Comment on: "Coherent perfect absorption: Zero reflection without linewidth suppression"

This comment refutes a recent claim that the polaromechanical normal-mode splitting observed in a 2025 study is invalid, arguing that the splitting is indeed present in a narrow frequency range and that the critics' reliance on total decay rates defined by spectral poles is irrelevant to the effective decay rate vanishing under coherent perfect absorption conditions.

The Gist

The Big Picture: A Scientific "He Said, She Said"

Imagine two groups of scientists are looking at the same experiment, but they are arguing about what they see.

• Group A (The Authors of this paper): They say, "We saw a clear sign that two different things (light and magnetism) are shaking hands so tightly that they become a single super-entity. We call this 'strong coupling,' and we see it as a split in the signal."
• Group B (The Critics, Ref. [1]): They say, "No, you didn't. The split you see is an illusion. The energy is still leaking out too fast for them to really hold hands, and your graph is just hiding the truth."

This paper is Group A's reply. They are saying: "You are looking at the wrong part of the graph and using the wrong ruler to measure the speed. If you look at the right spot with the right tool, our 'strong handshake' is real."

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The Core Concepts (Translated)

To understand the argument, we need to translate three physics concepts into everyday terms:

1. The "Strong Handshake" (Normal-Mode Splitting)

Imagine two pendulums hanging next to each other. If you push one, the energy usually just sloshes back and forth. But if they are connected by a very strong spring, they stop acting like two separate things and start acting like one new, heavier thing. In physics, when this happens, the signal splits into two distinct peaks.

• The Argument: Group A says they see this split. Group B says, "The spring isn't strong enough; the energy is leaking away too fast for a split to happen."

2. The "Leaky Bucket" vs. The "Magic Sponge" (Decay Rate)

Usually, when energy enters a system (like a cavity), it leaks out like water from a bucket with holes. This is called "decay."

• The Critics' View: They measured the size of the bucket (the total system) and said, "Look, the bucket is full of holes. The water leaks out fast. You can't have a strong handshake here."
• The Authors' View: They say, "You are measuring the whole bucket, but we are using a Magic Sponge (Coherent Perfect Absorption or CPA) at a very specific frequency. This sponge catches the leaking water perfectly. For a tiny, split-second moment, the bucket has zero holes. The water stays put, allowing the handshake to happen."

3. The "Zoom Lens" Problem (Linear vs. Logarithmic Scales)

This is the visual part of the argument.

• The Critics' View: They looked at the graph on a "Linear Scale" (a standard ruler). They said, "We don't see the split. The line looks flat."
• The Authors' View: They say, "That's because the graph is dominated by a huge spike in the middle. It's like trying to see a tiny ant standing next to an elephant. The elephant (the big spike) makes the whole picture look dark and hides the ant (the split).
  • The Fix: If you zoom in on just the area around the elephant (or remove the elephant from the view), you can clearly see the ant. When we zoom in on that tiny, narrow frequency range, the split is clearly visible."

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The Authors' Three Main Points

Here is how they dismantle the critics' argument, point by point:

1. "The Split is Real, You Just Can't See It"

The critics claimed there was no split in the "linear" (standard) graph.

• The Reply: The authors admit the split is hard to see on the full graph because one part of the data is so huge it "blinds" the viewer. But if you zoom in on the specific frequency where the "Magic Sponge" (CPA) is active, the split appears clearly. It's like a hidden message that only appears when you look at the right magnification.

2. "The Leaking Stops at the Exact Moment"

The critics argued that the system loses energy too fast (high decay rate) to allow strong coupling.

• The Reply: The critics measured the average leak rate of the whole system. But the authors used a "Magic Sponge" (CPA) that creates a temporary "gain" (like a pump filling the bucket) that perfectly cancels out the leak.
  • Analogy: Imagine a sink with a hole in the bottom. Usually, water drains fast. But if you turn on a faucet exactly at the right pressure to fill the hole, the water level stays perfect. At that exact moment, the "leak" is zero. The authors say the strong coupling happens only during this perfect balance, in a very narrow frequency range. The critics were looking at the sink when the faucet was off.

3. "You Are Using the Wrong Ruler"

The critics used a standard formula (looking at the "poles" of the math) to measure how fast energy leaves.

• The Reply: The authors say, "That formula measures the total system, not the effective system we are creating."
  • Analogy: If you want to know how fast a car is going, you shouldn't measure the speed of the traffic jam it's stuck in; you should measure the speed of the car itself. The critics measured the "traffic jam" (the total background noise), which looks slow and steady. The authors measured the "car" (the effective decay rate), which, thanks to the Magic Sponge, is moving incredibly slowly (or stopped), allowing the strong coupling to happen.

The Conclusion

The authors conclude that the critics are wrong because:

1. They missed the split because they didn't zoom in enough.
2. They measured the wrong thing (total decay instead of effective decay).
3. They ignored the special "Magic Sponge" effect (CPA) that temporarily stops energy from leaking, allowing the "strong handshake" to occur.

In short: The critics looked at the forest and said, "No trees here." The authors say, "You're standing in the wrong spot. If you look at this specific tree (the CPA frequency), you'll see it clearly, and it's definitely there."

Technical Summary

1. Problem Statement

The paper addresses a controversy arising from a recent publication (Ref. [1], Phys. Rev. Research 8, 013261 (2026)) which challenges the validity of a previous experimental claim (Ref. [2], Nat. Commun. 16, 5652 (2025)).

• The Challenge: Ref. [1] argues that the polaromechanical normal-mode splitting (NMS) observed in Ref. [2] is not genuine. Their argument rests on two points:
  1. No true splitting is visible in the linear-scale spectrum.
  2. Under the CPA condition, the total/intrinsic decay rate (defined by the imaginary part of the pole of the total output spectrum) remains unchanged, implying no linewidth suppression necessary for strong coupling.
• The Authors' Stance: Shen and Li assert that Ref. [1]'s conclusions are either false or irrelevant. They argue that the NMS is real, observable in linear scales under specific conditions, and that the "total decay rate" metric used by Ref. [1] fails to capture the physics of CPA-induced strong coupling.

2. Methodology

The authors employ a combination of data re-analysis and theoretical derivation to refute the claims of Ref. [1]:

• Spectral Re-analysis: They re-examine the experimental data from Ref. [2], presenting it in both logarithmic (dB) and linear scales. Crucially, they demonstrate how dynamic range issues in linear plots can obscure splitting features and show that removing high-amplitude background data reveals the hidden splitting.
• Non-Hermitian Hamiltonian Theory: They utilize a non-Hermitian Hamiltonian framework for the cavity-magnon system. They derive the effective decay rates and coupling strengths, specifically focusing on the conditions where CPA induces an "effective gain" in the cavity mode.
• Spectral Pole vs. Zero Analysis: They distinguish between two mathematical definitions of decay rates:
  • Pole-based ($\gamma$): The imaginary part of the pole of the total output spectrum $S_{tot}$ (used by Ref. [1]).
  • Zero-based ($\gamma_{eff}$): The imaginary part of the zero of the output spectrum (proposed by the authors as the correct metric for CPA).

3. Key Contributions

The paper makes three primary technical contributions:

A. Demonstration of Linear-Scale NMS

The authors prove that NMS exists in the linear-scale spectrum, contrary to Ref. [1]'s claim.

• The Artifact: In the full linear-scale plot, the signal intensity in the red-shaded frequency range (near the CPA frequency) is orders of magnitude larger than the rest of the spectrum. This dynamic range compresses the rest of the plot, making the splitting appear invisible ("dark").
• The Solution: By excluding the high-amplitude background data (creating a "blank area" in the plot), the splitting becomes clearly visible.
• Quantitative Proof: The observed splitting is 53.8 kHz, which matches the theoretical prediction of $2|G_+| \approx 51.4$ kHz. This value significantly exceeds the effective decay rates ($\kappa_+ \approx 0.45$ kHz, $\kappa_{b,eff} \approx 0.4$ kHz), confirming the system is in the strong-coupling regime.

B. Theoretical Mechanism: CPA-Induced Effective Gain

The authors clarify the physical mechanism allowing strong coupling under CPA:

• Effective Gain: CPA creates a condition where the cavity mode acquires an effective gain ($\kappa'_a$) that balances the magnon loss rate ($\kappa_m$).
• Vanishing Decay: At the CPA frequency ($\omega_{CPA}$), the effective decay rate of the polariton becomes zero ($\kappa_+ = (-\kappa'_a + \kappa_m)/2 = 0$).
• Narrowband Nature: This vanishing decay rate and the resulting strong coupling ($G_+ > \kappa_+$) occur only in a narrow frequency range around $\omega_{CPA}$. This explains why the splitting is not visible over a wide frequency range, distinguishing it from conventional NMS.

C. Redefining the Decay Rate Metric

The authors argue that Ref. [1] used the wrong metric to judge the system:

• Invariance of Total Decay: They concede that the total/intrinsic decay rate (pole of $S_{tot}$) remains unchanged under CPA.
• Relevance of Effective Decay: However, they argue this parameter is irrelevant to the observed NMS. The correct parameter is the effective decay rate ($\gamma_{eff}$), defined by the zero of the output spectrum.
• Physical Significance: $\gamma_{eff}$ vanishes at the CPA frequency (monochromaticity), directly characterizing the linewidth suppression and the strong coupling condition. The FWHM of the inverse spectrum ($1/|S_{tot}|^2$) corresponds to $\gamma_{eff}$, not the standard FWHM of $|S_{tot}|^2$.

4. Results

• Validation of Strong Coupling: The re-analysis confirms that the polaromechanical system satisfies the strong coupling condition ($G_+ > \kappa_+$) in a narrow band around the CPA frequency.
• Refutation of Ref. [1]: The claim that "zero reflection implies no linewidth suppression" is shown to be a misinterpretation. While the total linewidth (pole) is unchanged, the effective linewidth (zero) is suppressed, enabling the observed splitting.
• Consistency: The experimental data (splitting of ~53.8 kHz) aligns perfectly with the theoretical prediction derived from the non-Hermitian Hamiltonian, validating the original findings of Ref. [2].

5. Significance

• Clarification of CPA Physics: The paper resolves a critical misunderstanding regarding Coherent Perfect Absorption. It establishes that CPA can induce effective gain and vanishing effective decay rates, enabling strong coupling in hybrid systems (cavity-magnon-phonon) that would otherwise be in the weak coupling regime.
• Methodological Correction: It highlights the importance of choosing the correct spectral metric (poles vs. zeros) when analyzing systems with coherent interference or CPA. Relying solely on the pole of the spectrum can lead to false negatives regarding strong coupling.
• Experimental Verification: It reinforces the validity of using CPA to engineer exceptional points (EPs) and PT-symmetric Hamiltonians in experimental setups, providing a robust framework for future studies in quantum optomechanics and magnonics.

In conclusion, Shen and Li demonstrate that the polaromechanical NMS is a genuine physical phenomenon driven by CPA-induced effective gain and vanishing effective decay rates, and that the criticisms raised by Ref. [1] stem from an inappropriate application of spectral analysis metrics.