The Signal
Photon Pairs Improve Loss Estimates in Whispering-Gallery Resonators
A theoretical study finds that indistinguishable photon pairs can improve estimates of optical loss in a whispering-gallery-mode resonator under particular coupling conditions. The modeled advantage depends on retaining information from pho
Quantum.world Team · Written with AI · fact-checked ·
“For estimating the round-trip amplitude transmission at resonance and away from critical coupling, the photon-pair probe gives a higher QFI than the coherent-state probe, and photon-number-resolved detection saturates this QFI.”
Elnaz Darsheshdar, Callum Jones, Seyed Mostafa Moniri, Antonio Vidiella-Barranco, Jolly Xavier and Frank Vollmer, the paper’s authors, write
A study submitted to arXiv on October 23, 2026, in a manuscript dated October 26, finds that indistinguishable photon pairs can improve estimates of optical loss in a whispering-gallery-mode resonator, but only under particular operating conditions. The authors compare the pairs with coherent light at the same mean photon number, using a model that places the resonator in one arm of a balanced Mach–Zehnder interferometer.
Two photons probe a resonator’s losses
Whispering-gallery-mode resonators confine light as it circulates around a curved surface. Changes to a sample can alter the resonator’s absorption, transmission or resonance frequency; the paper asks whether photon pairs provide an advantage for measuring those changes when light is lost inside the device.
In the proposed setup, one photon enters each input of the interferometer. Hong–Ou–Mandel interference at the first beam splitter produces a two-photon N00N state: the photons travel together in one arm or the other. One arm contains the resonator, while the second provides a reference. The comparison accounts for outcomes in which neither, one or both photons are lost, rather than considering only pairs that emerge together.
The authors calculate quantum Fisher information, a measure of the information a probe can carry about an unknown parameter. For estimating the resonator’s round-trip transmission at resonance, they find that the pair probe can outperform a coherent-state probe away from critical coupling. The gain comes from the different probabilities of losing zero, one or two photons—not simply from the doubled phase response of a two-photon state.
The model’s advantage depends on coupling
The improvement is not universal. For estimating phase alone, the paper finds no photon-pair advantage over the coherent-state benchmark. The authors also distinguish relative improvement from absolute sensitivity: a large ratio between probes can occur where the total information is small, while the highest absolute information lies near critical coupling, where the relative advantage approaches one.
The paper tests the calculation against unresolved detuning fluctuations using representative source and resonance-jitter widths of 6.3 MHz and 0.46 MHz, respectively. Their combined effective width is about 6.32 MHz. In that model, with a reference round-trip amplitude transmission of 0.9997, the calculated quantum Fisher information ratio at zero nominal detuning is about 1.41 for a coupling amplitude of 0.99900. The corresponding ratio for photon-number-resolved detection is about 1.37.
Those modeled gains did not persist at the two other coupling amplitudes examined, 0.99968 and 0.99980, which lie closer to critical coupling or in the undercoupled regime. The calculations therefore point to a specific operating window, rather than a general benefit from sending paired photons into a resonator.
Counting losses matters more than coincidences
Accessing the predicted gain requires photon-number-resolved detection: the measurement must distinguish the different output photon counts and retain information carried by loss events. At resonance, ideal photon-number-resolved detection reaches the pair probe’s calculated information limit at regular, noncritical operating points. The photon-pair trials must also be heralded or otherwise clocked so that an empty output can be told apart from a trial in which no pair entered.
Coincidence-only detection, which records whether a pair arrives together, discards information in the other outcomes. It becomes particularly inefficient near a transmission zero, where the resonator transmits almost no light. The proposed measurement therefore calls for more than a pair source and a resonator: it needs a readout capable of resolving the full set of relevant outcomes.
Absorption sensing remains a proposed use
The analysis extends mathematically to absorption, absorbance and pump–probe measurements when a sample’s signal changes the resonator’s loss more than its resonance frequency. The authors suggest that such a method could help measure weak absorption while limiting optical exposure, but they do not report an experimental demonstration or model a particular sample’s response.
They identify several steps needed to assess a real system: accounting for finite photon-pair bandwidth, detector inefficiency, dark counts, imperfect photon indistinguishability and source-heralding efficiency. If a sample also shifts the resonance frequency, the dispersive contribution must be included alongside absorption. For now, the paper’s concrete result is a conditional theoretical advantage for loss estimation, contingent on coupling and a detector that counts more than coincidences.