{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:41:46Z","timestamp":1760233306731,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000104","name":"SBIR NASA","doi-asserted-by":"publisher","award":["80NSSC22PB067"],"award-info":[{"award-number":["80NSSC22PB067"]}],"id":[{"id":"10.13039\/100000104","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields\u2026 While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.<\/jats:p>","DOI":"10.3390\/s23010301","type":"journal-article","created":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T05:38:43Z","timestamp":1672205923000},"page":"301","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Phase Nanoscopy with Correlated Frequency Combs"],"prefix":"10.3390","volume":"23","author":[{"given":"Xiaobing","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Optical Science and Engineering, University of New Mexico, Albuquerque, NM 87106, USA"},{"name":"Center for High Technology Materials, University of New Mexico, Albuquerque, NM 87106, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6144-8456","authenticated-orcid":false,"given":"Matthias","family":"Lenzner","sequence":"additional","affiliation":[{"name":"Lenzner Research, 125 E Canyon View Dr, Tucson, AZ 85704, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Claude","family":"Diels","sequence":"additional","affiliation":[{"name":"School of Optical Science and Engineering, University of New Mexico, Albuquerque, NM 87106, USA"},{"name":"Center for High Technology Materials, University of New Mexico, Albuquerque, NM 87106, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1364\/JOSAB.16.002255","article-title":"Ultrasensitive frequency-modulation spectroscopy enhanced by a high-finesse optical cavity","volume":"16","author":"Ma","year":"1999","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/JQE.1972.1076854","article-title":"Ultrasensitive response of a cw dye laser to selective extinction","volume":"8","author":"Schawlow","year":"1972","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/S0030-4018(00)00483-1","article-title":"Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry\u2013Perot reference cavity","volume":"175","author":"Jones","year":"2000","journal-title":"Opt. Comm."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3568","DOI":"10.1103\/PhysRevLett.82.3568","article-title":"Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser","volume":"82","author":"Udem","year":"1999","journal-title":"Phys. Rev. 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Sensors, 22.","DOI":"10.3390\/s22093200"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1364\/OL.35.001181","article-title":"Precise intracavity phase measurement in an optical parametric oscillator with two pulses per cavity round-trip","volume":"35","author":"Velten","year":"2010","journal-title":"Opt. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"125403","DOI":"10.1088\/1612-2011\/11\/12\/125403","article-title":"Subharmonic synchronously intracavity pumped picosecond optical parametric oscillator for intracavity phase interferometry","volume":"11","author":"Vyhlidal","year":"2014","journal-title":"Laser Phys. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1694","DOI":"10.1103\/PhysRevD.23.1693","article-title":"Quantum-mechanical noise in an interferometer","volume":"23","author":"Caves","year":"1981","journal-title":"Phys. Rev. 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