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arxiv: 2506.12267 · v1 · submitted 2025-06-13 · 🪐 quant-ph

Fully Collective Superradiant Lasing with Vanishing Sensitivity to Cavity Length Vibrations

Jarrod T. Reilly , Simon B. J\"ager , John Cooper , Murray J. Holland This is my paper

Pith reviewed 2026-05-19 08:59 UTC · model grok-4.3

classification 🪐 quant-ph
keywords superradiant lasercollective pumpingatomic clockcavity couplingvibration sensitivitymulti-level atomscontinuous wave
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The pith

Multi-level atoms coupled to two cavities enable a superradiant laser with vibration sensitivity that can vanish at steady state.

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

The paper establishes that using an auxiliary cavity to couple to a distinct transition in multi-level atoms turns repumping into a fully collective process. This solves the problem of parasitic heating from spontaneous emission in attempts at continuous-wave active atomic clocks. With relevant atomic parameters, the system supports an O(100 microhertz) linewidth laser. Importantly, it identifies regimes where the sensitivity to cavity length vibrations is below O(10^{-14} per g) and can be exactly zero.

Core claim

Using multi-level atoms with collective pumping and decay on distinct transitions, the authors show that coupling to an auxiliary cavity makes the repumping process fully collective. This allows the system to overcome the lack of a generic lasing threshold found in two-level models and to operate as a continuous-wave superradiant laser with a linewidth of order 100 microhertz. The principal result is an operating regime, including specific parameter values, where the sensitivity to cavity length vibrations falls below order 10 to the minus 14 per g and vanishes completely even in the steady state.

What carries the argument

The auxiliary cavity that enforces fully collective repumping on a separate atomic transition from the lasing transition in the multi-level system.

If this is right

  • The system produces a continuous-wave superradiant laser with linewidth of O(100 μhz).
  • Vibration sensitivity to cavity length can be below O(10^{-14}/g).
  • Sensitivity can vanish at certain steady-state parameter values.
  • Distinct transitions for pumping and decay enable collective effects beyond two-level limits.

Where Pith is reading between the lines

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

  • This collective repumping approach may extend to other quantum optical systems for reducing environmental sensitivities.
  • It could lead to testable predictions for frequency stability in lab-based atomic clock prototypes.
  • The vanishing sensitivity point might serve as a robust operating condition for precision measurements insensitive to mechanical noise.

Load-bearing premise

The chosen multi-level atomic model with distinct transitions for collective pumping and decay holds without additional decoherence, losses, or non-collective effects in a real setup.

What would settle it

A direct measurement of the laser frequency's dependence on cavity length showing sensitivity greater than 10^{-14} per g or the inability to maintain the narrow linewidth due to unmodeled effects would disprove the central claim.

Figures

Figures reproduced from arXiv: 2506.12267 by Jarrod T. Reilly, John Cooper, Murray J. Holland, Simon B. J\"ager.

Figure 1
Figure 1. Figure 1: FIG. 1. The SU(3) superradiant laser. (a) Experimental con [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison between the fully collective SU(2) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Steady-state properties of the SU(3) superradiant laser [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

To date, realization of a continuous-wave active atomic clock has been elusive primarily due to parasitic heating from spontaneous emission while repumping the atoms. Here, we propose a solution to this problem by replacing the random emission with coupling to an auxiliary cavity, making repumping a fully collective process. While it is known that collective two-level models do not possess a generic lasing threshold, we show this restriction is overcome with multi-level atoms since collective pumping and decay can be performed on distinct transitions. Using relevant atomic parameters, we find this system is capable of producing an $\mathcal{O}$(100 $\mu$Hz)-linewidth continuous-wave superradiant laser. Our principal result is the potential for an operating regime with cavity length vibration sensitivity below $\mathcal{O}(10^{-14} / g)$, including a locus of parameter values where it completely vanishes even at steady-state.

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 multi-level atomic scheme for fully collective superradiant lasing in which collective pumping and decay occur on distinct transitions. This overcomes the absence of a generic lasing threshold in two-level collective models. Using relevant atomic parameters, the authors calculate an O(100 μHz) linewidth continuous-wave laser and identify an operating regime with cavity-length vibration sensitivity below O(10^{-14}/g), including a locus of parameters where the sensitivity vanishes exactly at steady state.

Significance. If the vanishing-sensitivity result holds under realistic conditions, the work would constitute a notable step toward practical continuous-wave active atomic clocks by removing parasitic heating from spontaneous emission and suppressing a dominant technical noise source. The multi-level collective approach is a direct extension of standard quantum-optics rate equations and therefore builds on established methods while addressing a concrete experimental limitation.

major comments (2)
  1. [Steady-state master-equation solution and sensitivity derivation] The exact cancellation that produces zero sensitivity is obtained from the steady-state solution of the master equation after setting single-atom spontaneous emission, inhomogeneous broadening, and non-collective scattering rates to zero or to the chosen parameter values. No quantitative robustness analysis is provided showing how small, physically unavoidable additions to these rates displace the zero-sensitivity locus or restore finite sensitivity at the 10^{-12}–10^{-13}/g level.
  2. [Abstract and principal-results section] The abstract asserts that calculations with relevant atomic parameters support both the linewidth and the sensitivity claims, yet the manuscript supplies neither explicit derivations of the steady-state frequency pull nor an error budget that quantifies the effect of the neglected decoherence channels on the reported O(10^{-14}/g) bound.
minor comments (2)
  1. [Results and parameter tables] The order-of-magnitude notation O(100 μHz) and O(10^{-14}/g) is acceptable for an initial proposal but would benefit from at least one concrete numerical example or table entry that shows the exact parameter set yielding the zero-sensitivity point.
  2. [Introduction and model section] A brief comparison figure or paragraph contrasting the multi-level collective threshold with the known two-level collective case would help readers immediately see where the new operating regime appears.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. The positive assessment of the work's potential significance for continuous-wave active atomic clocks is appreciated. Below we provide point-by-point responses to the major comments. We agree that additional analysis is needed to strengthen the presentation and will incorporate the requested elements in a revised manuscript.

read point-by-point responses

  1. Referee: [Steady-state master-equation solution and sensitivity derivation] The exact cancellation that produces zero sensitivity is obtained from the steady-state solution of the master equation after setting single-atom spontaneous emission, inhomogeneous broadening, and non-collective scattering rates to zero or to the chosen parameter values. No quantitative robustness analysis is provided showing how small, physically unavoidable additions to these rates displace the zero-sensitivity locus or restore finite sensitivity at the 10^{-12}–10^{-13}/g level.

    Authors: We agree that the exact vanishing of sensitivity is obtained in the idealized steady-state solution where single-atom spontaneous emission, inhomogeneous broadening, and non-collective scattering rates are set to zero. This isolates the fully collective regime and reveals the parameter locus at which the frequency pull cancels exactly. In the revised manuscript we will add a quantitative robustness section. Small but finite values for these rates, chosen to match realistic experimental conditions for the atomic species under consideration, will be introduced into the master equation. We will then map the resulting displacement of the zero-sensitivity locus and show that the vibration sensitivity remains below the O(10^{-14}/g) target for parameter ranges consistent with current cavity and atomic technology. revision: yes

  2. Referee: [Abstract and principal-results section] The abstract asserts that calculations with relevant atomic parameters support both the linewidth and the sensitivity claims, yet the manuscript supplies neither explicit derivations of the steady-state frequency pull nor an error budget that quantifies the effect of the neglected decoherence channels on the reported O(10^{-14}/g) bound.

    Authors: The abstract summarizes results obtained from numerical integration of the multi-level master equation using realistic atomic parameters. The steady-state frequency pull follows from the imaginary part of the collective eigenvalues once the system reaches the steady-state density matrix. To make this explicit, the revised manuscript will include a dedicated subsection deriving the frequency pull from the phase equation of the collective field and from the steady-state coherence. In addition, we will provide an error-budget table that estimates the contribution of each neglected decoherence channel (residual single-atom emission, inhomogeneous broadening, and non-collective scattering) to the vibration sensitivity, confirming that the O(10^{-14}/g) bound is preserved within the stated parameter regime. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation self-contained from master-equation steady state

full rationale

The paper solves the steady-state master equation for a multi-level collective system with distinct pumping and decay transitions to obtain the sensitivity to cavity-length vibrations, including the locus where it vanishes. This follows directly from the rate equations without any fitted parameter being relabeled as a prediction, without self-definitional closure, and without load-bearing self-citations that substitute for independent derivation. The result is a computed operating point from the chosen parameters and is externally falsifiable by experiment or by adding omitted decoherence channels; no step reduces by construction to its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard collective-atom rate equations, the known absence of a generic lasing threshold in two-level models, and a set of realistic but unspecified atomic parameters used to obtain the numerical linewidth and sensitivity values.

free parameters (1)
  • relevant atomic parameters
    Numerical values for decay rates, coupling strengths, and detunings drawn from a chosen atomic species to compute the 100 μHz linewidth and the 10^{-14}/g sensitivity bound.
axioms (1)
  • standard math Collective two-level models do not possess a generic lasing threshold
    Invoked explicitly in the abstract to motivate the switch to multi-level atoms.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. One knob to tune them all: Phase-controlled photon statistics and linewidth in partially pumped atomic ensembles

    quant-ph 2026-04 unverdicted novelty 6.0

    In partially pumped atomic ensembles, a tunable relative phase between pumped and unpumped emission contributions allows control of linewidth scaling and photon statistics from antibunched to bunched.

  2. One knob to tune them all: Phase-controlled photon statistics and linewidth in partially pumped atomic ensembles

    quant-ph 2026-04 unverdicted novelty 6.0

    In a minimal model of partially pumped atomic ensembles, collective dissipation induces interference that allows tuning linewidth from size-independent to extensive and photon statistics from antibunched to bunched vi...

Reference graph

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    Cases 14 C. Linewidth 14 D. Cavity pulling 16 References 17 I. DERIV A TION OF SU(3) SUPERRADIANT LASING MODEL In this section, we derive the SU(3) superradiant lasing model stud ied in the main text. A. Double cavity system Based on the couplings depicted in Fig. 1 of the main text, we begin with the Hamiltonian ˆH1 =ℏÉ xˆa xˆax + ℏÉ zˆa zˆaz + N∑ j=1 [ ...

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    We can describe the action of all superoperators in each k-sector where we find ˆ ˆL[ ˆR+] |k, r, r 3, r ′ 3ðð= √(r − r3)(r + r3 + 1) |k, r, r 3 + 1, r ′ 3ðð, (S38a) ˆ ˆR[ ˆR+] |k, r, r 3, r ′ 3ðð= √ ( r − k 2 + r′ 3 ) ( r − k 2 − r′ 3 + 1 ) |k, r, r 3, r ′ 3 − 1ðð, (S38b) ˆ ˆL[ ˆR− ] |k, r, r 3, r ′ 3ðð= √(r + r3)(r − r3 + 1) |k, r, r 3 − 1, r ′ 3ðð, (S38...

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    Here, we have an incoherent mixture of ˆ Ämf = ( |dð ïd|+ |sð ïs|)/ 2 which gives ïˆrzðss ≈ 0 while ïˆczðss ≈ ï ˆpzðss ≈ − 1/ 2

    All atoms in the ground states Fixing Ω at a suitably large value, the regime W j Γ c, Ω/N leads to the system essentially just performing damped Rabi flopping. Here, we have an incoherent mixture of ˆ Ämf = ( |dð ïd|+ |sð ïs|)/ 2 which gives ïˆrzðss ≈ 0 while ïˆczðss ≈ ï ˆpzðss ≈ − 1/ 2. Meanwhile, the coherences all decay to zero, ïˆc− ðss ≈ ï ˆp− ðss ≈ ...

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    This state gives ïˆrzðss ≈ 0, ïˆczðss ≈ ï ˆpzðss ≈ 1, and again ïˆc− ðss ≈ ï ˆp− ðss ≈ ï ˆr− ðss ≈ 0

    All atoms in the excited state In the opposite limit, W k Ω/N > Γ c, the atoms are pumped into the |uð state and thus we have to determine the stability of ˆÄmf = |uð ïu|. This state gives ïˆrzðss ≈ 0, ïˆczðss ≈ ï ˆpzðss ≈ 1, and again ïˆc− ðss ≈ ï ˆp− ðss ≈ ï ˆr− ðss ≈ 0. Plugging these steady-state values into Eq. (S59), we find ∂(¶ˆc− ) ∂t = iΩ 2 ¶ˆp− +...

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    Cases Combining our four conditions for stability together, we get three cases for the thresholds:

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    Case N Γc 2 < Ω < N Γ c: We expect lasing when W > Γ c and no lasing when W < Γ c, and so the threshold is W = Γ c

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    Case N Γc < Ω : We expect lasing when W > Ω2 N 2Γc and no lasing when W < Ω2 N 2Γc , and so the threshold is Ω = N √ W Γc. C. Linewidth We now calculate the linewidth of the output light. The general idea i s to use a phase diffusion argument which allows us to determine the coherence time of the mean-field quantit ies c, p, and r. The mean-field solution br...

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