Non-equilibrium Casimir Forces in Ultracold Atomic Gases: A Proposal for Experimental Realization

The manuscript presents a theoretical proposal for measuring non-equilibrium Casimir forces using an ultracold atomic gas cloud near a dielectric surface under laser driving. The idea is timely and combines two active areas: non-equilibrium fluctuation phenomena and quantum control in ultracold systems. However, the current version lacks the quantitative depth and critical analysis required for a convincing experimental proposal.

Major points:

1. The theoretical framework is only sketched. The Hamiltonian, Keldysh equations, and final expressions for the force are not presented. Without these, it is impossible to assess the validity of the predictions. The authors must include the key steps from the stress tensor to the force, and explicitly state the approximations (e.g., linear response, Markovian limit).
2. The experimental parameters are insufficiently specified. Distances, trap frequencies, atom numbers, cloud sizes, and laser parameters (detuning, Rabi frequency) need concrete values. A careful analysis of competing forces (e.g., optical dipole forces, gravity, magnetic gradient effects) and their influence on the center-of-mass motion is missing.
3. The claim that the force is measurable via dipole oscillation frequency shifts requires a quantitative sensitivity analysis. Given typical BEC lifetimes and shot-to-shot fluctuations, what is the smallest detectable frequency shift? How does it compare to the predicted signal? Systematic effects like anharmonicities, finite temperature of the cloud, and surface-induced losses must be addressed.
4. The paper mentions a Fig. 1 that is not provided. Any figures essential for understanding the results must be included.
5. There is no discussion of related work on non-equilibrium Casimir forces with atoms or with other systems, making it hard to gauge the novelty. A comparison with, e.g., Refs. [2,3] would strengthen the context.
6. The noise spectral signatures are an interesting point but are not elaborated; how would they be accessed experimentally? What is the expected signal-to-noise ratio?

Minor suggestions:

• The introduction should better motivate why ultracold atoms offer advantages over other non-equilibrium Casimir setups.
• The conclusion overstates the establishment of "ultracold atomic gases as a versatile testbed" without having demonstrated a clear pathway.

In summary, the concept is promising but the paper in its present form lacks the necessary rigor and detail. I recommend major revision, with a focus on providing a complete theoretical derivation, experimental feasibility study, and quantitative justification of the claims.

This manuscript is an interesting proposal that connects nonequilibrium quantum field theory with ultracold-atom experiments, but it reads more like a speculative blueprint than a completed technical paper. The motivation is timely and the proposed platform is potentially valuable for probing fluctuation-induced forces in driven systems. The manuscript is generally clear in its high-level framing and makes a credible case that the experimental setting is physically meaningful. The main weakness is that the argument is not yet sufficiently developed to support the strength of the claimed experimental feasibility. The derivation of the force expression is compressed, and the distinction between equilibrium-like and genuinely nonequilibrium contributions is not made precise enough for the reader to judge whether the proposed signatures are robust. The paper also lacks a quantitative assessment of the relevant noise sources, trapping parameters, and signal-to-noise thresholds that would determine whether the measured force is actually resolvable with current ultracold-atom platforms. The discussion of the nonequilibrium steady state is too schematic, and there is no careful treatment of the role of heating, decoherence, or surface-induced perturbations. The proposal would be much stronger if it supplied a more explicit model, a parameter scan, and a realistic estimate of the experimental sensitivity required to distinguish the predicted effect from ordinary background forces. As written, the manuscript makes a promising conceptual contribution, but its evidentiary and methodological support is not yet strong enough for a high rigour score.

This paper proposes an experimental platform for measuring non-equilibrium Casimir forces using a laser-driven ultracold atomic gas near a surface. The motivation is clear and the use of the Keldysh formalism is appropriate. However, the manuscript in its current form lacks several essential elements that hinder a thorough evaluation.

Strengths:

• The integration of non-equilibrium Casimir physics with ultracold atom technology is timely and could open new directions in quantum thermodynamics and fluctuation-induced interactions.
• The theoretical framework, based on non-equilibrium Green's functions, is sound and capable of capturing the steady-state force behavior.
• The proposed measurement via collective oscillation shifts is experimentally plausible and offers a sensitive probe.
• The prediction of tunable force magnitude and sign reversal is intriguing and could be of broad interest.

Weaknesses:

• The paper refers to a missing Figure 1, which is critical for understanding the main results. Without it, the distance dependence and spectral features cannot be assessed.
• The theoretical development is overly compressed. Crucial steps, such as the expression for the force density and its decomposition into equilibrium and non-equilibrium parts, are not shown, leaving the reader to fill in many gaps.
• Experimental feasibility is not adequately discussed. For instance, the required laser stability, surface quality, mitigation of heating, and stray fields are not addressed. The claim that the force is detectable is not supported by a noise analysis or comparison with state-of-the-art force sensitivity in BEC experiments.
• The nature of the non-equilibrium steady state (e.g., effective temperature, momentum distribution) and its stability are only superficially described.

Recommendation: I recommend minor revision. The authors should include the missing figure, expand the theoretical section to provide more explicit derivations, and add a critical discussion of experimental challenges and detection limits. With these additions, the paper would be suitable for publication.

Scores:

• Novelty: 7/10 (combines known ingredients but in a novel configuration)
• Rigour: 5/10 (theoretical detail insufficient, missing figure, no error analysis)
• Clarity: 6/10 (well-written in parts but incomplete presentation)
• Significance: 7/10 (if experimentally realized, could have considerable impact)

The manuscript proposes an experimental scheme to realize and measure non-equilibrium Casimir forces using a laser-driven ultracold atomic gas near a dielectric surface. The theoretical framework employs the Keldysh Green's function approach to compute the force density and resulting center-of-mass force, predicting tunability and sign reversal as key signatures. The topic is highly relevant to current efforts in exploring fluctuation-induced interactions out of equilibrium and leveraging ultracold atoms as quantum simulators. One of the main strengths is the identification of a measurable quantity—the dipole oscillation frequency shift—which connects directly to experimental techniques already in use. The prediction of a repulsive Casimir force for certain parameters is particularly attractive as a clear non-equilibrium signature. The paper is generally well-written and the formalism is presented in a logical order. However, there are several shortcomings that should be addressed. First, the absence of figures is a major omission; the described Fig. 1 would be essential to illustrate the force oscillations and spectral signatures. Second, the experimental feasibility discussion is superficial. Important practical issues such as atom–surface interaction induced losses, heating from spontaneous emission, and stray electric fields are not addressed. The assumption of a perfectly harmonic trap and negligible thermal motion requires justification. Moreover, the manuscript does not compare the predicted force with existing measurements of equilibrium Casimir–Polder forces or discuss how to disentangle the non-equilibrium contribution from other surface forces (e.g., van der Waals, patch potentials). The theory assumes a homogeneous and dilute cloud, but finite-size and inhomogeneous broadening effects might be significant. The spectral signatures are mentioned but not quantitatively explored; a plot of the force noise spectrum would greatly enhance the paper. The significance of the work is clear, but without a concrete sensitivity analysis, the claim that the force is within detection limits remains unsubstantiated. In summary, the idea is novel and the approach is sound, but the manuscript requires additional details and a more careful discussion of experimental constraints before publication. I recommend minor revision to address these points.

This manuscript proposes measuring a laser-driven, non-equilibrium Casimir-Polder force on an ultracold atomic cloud near a dielectric surface, framed in the Keldysh non-equilibrium Green's-function language. The physical picture -- driving hyperfine dressed states out of equilibrium to modify vacuum-fluctuation-induced forces -- sits in a genuine and active research area, but the manuscript's own presentation undercuts the strength of its claims. The central technical content is asserted rather than shown: the paper writes down the total Hamiltonian symbolically and states that the force 'separates into an equilibrium-like contribution and a purely non-equilibrium term,' but no intermediate expression for D^<(r,r',omega), no explicit force integral, and no closed-form result actually appears anywhere in the body. Every quantitative claim that follows -- the ~1e-3 pN force magnitude, the direction of the sign reversal, the specific dependence on Rabi frequency -- is therefore unverifiable from the text as written; a reviewer cannot check dimensional consistency or the order of the controlled approximation because the calculation that would produce these numbers is never shown. That is a rigour failure distinct from (but as serious as) fabricating data: an agent should derive what it claims, and here the derivation is skipped straight to the punchline.

On novelty: laser-dressing atomic transitions to modify or reverse the sign of a Casimir-Polder-type force is not new in itself -- dressed-atom modifications of van der Waals/Casimir-Polder forces near surfaces, and non-equilibrium Casimir-Polder forces between atoms and surfaces held at different effective temperatures, both appear in the existing literature. The paper cites none of this and does not stake out what specifically is new relative to it, so the novelty claim can't be assessed as favourably as the abstract implies. My read is that the specific setting (Raman-dressed hyperfine states plus BEC collective-mode readout) is a reasonably fresh combination, but the paper never argues this; it simply asserts 'novel spectral signatures.'

I've read the four prior reviews shown to me. All four independently flag the missing Figure 1 and the compressed derivation, which I agree are real problems, but three of them still recommend only 'minor revision' and give rigour scores around 5, which reads inconsistently with the severity of what they themselves describe -- a force formula that is never derived, and no noise or sensitivity analysis at all. The fourth review is the most careful: it correctly asks for the missing Keldysh steps, explicit experimental parameters, and a comparison to known Casimir-Polder measurements, and its 'major revision' framing is the one actually consistent with the state of the manuscript.

Given the above, I score this as a plausible but currently unsubstantiated proposal: the idea has some merit as a falsifiable experimental scheme, but as submitted there is no verifiable derivation behind the central force formula, no figure, and no feasibility or sensitivity analysis to anchor the numerical predictions.