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arxiv: 2605.30815 · v1 · pith:EPWDLCVNnew · submitted 2026-05-29 · 🪐 quant-ph · physics.atom-ph

Dissipative generation of spin squeezing in the resolved vacuum Rabi splitting limit

Edwin Chaparro , Eric Yilun Song , Diego Barberena , James K. Thompson , Ana Maria Rey , Jeremy T. Young This is my paper

Pith reviewed 2026-06-28 22:11 UTC · model grok-4.3

classification 🪐 quant-ph physics.atom-ph
keywords spin squeezingdissipative entanglementcavity QEDone-axis twistingvacuum Rabi splittingoptical atomic clocksstrontium-87symmetry-protected dynamics
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The pith

Symmetry-protected dissipative spin squeezing works in the resolved vacuum Rabi splitting regime of cavity QED.

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

The paper establishes that symmetry-protected dissipative spin squeezing remains possible even when cavity photons cannot be adiabatically eliminated and instead participate actively in the dynamics. Using a driven three-level ensemble of strontium-87 atoms inside an optical cavity, smooth ramps of drive strength and detuning steer the system into a stable low-photon window. In that window sector-resolving photon leakage is suppressed, a sector-dependent geometric phase produces effective one-axis twisting, and more than 25 dB of squeezing is generated for 100 000 atoms while saturating the ideal N to the minus two-thirds scaling. The protocol ends by transferring the entanglement directly onto the long-lived clock states.

Core claim

In the resolved vacuum Rabi splitting limit, driven-dissipative evolution under smooth parameter ramps reaches a stable low-photon regime in which nonadiabatic cavity excitations and sector-resolving leakage remain controlled; the resulting sector-dependent geometric phase implements effective one-axis twisting, yielding more than 25 dB of squeezing for 10^5 atoms that closely follows the ideal scaling ξ_min² ∝ N^{-2/3} and can be transferred to clock states.

What carries the argument

The sector-dependent geometric phase that realizes effective one-axis twisting once the driven-dissipative dynamics enters the stable low-photon regime.

If this is right

  • More than 25 dB of squeezing is generated for experimentally realistic parameters with 10^5 atoms.
  • At fixed cooperativity the achieved squeezing is comparable to the unresolved-regime case but occurs on a substantially shorter physical timescale.
  • The generated entanglement can be transferred directly to the long-lived clock states by turning the drive off.
  • Symmetry-protected dissipative dynamics extends to cavity-QED platforms operating near or inside the resolved vacuum Rabi splitting limit.
  • The approach provides a practical route to beyond-standard-quantum-limit performance in optical-clock systems.

Where Pith is reading between the lines

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

  • The same ramp protocol may be adaptable to other three-level atomic species or different cavity geometries that also operate in the resolved regime.
  • Because the squeezing reaches the ideal one-axis-twisting limit on shorter times, the method could reduce the impact of technical noise sources that accumulate over longer durations.
  • Direct transfer to clock states suggests the squeezed ensemble could be used immediately in clock interrogation sequences without additional mapping steps.

Load-bearing premise

Smooth ramps of the drive amplitude and detunings allow the system to enter and remain in a stable low-photon regime where nonadiabatic excitations and sector-resolving leakage stay controlled.

What would settle it

Perform the protocol with 10^5 strontium atoms in a cavity tuned to the resolved vacuum Rabi regime and measure whether the final clock-state squeezing exceeds 25 dB while matching the predicted N^{-2/3} scaling.

Figures

Figures reproduced from arXiv: 2605.30815 by Ana Maria Rey, Diego Barberena, Edwin Chaparro, Eric Yilun Song, James K. Thompson, Jeremy T. Young.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: shows how the role of photons extends from the transient dynamics to the steady-state operating landscape. In the UVRS regime, [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: summarizes the optimal squeezing and optimal time across parameter space, together with the corre￾sponding regime classification from Table I. Purple, gray, and pink denote regimes I, II, and III, re￾spectively. The color transparency highlights the gradual crossover between neighboring regimes, reflecting that the boundaries are not sharply defined and that each region is classified according to the domin… view at source ↗
Figure 8
Figure 8. Figure 8: summarizes the matched-cooperativity com￾parison for N = 105 . The top row shows the optimized squeezing gain ξ 2 min, while the bottom row shows the corresponding optimal time log10(NΓ0tmin). The stars mark the global optimum within the displayed window after this local-dephasing-limited time optimization; as in Figs. 6 and 7, stars associated with optima on the lower boundary αin/αref = 0 are plotted sli… view at source ↗
Figure 9
Figure 9. Figure 9: (b) highlights the main practical distinction be￾tween the two regimes. Although the optimized squeez￾ing and the scaled time remain close to the OAT trend over the explored range of N, the two regimes are not equivalent in laboratory units: the RVRS implemen￾tation reaches comparable squeezing on a substantially shorter physical timescale given its shorter timescale γ −1 d . VIII. CONCLUSIONS AND OUTLOOK … view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Steady-state normalized spin projection [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
read the original abstract

Harnessing dissipation in the presence of strong symmetries has recently emerged as a promising route for generating entanglement in atomic clocks. However, previous proposals relied on regimes where cavity photons can be adiabatically eliminated, significantly limiting their applicability to experimentally relevant cavity-QED regimes that lie in or near the resolved vacuum Rabi splitting regime. Here we show that symmetry-protected dissipative spin squeezing can be realized even when cavity photons actively participate in the dynamics, extending the experimental relevance of the protocol. We study a three-level ensemble of $^{87}\mathrm{Sr}$ atoms coupled to an optical cavity in the resolved vacuum Rabi splitting regime and demonstrate that, with smooth ramps of the drive amplitude and detunings, the driven-dissipative dynamics enters a stable low-photon regime in which nonadiabatic cavity excitations and sector-resolving photon leakage can be controlled. Within this low-photon operating window, sector-resolving photon leakage is suppressed and the sector-dependent geometric phase realizes effective one-axis twisting. At the end of the protocol the entanglement can also be efficiently transferred directly onto the long-lived clock states by turning the drive off. For experimentally realistic parameters, we theoretically show that more than $25\,\mathrm{dB}$ of squeezing can be generated for $10^5$ atoms, closely saturating the ideal one-axis twisting scaling $\xi_{\min}^2 \propto N^{-2/3}$. At fixed cooperativity, the optimized squeezing remains broadly comparable to the unresolved-regime implementation, while the resolved-regime implementation reaches comparable squeezing on a substantially shorter physical timescale. These results establish symmetry-protected dissipative dynamics as a practical route to beyond the standard-quantum-limit performance in optical-clock platforms.

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 proposes a driven-dissipative protocol for symmetry-protected spin squeezing in a three-level 87Sr ensemble coupled to an optical cavity in the resolved vacuum Rabi splitting regime. Smooth ramps of drive amplitude and detunings are used to reach a stable low-photon regime in which nonadiabatic excitations and sector-resolving leakage are suppressed, allowing the sector-dependent geometric phase to implement effective one-axis twisting; the protocol ends by transferring entanglement to clock states. For realistic parameters the work reports >25 dB squeezing at N=10^5 atoms that saturates the ideal ξ_min² ∝ N^{-2/3} scaling and reaches comparable performance to the unresolved regime on shorter timescales.

Significance. If the low-photon regime is robustly realized, the result meaningfully extends dissipative squeezing methods to experimentally relevant cavity-QED parameters, providing a concrete route to entanglement-enhanced optical clocks with shorter protocol times at fixed cooperativity. The use of realistic Sr parameters and the explicit transfer step to long-lived clock states are practical strengths.

major comments (2)
  1. [numerical results / protocol description] The central claim of >25 dB squeezing at N=10^5 (abstract and numerical-results section) rests on the driven-dissipative dynamics remaining in a stable low-photon regime under the chosen smooth ramps. No explicit scaling or tabulated values of steady-state photon population versus N (or versus ramp duration) are provided for the largest system sizes, leaving the quantitative margin by which nonadiabatic excitations and sector-resolving leakage remain negligible unverified.
  2. [results / comparison paragraph] The statement that the optimized squeezing 'remains broadly comparable' to the unresolved-regime implementation at fixed cooperativity (abstract) is load-bearing for the practical-advantage claim, yet the specific cooperativity value employed in the resolved-regime simulations is not stated, preventing direct verification of the comparison.
minor comments (2)
  1. [figures] Figure captions and axis labels should explicitly state the ramp functional form and the precise definition of the squeezing parameter ξ² used in all panels.
  2. [methods / parameter table] The manuscript would benefit from a short table listing the numerical values of all drive amplitudes, detunings, and decay rates employed for the N=10^5 case.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and will revise the manuscript to improve verifiability of the claims.

read point-by-point responses

  1. Referee: The central claim of >25 dB squeezing at N=10^5 (abstract and numerical-results section) rests on the driven-dissipative dynamics remaining in a stable low-photon regime under the chosen smooth ramps. No explicit scaling or tabulated values of steady-state photon population versus N (or versus ramp duration) are provided for the largest system sizes, leaving the quantitative margin by which nonadiabatic excitations and sector-resolving leakage remain negligible unverified.

    Authors: We agree that explicit data on photon population scaling would strengthen the central claim. In the revised manuscript we will add a new figure (or supplementary table) showing steady-state photon number versus N up to 10^5 and versus ramp duration for the protocol parameters, thereby quantifying the margin by which the low-photon regime is maintained and nonadiabatic leakage suppressed. revision: yes

  2. Referee: The statement that the optimized squeezing 'remains broadly comparable' to the unresolved-regime implementation at fixed cooperativity (abstract) is load-bearing for the practical-advantage claim, yet the specific cooperativity value employed in the resolved-regime simulations is not stated, preventing direct verification of the comparison.

    Authors: We will explicitly state the cooperativity value (C = g²/(κγ)) used in the resolved-regime simulations both in the abstract and in the numerical-results section, allowing direct comparison at fixed C with the unresolved-regime results. This addition will make the practical-advantage claim verifiable without altering the reported performance. revision: yes

Circularity Check

0 steps flagged

No circularity: result from explicit dynamical simulation of master equation

full rationale

The paper derives the >25 dB squeezing claim from numerical integration of the driven-dissipative master equation under smooth ramps that stabilize a low-photon regime, realizing effective one-axis twisting via sector-dependent geometric phase. This is not equivalent to any input parameter by construction, nor does it rename a fitted quantity as a prediction. No load-bearing self-citation chain or ansatz smuggling is required for the central scaling result; the protocol is self-contained against external benchmarks of cavity-QED parameters. Minor self-citations to prior symmetry-protected squeezing work exist but are not used to force the present numerical outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard cavity-QED master-equation modeling and the domain assumption that smooth ramps produce a controllable low-photon window; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • standard math Driven-dissipative master equation for three-level atoms coupled to a cavity
    The dynamics are described using the standard quantum-optical model for cavity QED.
  • domain assumption Existence of a stable low-photon regime under smooth parameter ramps where sector-resolving leakage is suppressed
    This premise is required for the geometric-phase twisting to dominate and produce the reported squeezing.

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Reference graph

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    The columns correspond to differ- ent resonance choices, while the row labels distinguish the UVRS and RVRS regimes

    Comparison of resonance conditions Figure 10 compares the steady-state normalized spin projection⟨ ˆJ z⟩ss/(NJ /2) in the (∆ c/(NΓ0), αin/αref) plane for the three resonance conditions used in the mean-field analysis. The columns correspond to differ- ent resonance choices, while the row labels distinguish the UVRS and RVRS regimes. The comparison shows t...

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    We remove it by working in a frame rotating at ωB = δσ 2 cos ˜θJ ,ˆw ωB(t) =e iωB t ˆw(t),ˆw∈ { ˆd,ˆe}, (D2) so that the mean-field amplitudes are time independent

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    Quadratic HP Hamiltonian and cavity elimination Displacing the cavity field as ˆa=α+ ˆa ′, withαthe mean-field cavity amplitude, and keeping terms up to quadratic order in ˆs, ˆȷ, and ˆa′ gives ˆHHP ≃g r NJ 2 " ei˜ϕJ iˆpȷ −cos ˜θJ ˆxȷ − p f↑ sin ˜θJ ˆxs ˆa′+h.c. # −∆ cˆa′†ˆa′ −δ σ sec ˜θJ ˆȷ†ˆȷ. (D7) with cavity jump operator ˆℓHP = ˆa′. Setting∂ tˆa′ ≃0 ...

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    Elimination of the fast driven-manifold mode The remaining mode ˆȷrelaxes rapidly towards a steady-state behavior relative to the squeezing dynamics in ˆsand can likewise be adiabatically eliminated. Setting ∂tˆȷ≃0 gives ˆȷ=Vj(ˆs+ ˆs†),ˆȷ † =V ∗ j (ˆs+ ˆs†),(D12) with Vj = cja∗ j −c ∗ j bj |aj|2 − |bj|2 ,(D13) where cj = g2NJ sin ˜θJ p f↑ κ2 + 4∆2c κ+ 2i∆...

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