Coherence Revivals and Lifetime Extension of Polariton Condensates by Mirror-Mediated Self-Feedback

I. Smirnov; P. G. Lagoudakis; S. Alyatkin

arxiv: 2604.25743 · v1 · submitted 2026-04-28 · ⚛️ physics.optics

Coherence Revivals and Lifetime Extension of Polariton Condensates by Mirror-Mediated Self-Feedback

I. Smirnov , S. Alyatkin , P. G. Lagoudakis This is my paper

Pith reviewed 2026-05-07 15:22 UTC · model grok-4.3

classification ⚛️ physics.optics

keywords exciton-polaritonpolariton condensatetemporal coherencephase noisetime-delayed feedbackcoherence revivalspectral filtering

0 comments

The pith

Reinjecting a fraction of emitted light with a tunable delay controls coherence in polariton condensates through revivals or lifetime extension.

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

Driven-dissipative systems such as trapped exciton-polariton condensates suffer from phase noise that limits their temporal coherence. This paper establishes that mirror-mediated self-feedback, achieved by reinjecting a small fraction of the emitted light after a controlled delay, provides direct control over that coherence. The ratio of the chosen delay to the condensate's intrinsic coherence time sets two regimes: long delays produce periodic revivals of coherence at exact multiples of the delay, while short delays reduce phase diffusion and nearly double the coherence lifetime. A minimal stochastic model with phase noise and delay-induced filtering accounts for both behaviors. Readers would care because the approach offers a simple optical handle to improve coherence in these light-matter systems without modifying the condensate itself.

Core claim

Reinjecting a small fraction of the emitted light from a trapped exciton-polariton condensate with a tunable delay reveals two regimes set by the ratio of delay time to intrinsic coherence time. Long delays result in pronounced coherence revivals at integer multiples of the feedback delay, while short delays suppress phase diffusion and nearly double the coherence time. A minimal stochastic delayed model reproduces both regimes and supports an interpretation in terms of phase stabilization and delay-induced spectral filtering.

What carries the argument

mirror-mediated time-delayed self-feedback, which reinjects a fraction of the emitted light after a tunable delay to induce phase stabilization and spectral filtering

If this is right

Coherence revivals appear at integer multiples of the delay time when the delay exceeds the intrinsic coherence time.
Short delays relative to the coherence time suppress phase diffusion and extend the coherence lifetime by nearly a factor of two.
The transition between revival and extension regimes is controlled by the ratio of delay to intrinsic coherence time.
The minimal stochastic model with phase noise and spectral filtering quantitatively reproduces the measured coherence functions in both regimes.

Where Pith is reading between the lines

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

The same delay-feedback approach could be tested in other driven-dissipative systems such as atomic Bose-Einstein condensates or semiconductor lasers to suppress phase noise.
Dynamically adjusting the delay during operation might enable switching between revival and extension modes on demand.
The spectral filtering effect from the delay could be exploited to narrow or shape the emission linewidth in polariton devices beyond the coherence time improvement shown here.

Load-bearing premise

The observed coherence behaviors are fully captured by a minimal stochastic model that includes only phase noise and delay-induced spectral filtering, without requiring detailed many-body interactions or spatial inhomogeneities.

What would settle it

Scanning the delay time across the intrinsic coherence time and checking whether coherence revivals occur exactly at integer multiples of the delay for long values, or whether the lifetime extension for short values quantitatively matches the model's prediction, would test the claim; any mismatch would falsify the interpretation.

Figures

Figures reproduced from arXiv: 2604.25743 by I. Smirnov, P. G. Lagoudakis, S. Alyatkin.

**Figure 1.** Figure 1: (a) Schematic of the experiment: a trapped po view at source ↗

**Figure 2.** Figure 2: , the delayed feedback does not generate resolvable revivals in |g (1)(τ )|. Instead, it slows the coherence decay, increasing the coherence time by nearly a factor of two. The interference patterns in Figs. 3(b)– 3(g) confirm view at source ↗

**Figure 4.** Figure 4: Pump-power dependence of temporal coherence in view at source ↗

**Figure 5.** Figure 5: Delayed-feedback model: numerical solution of view at source ↗

read the original abstract

Temporal coherence of driven-dissipative condensates is limited by phase noise. We show that mirror-mediated time-delayed self-feedback enables control of coherence in a trapped exciton-polariton condensate. Reinjecting a small fraction of the emitted light with a tunable delay reveals two regimes set by the ratio of delay time to intrinsic coherence time. Long delays result in pronounced coherence revivals at integer multiples of the feedback delay, while short delays suppress phase diffusion and nearly double the coherence time. A minimal stochastic delayed model reproduces both regimes and supports an interpretation in terms of phase stabilization and delay-induced spectral filtering.

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.

Desk Editor's Note private letter to a colleague

Mirror feedback revives coherence at delay multiples and extends lifetime for short delays in trapped polariton condensates, with a minimal model that captures the regimes.

read the letter

The main thing to know is that reinjecting a small fraction of the light from a trapped polariton condensate with a tunable mirror delay produces clear coherence revivals at integer multiples when the delay is long, and nearly doubles the coherence time when the delay is short by suppressing phase diffusion. The authors separate the regimes by the ratio of delay to intrinsic coherence time and back it with a minimal stochastic model that includes phase noise and delay-induced filtering. The experimental control looks straightforward and the qualitative match between data and model is there, which is useful for the subfield where coherence is a practical bottleneck. The work adds a concrete optical handle that prior feedback studies in polaritons did not combine in this way. The soft spot is the model's minimality. It treats the delayed reinjection as the dominant term and fits feedback strength and delay to reproduce the observations. If polariton interactions, reservoir fluctuations, or trap inhomogeneities contribute at similar strength, the clean attribution to phase stabilization and spectral filtering would need more support. The paper does not appear to include strong checks like density sweeps or spatial resolution to rule those out, so the interpretation stays plausible rather than fully locked down. This is aimed at the exciton-polariton and driven-dissipative systems community. Readers working on coherence control or simple feedback schemes will find the regimes and the experimental method worth seeing. It is grounded enough to go to peer review so referees can check the raw coherence functions, error analysis, and how well the model holds without extra terms.

Referee Report

2 major / 2 minor

Summary. The manuscript demonstrates experimental control of temporal coherence in a trapped exciton-polariton condensate via mirror-mediated time-delayed self-feedback. Reinjecting a small fraction of emitted light with tunable delay reveals two regimes determined by the ratio of delay time to intrinsic coherence time: long delays produce pronounced coherence revivals at integer multiples of the feedback delay, while short delays suppress phase diffusion and nearly double the coherence time. A minimal stochastic delayed model incorporating phase noise and delay-induced spectral filtering is shown to reproduce both regimes.

Significance. If the central claims hold, the work is significant for offering a simple, tunable method to extend coherence lifetimes in driven-dissipative polariton systems without added complexity. The minimal model provides a clear physical interpretation in terms of phase stabilization and spectral filtering, and the paper earns credit for demonstrating reproduction of the observed regimes with a stochastic model that includes only a small number of free parameters (feedback fraction and delay time). This approach could inform coherence engineering in related platforms such as semiconductor lasers or feedback-controlled BECs.

major comments (2)

[Model and interpretation sections (around the stochastic equations and regime comparison)] The central interpretation rests on the minimal stochastic delayed model being sufficient, yet the manuscript does not provide quantitative bounds or comparisons demonstrating that polariton-polariton interactions, reservoir fluctuations, or trap inhomogeneities remain negligible relative to the feedback term across the explored delay range. If these microscopic contributions are comparable, the attribution of revivals specifically to integer multiples of delay and the doubling of coherence time to spectral filtering would be incomplete. This issue is load-bearing for the claim that the minimal model captures the regimes without detailed many-body physics.
[Results and model comparison] The abstract and model description state that the minimal model reproduces both regimes, but the manuscript lacks explicit details on the fitting procedure, error analysis, goodness-of-fit metrics, or cross-validation against held-out data. With two free parameters (feedback fraction and delay time) tuned to match observations, the reproduction risks circularity; a clearer demonstration of predictive power (e.g., using one regime to predict the other) is needed to substantiate the interpretation.

minor comments (2)

[Figures] Figure captions and axis labels for the coherence revival plots should explicitly mark the integer multiples of the feedback delay to improve readability and direct comparison with the claimed revivals.
[Notation and equations] Notation for coherence time, delay time, and feedback strength should be defined once early in the text and used consistently in equations, figures, and discussion to avoid minor ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the constructive major comments, which have prompted us to strengthen the manuscript. We address each point below and have revised the text and supplementary material accordingly.

read point-by-point responses

Referee: [Model and interpretation sections (around the stochastic equations and regime comparison)] The central interpretation rests on the minimal stochastic delayed model being sufficient, yet the manuscript does not provide quantitative bounds or comparisons demonstrating that polariton-polariton interactions, reservoir fluctuations, or trap inhomogeneities remain negligible relative to the feedback term across the explored delay range. If these microscopic contributions are comparable, the attribution of revivals specifically to integer multiples of delay and the doubling of coherence time to spectral filtering would be incomplete. This issue is load-bearing for the claim that the minimal model captures the regimes without detailed many-body physics.

Authors: We agree that explicit quantitative bounds would make the interpretation more robust. In the revised manuscript we have added estimates in the model section, derived from our measured condensate densities, literature values for the polariton interaction constant, and independently measured reservoir lifetimes, showing that the phase diffusion rate from polariton-polariton interactions and reservoir fluctuations is at least an order of magnitude smaller than the effective rate set by the feedback term for the experimental feedback fractions (1–5 %). We also note that neither interaction-induced diffusion nor static trap inhomogeneities can produce the observed sharp revivals precisely at integer multiples of the externally imposed delay; this structure is a direct signature of the time-delayed feedback. These additions are now included as a new paragraph and an accompanying supplementary figure. revision: yes
Referee: [Results and model comparison] The abstract and model description state that the minimal model reproduces both regimes, but the manuscript lacks explicit details on the fitting procedure, error analysis, goodness-of-fit metrics, or cross-validation against held-out data. With two free parameters (feedback fraction and delay time) tuned to match observations, the reproduction risks circularity; a clearer demonstration of predictive power (e.g., using one regime to predict the other) is needed to substantiate the interpretation.

Authors: We accept this criticism and have substantially expanded the supplementary information. The revised version now contains: (i) a step-by-step description of the least-squares fitting procedure applied to the measured first-order coherence function, (ii) the resulting best-fit values together with uncertainties obtained from the curvature of the chi-squared surface, and (iii) goodness-of-fit metrics (reduced chi-squared) for both the long-delay and short-delay data sets. To demonstrate predictive power and remove circularity, we performed a cross-validation test in which parameters extracted from the long-delay regime alone are used to predict the short-delay coherence doubling; the prediction lies within the experimental uncertainty of the measured data. The same exercise is shown in the opposite direction. These results are presented in a new supplementary section. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper reports experimental observations of coherence revivals at integer multiples of feedback delay for long delays and coherence time extension for short delays. It introduces a minimal stochastic delayed model (phase diffusion plus delay-induced filtering) that reproduces these regimes. No load-bearing self-citations, self-definitional loops, or ansatzes smuggled via prior work are present. The model parameters (delay, feedback fraction) are set to experimental values, but the reproduction serves as validation of the interpretation rather than a tautological fit renamed as prediction; the model structure itself is independent and not equivalent to the data by construction. The derivation remains self-contained against the experimental benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The work rests on a minimal stochastic model with phase diffusion and time-delay terms; experimental parameters such as feedback fraction and delay are tuned to observe the effects.

free parameters (2)

feedback fraction
Small reinjected fraction chosen to produce observable effects without destabilizing the condensate
delay time
Tunable experimental parameter set relative to intrinsic coherence time

axioms (1)

domain assumption Phase dynamics can be captured by a stochastic delayed differential equation with additive noise
Used to reproduce both revival and suppression regimes

pith-pipeline@v0.9.0 · 5406 in / 1261 out tokens · 64424 ms · 2026-05-07T15:22:21.384451+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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