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arxiv: 2509.05717 · v2 · submitted 2025-09-06 · 🪐 quant-ph

Deterministic nuclear spin squeezing and squeezing by continuous measurement using vector and tensor light shifts

Ali Moshiri , Alice Sinatra This is my paper

Pith reviewed 2026-05-18 17:50 UTC · model grok-4.3

classification 🪐 quant-ph
keywords nuclear spin squeezingvector light shifttensor light shiftcontinuous measurementquantum non-demolitionytterbium-173strontiumhelium
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The pith

Joint vector and tensor light shifts create short-time measurement squeezing and longer-time deterministic squeezing of nuclear spins.

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

The paper examines how vector and tensor light shifts act together on large-spin atoms prepared in a polarized state. It shows that the ratio ε of tensor to vector coupling, together with the continuous-measurement rate Γ, sets two distinct regimes: quantum non-demolition squeezing at short times and deterministic squeezing at longer times. The analysis is applied to fermionic isotopes of strontium, ytterbium and helium that possess purely nuclear ground-state spins and very low decoherence. For ytterbium-173 in a cavity of the kind already demonstrated, the combined shifts are predicted to reduce atomic spin variance to 0.03 within roughly 50 milliseconds.

Core claim

Depending on the ratio ε between tensor and vector coupling and the measurement rate Γ, the joint light shifts produce quantum non-demolition measurement squeezing for times shorter than (√ε Γ)^{-1} and deterministic squeezing for times longer than (ε Γ)^{-1}.

What carries the argument

The ratio ε of tensor to vector light-shift couplings, which governs the crossover between continuous-measurement squeezing and deterministic squeezing in polarized nuclear spins.

If this is right

  • Nuclear-spin variance reduction becomes available without continuous measurement once the deterministic regime is reached.
  • Fermionic isotopes with purely nuclear ground states gain a practical route to squeezing because of their intrinsically low decoherence.
  • Cavity parameters already realized in existing experiments suffice to reach variance reductions of order 0.03.

Where Pith is reading between the lines

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

  • The same light-shift combination could be tested in optical lattices or free-space ensembles to check whether the predicted time scales hold outside cavities.
  • If the deterministic regime works as described, it may relax the need for high-finesse cavities in future spin-squeezing metrology.

Load-bearing premise

The atoms remain polarized and the combined vector and tensor light shifts dominate all other decoherence channels over the time scales set by ε and Γ.

What would settle it

Direct measurement of the nuclear spin variance in ytterbium-173 atoms inside a cavity showing no reduction below the initial value once the interaction time exceeds (ε Γ)^{-1}.

Figures

Figures reproduced from arXiv: 2509.05717 by Alice Sinatra, Ali Moshiri.

Figure 1
Figure 1. Figure 1: Diagram of the 1S0 → 3P1 transition for 173Yb. ∆ is the detuning between the light and the 1S0 → 3P0 transition of 176Yb. Hyperfine level energy values extracted are taken from [38]. −4 −2 0 2 4 6 8 10 −1 0 1 detuning (GHz) α v ,α t (a.u.) α v α t 10 20 30 −4 −2 0 2 4 ·10−4 α t [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Dimensionless constants of vectorial and tensorial couplings ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 173Yb. From left to right, as a function of the detuning (in GHz): (left) ε = ∆P 2 deter/∆P 2 t=0 inverse of the metrological gain. (middle) εΓ deterministic squeezing ratio divided by 2. (right) B0 magnetic field along x to compensate for the lightshift. Cavity parameters [1]: κ = 2π × 153kHz; nph = 7.3 × 105 ; ΩRabi = 2π × 21.7kHz. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: 87Sr. From left to right, depending on the detuning (in GHz): (left) ε = ∆P 2 deter/∆P 2 t=0 inverse of the metrological gain. (middle) εΓ deterministic compression ratio divided by 2. (right) B0 magnetic field along x to compensate for lightshift. Cavity parameters [1]: κ = 2π × 153kHz; nph = 9 × 105 ; ΩRabi = 2π × 5.5kHz. 8 9 10 8 · 10−2 9 · 10−2 0.1 0.11 ∆/2π (GHz) ε 8 9 10 0.5 0.7 1 2 3 ∆/2π (GHz) ε Γ … view at source ↗
Figure 5
Figure 5. Figure 5: 87Sr. From left to right, depending on the detuning (in GHz): (left) ε = ∆P 2 deter/∆P 2 t=0 inverse of metrological gain. (middle) εΓ deterministic squeezing ratio divided by 2. (right) B0 magnetic field along x to compensate for lightshift. Cavity parameters [39]: κ = 2π × 10MHz; nph = 2.8 × 105 ; ΩRabi = 2π × 937kHz. reduction in variance of P and the deterministic squeezing rate as a function of the fr… view at source ↗
Figure 6
Figure 6. Figure 6: Schematic diagram of spin squeezing by Faraday effect and continuous [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: QND measurement of quadrature P by continuous measurement of Xc in the absence of a tensor term: on the left, quantum average value of P for four realizations of the experiment: each trajectory converges to a fixed but unpredictable value; on the right, variance of P (see (C.8)), independent of the trajectory. Parameters: ε = 0; γ˜ = 10−3 . 10−1 100 101 102 −1 0 1 τ ¯p = 〈φ(t)|P|φ(t)〉 (a) 20 40 60 80 100 1… view at source ↗
Figure 8
Figure 8. Figure 8: Quasi-QND measurement of quadrature P by continuous measurement of Xc in the presence of the tensor term: on the left, quantum mean value of P for four realizations of the experiment: existence of a time window known as quasi-QND (between the two dotted lines). On the right, the variance of P (see (C.8)), independent of the trajectory, remains greater than ε/2 (dotted line). Parameters: ε = 10−2 ; γ˜ = 10−… view at source ↗
Figure 9
Figure 9. Figure 9: Quasi-QND measurement of P by continuous measurement of Xc : temporal evolution of the mean m(τ) (thin line) and variance V(τ) of P (thick line) conditioned to the signal. The blue dotted line shows the squeezing time in 1/ p ε corresponding to the maximum signal. For this time, the variance conditioned to the signal is VQND ≃ p ε 4 (thick black dotted line). Parameters: ε = 10−2 ; γ˜ = 10−3 . towards zero… view at source ↗
Figure 10
Figure 10. Figure 10: Time evolution of V(τ) = Varσ=S(P) variance of P conditioned to the signal (solid line) and of ∆P 2 the variance of P (dotted line). The hatched areas correspond to the two possible squeezing regimes: quasi-QND, deterministic. Parameters: ε = 10−2 ; γ˜ = 0. ε,γ˜ ≪ 1 3 : τ max QND ≃ 1 Ç ε + γ˜ 6 ; mQND ≃ 1 − vt ε + γ˜ 6 ; VQND ≃ 1 4 Æ ε + γ/˜ 6 + 1 6 γ˜ p ε + γ/˜ 6 (41) At the limit ε → 0, this gives back … view at source ↗
Figure 11
Figure 11. Figure 11: Dimensionless constants of the vectorial and tensorial couplings for the [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Deterministic three-mode squeezing: time evolution of quantum [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
read the original abstract

We study the joint effects of vector and tensor light shifts in a set of large spin atoms, prepared in a polarized state and interacting with light. Depending on the ratio $\epsilon$ between tensor and vector coupling and a measurement rate $\Gamma$, we identify a regime of quantum non-demolition measurement squeezing for times shorter than $(\sqrt{\epsilon}\Gamma)^{-1}$, and a deterministic squeezing regime for times longer than $(\epsilon \Gamma)^{-1}$. We apply our results to fermionic isotopes of strontium, ytterbium, and helium, which are atoms with purely nuclear spin in their ground state, benefiting from very low decoherence. For ytterbium 173, with a cavity such as that of \cite{Thompson2021}, it would be possible to achieve an atomic spin variance reduction of $0.03$ in $\simeq 50 \rm ms$.

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 / 2 minor

Summary. The manuscript analyzes the joint action of vector and tensor light shifts on large-spin atoms held in a polarized state. It derives two distinct squeezing regimes controlled by the tensor-to-vector ratio ε and the measurement rate Γ: a QND measurement squeezing regime active for times shorter than (√ε Γ)^{-1} and a deterministic squeezing regime for times longer than (ε Γ)^{-1}. The framework is applied to fermionic isotopes of strontium, ytterbium and helium; for 173Yb in a cavity comparable to that of Thompson et al. (2021) the authors predict an atomic spin variance of 0.03 after roughly 50 ms.

Significance. If the regime separation and numerical forecast survive detailed scrutiny, the work supplies a concrete, low-decoherence route to deterministic nuclear-spin squeezing that could benefit quantum metrology and sensing protocols. The explicit time-scale hierarchy in terms of measurable parameters ε and Γ offers a useful experimental design tool. The absence of step-by-step derivations, error budgets or direct comparison with the full master equation nevertheless keeps the immediate impact modest.

major comments (2)
  1. [deterministic regime derivation] The deterministic-squeezing regime (abstract and the section deriving the long-time dynamics) rests on the assumption that the collective spin remains inside the polarized manifold for t ≫ (ε Γ)^{-1}. The tensor term proportional to ε can generate differential phases across m_F sublevels; no quantitative bound is given showing that these phases remain negligible compared with the squeezing timescale, which directly affects whether the reported variance reduction of 0.03 is attainable.
  2. [application to Yb-173] The numerical prediction of 0.03 variance reduction for 173Yb in ≃50 ms (abstract) is stated without an accompanying error analysis or explicit dependence on the cavity parameters taken from Thompson2021. Because the result is presented as a concrete experimental target, the missing propagation of uncertainties in Γ, ε and residual decoherence rates weakens the claim.
minor comments (2)
  1. Notation for the vector and tensor coupling strengths is introduced without a compact table relating them to the physical parameters of the cited cavity; adding such a table would improve readability.
  2. The abstract states clear regime boundaries yet the main text does not include a short appendix or figure that plots the crossover times versus ε for fixed Γ; such a plot would help experimentalists.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: The deterministic-squeezing regime (abstract and the section deriving the long-time dynamics) rests on the assumption that the collective spin remains inside the polarized manifold for t ≫ (ε Γ)^{-1}. The tensor term proportional to ε can generate differential phases across m_F sublevels; no quantitative bound is given showing that these phases remain negligible compared with the squeezing timescale, which directly affects whether the reported variance reduction of 0.03 is attainable.

    Authors: We agree that an explicit quantitative bound on the differential phases induced by the tensor light shift would strengthen the justification for remaining in the polarized manifold. Our derivation of the long-time deterministic regime assumes that tensor-induced dephasing across sublevels remains perturbative on the squeezing timescale set by εΓ. In the revised manuscript we will insert a short subsection that estimates the accumulated phase spread δφ ≈ ε Γ t for t ∼ (ε Γ)^{-1} and shows that, for the 173Yb parameters used, δφ remains ≪ 1 radian while the squeezing variance reaches 0.03. This bound directly supports the validity of the reported result. revision: yes

  2. Referee: The numerical prediction of 0.03 variance reduction for 173Yb in ≃50 ms (abstract) is stated without an accompanying error analysis or explicit dependence on the cavity parameters taken from Thompson2021. Because the result is presented as a concrete experimental target, the missing propagation of uncertainties in Γ, ε and residual decoherence rates weakens the claim.

    Authors: We concur that an explicit dependence on cavity parameters and a brief error budget would make the numerical target more useful. The quoted variance of 0.03 is obtained by inserting the measured cavity linewidth and atom-cavity coupling strength from Thompson et al. (2021) into our expression for the long-time squeezing variance, together with the calculated tensor-to-vector ratio ε for 173Yb. In the revised manuscript we will add a short paragraph (and accompanying figure or table) that (i) writes the variance explicitly in terms of Γ and ε, (ii) propagates the reported uncertainties in those quantities, and (iii) estimates the effect of residual decoherence rates consistent with the same cavity. This will clarify the robustness of the 50 ms prediction. revision: yes

Circularity Check

0 steps flagged

Derivation of squeezing regimes is self-contained

full rationale

The paper derives the identified QND measurement squeezing regime for t ≪ (√ε Γ)^{-1} and deterministic squeezing regime for t ≫ (ε Γ)^{-1} directly from the joint vector and tensor light-shift Hamiltonian acting on a polarized collective spin, with the time-scale hierarchy following from the relative strength ε of the tensor term and the measurement rate Γ in the master equation. The numerical projection for Yb-173 uses external cavity parameters quoted from Thompson2021 and does not reduce any central claim to a tautological fit or self-definition. No load-bearing step collapses to a prior self-citation, ansatz smuggling, or renaming of an input; the polarized-state assumption is stated explicitly as a modeling choice rather than derived from the result itself.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions about polarized-state light-atom interactions and the dominance of vector plus tensor shifts; ε and Γ function as tunable physical parameters rather than fitted constants.

free parameters (2)
  • ε
    Ratio of tensor to vector coupling strength that sets the boundary between squeezing regimes.
  • Γ
    Measurement rate that determines the characteristic times (√ε Γ)^{-1} and (ε Γ)^{-1}.
axioms (1)
  • domain assumption Atoms are prepared in a polarized state and interact with light primarily through vector and tensor shifts without dominant competing decoherence channels in the identified time windows.
    Invoked when the joint effects are studied and regimes are defined.

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

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