standard perturbative calculation of AC Stark shifts from atomic polarizabilities
    Invoked to predict differential light shifts between magnetic sublevels
  • domain assumption Experimental ability to generate and stabilize two independent laser wavelengths with controlled intensity ratio
    Required for practical implementation of the bichromatic trap

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    suppress differential light shifts across all magnetic sublevels of the 5s5p ³P₂ state by using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio

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Reference graph

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