Luca Maggio, Danilo Triggiani, Paolo Facchi, Vincenzo Tamma
{"title":"Quantum-limited estimation of the frequency shift between two interfering photons by time sampling of their quantum beats","authors":"Luca Maggio, Danilo Triggiani, Paolo Facchi, Vincenzo Tamma","doi":"10.1140/epjp/s13360-025-06903-y","DOIUrl":null,"url":null,"abstract":"<div><p>We present a sensing scheme for estimating the frequency difference of two non-entangled photons. The technique consists of time-resolving sampling measurements at the output of a beam splitter. With this protocol, we can achieve the ultimate precision for the estimation of the frequency shift between two non-entangled photons, overcoming the limits in precision and the range of detection of frequency-resolving detectors employed in standard direct measurements of the frequencies. The sensitivity can be increased by increasing the coherence time of the photons. We show that, already with <span>\\(\\sim 1000\\)</span> sampling measurements, the Cramér–Rao bound for the specific input state chosen is saturated independently of the value of the difference in frequency.</p></div>","PeriodicalId":792,"journal":{"name":"The European Physical Journal Plus","volume":"140 10","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epjp/s13360-025-06903-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal Plus","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjp/s13360-025-06903-y","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We present a sensing scheme for estimating the frequency difference of two non-entangled photons. The technique consists of time-resolving sampling measurements at the output of a beam splitter. With this protocol, we can achieve the ultimate precision for the estimation of the frequency shift between two non-entangled photons, overcoming the limits in precision and the range of detection of frequency-resolving detectors employed in standard direct measurements of the frequencies. The sensitivity can be increased by increasing the coherence time of the photons. We show that, already with \(\sim 1000\) sampling measurements, the Cramér–Rao bound for the specific input state chosen is saturated independently of the value of the difference in frequency.
我们提出了一种估计两个非纠缠光子的频率差的传感方案。该技术包括在分束器的输出处进行时间分辨采样测量。利用该协议,我们可以达到估计两个非纠缠光子之间频移的最终精度,克服了标准频率直接测量中使用的频率分辨探测器在精度和探测范围上的限制。可以通过增加光子的相干时间来提高灵敏度。我们表明,已经通过\(\sim 1000\)采样测量,所选特定输入状态的cram r - rao界是饱和的,与频率差的值无关。
期刊介绍:
The aims of this peer-reviewed online journal are to distribute and archive all relevant material required to document, assess, validate and reconstruct in detail the body of knowledge in the physical and related sciences.
The scope of EPJ Plus encompasses a broad landscape of fields and disciplines in the physical and related sciences - such as covered by the topical EPJ journals and with the explicit addition of geophysics, astrophysics, general relativity and cosmology, mathematical and quantum physics, classical and fluid mechanics, accelerator and medical physics, as well as physics techniques applied to any other topics, including energy, environment and cultural heritage.