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arxiv: 2606.02500 · v1 · pith:EIDMMCZZnew · submitted 2026-06-01 · ⚛️ physics.atom-ph · cond-mat.quant-gas· quant-ph

Creating and Probing Spin-Squeezed States of Molecules

Connor M. Holland , Callum L. Welsh , Yukai Lu , David Wellnitz , Xing-Yan Chen , Ana Maria Rey , Lawrence W. Cheuk This is my paper

Pith reviewed 2026-06-28 11:34 UTC · model grok-4.3

classification ⚛️ physics.atom-ph cond-mat.quant-gasquant-ph
keywords spin squeezingpolar moleculesoptical tweezersdipolar exchangequantum entanglementmetrological gaindynamical decoupling
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The pith

Spin-squeezed states have been created for the first time in polar molecules using dipolar exchange in an optical tweezer array, producing up to 3 dB metrological gain.

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

The paper shows that spin-squeezed states can be generated in CaF molecules trapped individually in optical tweezers by encoding the spin in rotational levels that interact through dipolar exchange. Dynamical decoupling sequences isolate this interaction and suppress other noise sources, yielding measurable metrological gain along with direct signatures of entanglement. The authors further use Floquet engineering to create longer-range correlations while keeping the squeezing intact and demonstrate that the states survive transfer into non-interacting hyperfine levels. A reader would care because molecules offer strong, tunable long-range interactions and rich sensitivity to external fields, so a working route to entanglement in this platform directly expands the set of systems available for quantum-enhanced measurements.

Core claim

The central discovery is the first creation of metrologically useful spin-squeezed states in polar CaF molecules. The spin is encoded in rotational levels coupled directly by dipolar exchange interactions. Appropriate dynamical decoupling yields up to 3.0(3) dB of metrological gain (2.2(3) dB without correction). Floquet engineering produces richer Hamiltonians that preserve squeezing while building longer-range correlations. Site-resolved measurements confirm enhanced sensitivity to both homogeneous and inhomogeneous fields, bipartite entanglement, and EPR steering. The squeezed states are transferred into long-lived hyperfine levels where the enhancement lasts up to 100 ms.

What carries the argument

Spin-squeezed states produced by dipolar exchange interactions between rotational levels of molecules, isolated and shaped by dynamical decoupling and Floquet engineering.

If this is right

  • The entangled states improve sensitivity to both uniform and spatially varying electromagnetic fields.
  • Direct measurements reveal bipartite entanglement and Einstein-Podolsky-Rosen steering between molecules.
  • The squeezed states can be stored in non-interacting hyperfine levels for up to 100 ms while retaining the metrological advantage.
  • Floquet engineering allows the same squeezing to coexist with tunable longer-range quantum correlations.

Where Pith is reading between the lines

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

  • The same decoupling and engineering methods could be applied to other polar species to tailor interactions for specific sensing targets.
  • Scaling the tweezer array size while preserving the per-molecule squeezing would test whether molecular platforms can reach the large-N regime needed for practical quantum sensors.
  • Transfer into long-lived states opens a route to hybrid molecular-atom or molecular-ion experiments that combine squeezing with different interrogation techniques.

Load-bearing premise

The observed metrological gain arises from quantum spin squeezing rather than residual classical correlations or undetected measurement artifacts.

What would settle it

Repeating the gain measurement after the decoupling sequences are removed or the molecular dipoles are oriented to cancel exchange while all other controls remain identical, and finding no gain, would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.02500 by Ana Maria Rey, Callum L. Welsh, Connor M. Holland, David Wellnitz, Lawrence W. Cheuk, Xing-yan Chen, Yukai Lu.

Figure 1
Figure 1. Figure 1: FIG. 1. Spin-Squeezing in a CaF Molecular Tweezer Array. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. XX Squeezing Dynamics and Metrological Perfor [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Metrological Gain and Correlations for XXZ Squeez [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Bipartite Entanglement, EPR Steering, and Storage [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. SRI Sequence and Histograms: (a) SRI begins with molecules in the rotational encoding. Application of [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Determining Model Parameters from Two-Molecule Data. (a) Sum of residuals [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. XY8 and Floquet Pulse Sequences. (a) XY8 sequence. [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Determining Strength of Transduction Noise. (a) [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Scalable Spin-squeezing in 2D Square Lattices. Nu [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spin Squeezing Dynamics. (a,b,c) Normalized spin variance Var[ [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Squeezed State Properties versus Ising Strength (∆). (a) Normalized spin variance Var[ [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Properties of Hyperfine-Transduced States vs Storage Duration. (a) Normalized spin variance Var[ [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗
read the original abstract

Polar molecules are a promising platform for quantum-enhanced sensing and precision tests of fundamental physics, owing to their strong long-range dipolar interactions, broad sensitivity to electromagnetic fields, and sensitivity to potential physics beyond the Standard Model. However, the creation of metrologically useful entangled states in molecular systems has remained elusive. Here, we report the first observation of a class of metrologically useful entangled states - spin-squeezed states - in polar CaF molecules trapped in an optical tweezer array. The spin degree of freedom is encoded in rotational levels which are directly coupled by dipolar exchange interactions. By harnessing appropriate dynamical decoupling schemes we observe up to 3.0(3)dB of metrological gain, (2.2(3)dB without measurement correction) from direct exchange interactions. Using Floquet engineering, we further realize richer Hamiltonians that preserve spin squeezing while enabling the development of longer-range quantum correlations. Using site- and spin-resolved measurements we demonstrate that these entangled states enhance sensitivity to both homogeneous and spatially varying fields, and reveal strong non-classical correlations, including bipartite entanglement and Einstein-Podolsky-Rosen steering. Finally, we transfer the spin-squeezed states into long-lived and non-interacting hyperfine states, where the metrological enhancement persists for up to 100ms. Our results establish molecular optical tweezer arrays as a scalable platform for generating, controlling, characterizing, and storing entangled states of molecules, opening new opportunities for quantum-enhanced sensing and precision tests of fundamental physics.

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

0 major / 2 minor

Summary. The manuscript reports the first observation of spin-squeezed states in polar CaF molecules trapped in an optical tweezer array. Spin is encoded in rotational levels coupled by dipolar exchange; dynamical decoupling and Floquet engineering are used to generate up to 3.0(3) dB metrological gain (2.2(3) dB uncorrected). Site- and spin-resolved measurements demonstrate non-classical correlations (bipartite entanglement witnesses, EPR steering), sensitivity to both homogeneous and inhomogeneous fields, and transfer of the squeezed states to long-lived hyperfine levels where the gain persists for ~100 ms.

Significance. If the central claims hold, this establishes molecular tweezer arrays as a viable platform for scalable entangled-state generation and storage. The direct use of dipolar exchange, the quantitative metrological gain with controls, the demonstration of both uniform and spatially varying field sensitivity, and the 100 ms storage time are all load-bearing strengths. The experimental controls (interaction-off sequences, scaling with time/strength, residual decoherence bounds) directly address attribution to squeezing rather than classical effects.

minor comments (2)
  1. [Abstract] Abstract: the parenthetical '(2.2(3)dB without measurement correction)' should be expanded in the main text to define the correction procedure and its uncertainty budget (e.g., § on data analysis or supplementary methods).
  2. [Methods / Results] The manuscript should include a concise table or paragraph summarizing the residual decoherence rates measured in the interaction-off control sequences and the corresponding classical gain upper bound.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and their recommendation to accept. We are pleased that the central claims regarding the first observation of spin-squeezed states in polar molecules, the metrological gain, and the storage in long-lived states are viewed as load-bearing strengths.

Circularity Check

0 steps flagged

No significant circularity

full rationale

This is an experimental paper reporting direct observations of spin-squeezed states and metrological gain in CaF molecules via measured correlations and controls. No derivation chain exists that reduces reported dB values or entanglement witnesses to quantities fitted from the same dataset or to self-citations. The central claims rest on site-resolved measurements, interaction-time scaling, and disabled-interaction controls, all of which are independent of any internal fitting loop. The result is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced; the work is an experimental demonstration relying on established molecular physics and quantum optics techniques.

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discussion (0)

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Reference graph

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    A microwave pulse transfers|0⟩molecules to|↑⟩

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    This is done with 30 ms Λ-imaging

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    ApplyR ⊗N to the measured outcome vectorP meas (dimension 4 N), yielding the occupation probabil- ity vectorP occ (dimension 3N). 6

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    Normalize the resulting vector’s sum to 1. Before normalization, this vector can be written as Pocc,PS = diag{1,1,0} ⊗N · R⊗N ·P meas = [diag{1,1,0} · R] ⊗N ·P meas.(11) Since diag{1,1,0} · Rcontains a row of zeros, the cor- rection matrix reduces to dimension 2×4, significantly reducing computational overhead. Expectation values and uncertainties are com...

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    This gives us the full 3D motional eigenstates

    and↑(l= 8). This gives us the full 3D motional eigenstates. To disentangle thex,y, andzcomponents, we take three 1D cuts of the Hamiltonian. We define ˆH(x) 0,l andE (x) n,l by fixingy=z= 0 to computeω x = (E(x) 3,1 −E (x) 3,0 )/ℏandδ x,th = (E (x) 8,1 −E (x) 8,0 )/ℏ−ω x. We analogously computeω y andδ y,th forx=z= 0, and ωz andδ z,th forx=y= 0. We call t...

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    Crucially, for⃗ n 1 =⃗ n′ 2 and⃗ n2 =⃗ n′ 1, ϕ⃗ n′ 1,↑(0), ϕ⃗ n′ 2,↓(m) ˆHdd |ϕ⃗ n1,↓(0), ϕ⃗ n2,↑(m)⟩ ≪J typically does not contribute to the dynamics on exper- imental time scales. Therefore, we only keep the terms corresponding to⃗ n1 =⃗ n′ 1 and⃗ n2 =⃗ n′ 2, and ˆHdd reduces to a spin model ˆHdd,eff = X i,j Jij(⃗ n(i), ⃗ n(j)) 2 h ˆs(x) i ˆs(x) j + ˆs(...

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    Guess the parametersJ,δ, ∆ϕ, andγ deph

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    OptimizeJusing the two-particle interacting data [Fig. 2(a)]

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    Find a preliminary optimum forδusing the two- particle interactions [Fig. 2(b)]

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    Find a cross-correlated region of confidence be- tweenγ deph and ∆ϕ[Fig. 2(c)]

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    This fully constrainsγ deph and ∆ϕtogether with the previous step, and provides a more constrained range forδ[Fig

    Run a 2D scan of the variance of non-interacting molecules for a joint scan ofδand ∆ϕ, using the optimalγ deph determined in step 4 for each ∆ϕ. This fully constrainsγ deph and ∆ϕtogether with the previous step, and provides a more constrained range forδ[Fig. 2(h)]

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    −iτp ˆHmol + ˆHMW,α − i 2 X k ˆL† k ˆLk !# , (40) ˜Uf,1 = exp

    Restart from step 2. with the new optimalJ,δ, ∆ϕ, andγ deph. The fitting procedure is illustrated for the final pa- rameters in Fig. 2. ForJ, we find a clear optimum aroundJ/h= 36 Hz. Forδ, we initially find a wide region of confidence−900 Hz< δ <700 Hz, which is wider than the∼500 Hz variations we expect experi- mentally. Forγ deph and ∆ϕ, we find a corr...

    2000

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    Yes,” randomly choose the appropriate quantum jump and apply it (see below) [17]; If “No,

    Apply the jump gateJas follows: (a) Draw a uniformly distributed random number 0≤p≤1. (b) Check whether⟨ψ ′|ψ′⟩< p? (c) If “Yes,” randomly choose the appropriate quantum jump and apply it (see below) [17]; If “No,” renormalize the state|ψ ′⟩

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    Repeat. To choose the appropriate jump, we compute the jump weightsw k =⟨ψ ′| ˆL† k ˆLk |ψ′⟩, such that the corresponding probabilities arep k =w k/(P k wk). Then, to apply the jump, we compute|ψ ′′⟩= ˆLk |ψ′⟩/ √wk. The implemen- tation of this algorithm is illustrated in Fig. 3. To increase efficiency, we reuse the same thermal dis- tribution and thus th...

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    Noise-Modified Theory Curves and Fit Procedure When comparing between theory and experiment, we account for correlated rotation noise during transduction by modifying theory curves computed according to the equations above. Specifically, we multiply the collective spin lengths by the Gaussian suppression factor, so that ⟨ ˆSy⟩th → ⟨ ˆSy⟩the−σ2 .(50) The v...

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