{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T23:24:05Z","timestamp":1762039445479,"version":"build-2065373602"},"reference-count":45,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,5,26]],"date-time":"2021-05-26T00:00:00Z","timestamp":1621987200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deutsche Forschungsge-meinschaft (DFG) within the Emmy-Noether-Programm","award":["RA 2842\/1-1"],"award-info":[{"award-number":["RA 2842\/1-1"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We theoretically analyze the phase sensitivity of the Induced-Coherence (Mandel-Type) Interferometer, including the case where the sensitivity is \"boosted\" into the bright input regime with coherent-light seeding. We find scaling which reaches below the shot noise limit, even when seeding the spatial mode which does not interact with the sample \u2013 or when seeding the undetected mode. It is a hybrid of a linear and a non-linear (Yurke-Type) interferometer, and aside from the supersensitivity, is distinguished from other systems by \"preferring\" an imbalance in the gains of the two non-linearities (with the second gain being optimal at <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">low<\/mml:mtext><\/mml:mrow><\/mml:math> values), and non-monotonic behavior of the sensitivity as a function of the gain of the second non-linearity. Furthermore, the setup allows use of subtracted intensity measurements, instead of direct (additive) or homodyne measurements \u2013 a significant practical advantage. Bright, super-sensitive phase estimation of an object with different light fields for interaction and detection is possible, with various potential applications, especially in cases where the sample may be sensitive to light, or is most interesting in frequency domains outside what is easily detected, or when desiring bright-light phase estimation with sensitive\/delicate detectors. We use an analysis in terms of general squeezing and discover that super-sensitivity occurs only in this case \u2013 that is, the effect is not present with the spontaneous-parametric-down-conversion approximation, which many previous analyses and experiments have focused on.<\/jats:p>","DOI":"10.22331\/q-2021-05-26-458","type":"journal-article","created":{"date-parts":[[2021,5,26]],"date-time":"2021-05-26T09:00:53Z","timestamp":1622019653000},"page":"458","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Versatile Super-Sensitive Metrology Using Induced Coherence"],"prefix":"10.22331","volume":"5","author":[{"given":"Nathaniel R.","family":"Miller","sequence":"first","affiliation":[{"name":"University of Dayton, Department of Physics, Dayton, OH, 45469, United States"},{"name":"Louisiana State University, Department of Physics and Astronomy, Baton Rouge, LA, 70803, United States"}]},{"given":"Sven","family":"Ramelow","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Humboldt-University Berlin, Berlin 12489, Germany"}]},{"given":"William N.","family":"Plick","sequence":"additional","affiliation":[{"name":"University of Dayton, Department of Physics, Dayton, OH, 45469, United States"}]}],"member":"9598","published-online":{"date-parts":[[2021,5,26]]},"reference":[{"key":"0","unstructured":"``Ein neuer Interferenzrefraktor'', L. Zehnder, Zeitschrift f\u00fcr Instrumentenkunde 11, 275 (1891)."},{"key":"1","unstructured":"``\u00dcber einen Interferenzrefraktor'', L. Mach, Zeitschrift f\u00fcr Instrumentenkunde 12, 89 (1892)."},{"key":"2","doi-asserted-by":"publisher","unstructured":"``Quantum-mechanical noise in an interferometer'', C.M. Caves, Phys. Rev. D 23, 1693 (1981).","DOI":"10.1103\/PhysRevD.23.1693"},{"key":"3","doi-asserted-by":"publisher","unstructured":"``Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light'', The LIGO Scientific Collaboration, Nat. Photonics 7, 613 (2013).","DOI":"10.1038\/nphoton.2013.177"},{"key":"4","doi-asserted-by":"publisher","unstructured":"``Quantum optical metrology \u2014 the lowdown on high-N00N states'', J.P. Dowling, Contemp. Phys. 49, 125 (2008).","DOI":"10.1080\/00107510802091298"},{"key":"5","doi-asserted-by":"publisher","unstructured":"``Quantum-enhanced interferometry with weak thermal light'', S.M.H. Rafsanjani, M. Mirhosseini, O.S. Maga\u00f1a-Loaiza, B.T. Gard, R. Birrittella, B.E. Koltenbah, C.G. Parazzoli, B.A. Capron, C.C. Gerry, J.P. Dowling, and R.W. Boyd, Optica 4, 487 (2017).","DOI":"10.1364\/OPTICA.4.000487"},{"key":"6","doi-asserted-by":"publisher","unstructured":"``Nonlinear interferometers in quantum optics'', M.V. Chekhova, and Z.Y. Ou, Advances in Optics and Photonics 8, 104 (2016).","DOI":"10.1364\/AOP.8.000104"},{"key":"7","doi-asserted-by":"publisher","unstructured":"``Quantum SU(1,1) interferometers: Basic principles and applications'', Z.Y. Ou, and X. Li, APL Photonics 5, 080902 (2020).","DOI":"10.1063\/5.0004873"},{"key":"8","doi-asserted-by":"publisher","unstructured":"``SU(2) and SU(1,1) interferometers'', B. Yurke, S.L. McCall, and J.R. Klauder, Phys. Rev. A 33, 4033 (1985).","DOI":"10.1103\/PhysRevA.33.4033"},{"key":"9","doi-asserted-by":"publisher","unstructured":"``Coherent-light-boosted, sub-shot noise, quantum interferometry'', W.N. Plick, J.P. Dowling, and G.S. Agarwal, New J. Phys. 12, 083014 (2010).","DOI":"10.1088\/1367-2630\/12\/8\/083014"},{"key":"10","doi-asserted-by":"publisher","unstructured":"``Effect of losses on the performance of an SU(1,1) interferometer'', A.M. Marino, N.V. Corzo Trejo, and P.D. Lett, Phys. Rev. A 86, 023844 (2012).","DOI":"10.1103\/PhysRevA.86.023844"},{"key":"11","doi-asserted-by":"publisher","unstructured":"``Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer'', Z.Y. Ou, Phys. Rev. A 85 023815 (2012).","DOI":"10.1103\/PhysRevA.85.023815"},{"key":"12","doi-asserted-by":"publisher","unstructured":"``Sub-shot-noise-limited phase estimation via SU(1,1) interferometer with thermal states'', X. Ma, C. You, S. Adhikari, E.S. Matekole, R.T. Glasser, H. Lee, and J.P. Dowling, Optics Exp. 26, 18492 (2018).","DOI":"10.1364\/OE.26.018492"},{"key":"13","doi-asserted-by":"publisher","unstructured":"``Phase sensitivity of gain-unbalanced nonlinear interferometers'', E. Giese, S. Lemieux, M. Manceau, R. Fickler, and R.W. Boyd, Phys. Rev. A 96, 053863 (2017).","DOI":"10.1103\/PhysRevA.96.053863"},{"key":"14","doi-asserted-by":"publisher","unstructured":"``Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing'', M. Manceau, F. Khalili, and M. Chekhova, New J. Phys. 19, 013014 (2017).","DOI":"10.1088\/1367-2630\/aa53d1"},{"key":"15","doi-asserted-by":"publisher","unstructured":"``The phase sensitivity of a fully quantum three-mode nonlinear interferometer'', J. Fl\u00f3rez, E. Giese, D. Curic, L. Giner, R.W. Boyd, and J.S. Lundeen, New J. Phys. 20, 123022 (2018).","DOI":"10.1088\/1367-2630\/aaf3d2"},{"key":"16","doi-asserted-by":"publisher","unstructured":"``Conclusive Precision Bounds for SU(1,1) Interferometers'', C. You, S. Adhikari, X. Ma, M. Sasaki, M. Takeoka, and J.P. Dowling, Phys. Rev. A 99, 042122 (2019).","DOI":"10.1103\/PhysRevA.99.042122"},{"key":"17","doi-asserted-by":"publisher","unstructured":"``Realization o`f a nonlinear interferometer with parametric amplifiers'', J. Jing, C. Liu, Z. Zhou, Z.Y. Ou, and W. Zhang, App. Phys. Lett. 99, 011110 (2011).","DOI":"10.1063\/1.3606549"},{"key":"18","doi-asserted-by":"publisher","unstructured":"``Quantum metrology with parametric amplifier-based photon correlation interferometers'', F. Hudelist, J. Kong, C. Liu, Z.Y. Ou, and W. Zhang, Nat. Comm. 5, 3049 (2014).","DOI":"10.1038\/ncomms4049"},{"key":"19","doi-asserted-by":"publisher","unstructured":"``Naturally stable Sagnac-Michelson nonlinear interferometer'', J.M. Lukens, N.A. Peters, and R.C. Pooser, Opt. Lett. 41, 5438 (2016).","DOI":"10.1364\/OL.41.005438"},{"key":"20","doi-asserted-by":"publisher","unstructured":"``Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer'', B.E. Anderson, P. Gupta, B.L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K.M. Jones, and P.D. Lett, Optica 4, 2334 (2017).","DOI":"10.1364\/OPTICA.4.000752"},{"key":"21","doi-asserted-by":"publisher","unstructured":"``Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer'', M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, Phys. Rev. Lett. 119, 223604 (2017).","DOI":"10.1364\/OL.41.005438"},{"key":"22","doi-asserted-by":"publisher","unstructured":"``Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers'', B.E. Anderson, B.L. Schmittberger, P. Gupta, K.M. Jones, and P.D. Lett, Phys. Rev. A 95, 063843 (2017).","DOI":"10.1103\/PhysRevA.95.063843"},{"key":"23","doi-asserted-by":"publisher","unstructured":"``Atom-Light Hybrid Interferometer'', B. Chen, C. Qiu, S. Chen, J. Guo, L.Q. Chen, Z.Y. Ou, and W. Zhang, Phys. Rev. Lett. 115, 043602 (2015).","DOI":"10.1103\/PhysRevLett.115.043602"},{"key":"24","doi-asserted-by":"publisher","unstructured":"``Pumped-Up SU(1,1) Interferometry'', S.S. Szigeti, R.J. Lewis-Swan, and S.A. Haine, Phys. Rev. Lett. 118, 150401 (2017).","DOI":"10.1103\/PhysRevLett.118.150401"},{"key":"25","unstructured":"``SU(2)-in-SU(1,1) nested interferometer'', W. Du, J. Kong, J. Jia, S. Ming, C.H. Yuan, J.F.Chen, Z.Y.Ou, M.W. Mitchell, and W. Zhang, arXiv:2004.14266v1 (2020)."},{"key":"26","doi-asserted-by":"publisher","unstructured":"``Quantum Interferometer Combining Squeezing and Parametric Amplification'', X. Zuo, Z. Yan, Y. Feng, J. Ma, X. Jia, C. Xie, and K. Peng, Phys. Rev. Let. 124, 173602 (2020).","DOI":"10.1103\/PhysRevLett.124.173602"},{"key":"27","doi-asserted-by":"publisher","unstructured":"``Induced Coherence and Indistinguishably in Optical Interference'', X.Y. Zou, L.J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).","DOI":"10.1103\/PhysRevLett.67.318"},{"key":"28","doi-asserted-by":"publisher","unstructured":"``Quantum imaging with undetected photons'', G. Barreto Lemos, V. Borish, G.D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).","DOI":"10.1038\/nature13586"},{"key":"29","doi-asserted-by":"publisher","unstructured":"``Theory of quantum imaging with undetected photons'', M. Lahiri, R. Lapkiewicz, G. Barreto Lemos, and A. Zeilinger, Phys. Rev. A 92, 013832 (2015).","DOI":"10.1103\/PhysRevA.92.013832"},{"key":"30","doi-asserted-by":"publisher","unstructured":"``Delayed-choice gedanken experiments and their realizations'', X. Ma, J. Kofler, and A. Zeilinger, Rev. Mod. Phys. 88, 015005 (2016).","DOI":"10.1103\/RevModPhys.88.015005"},{"key":"31","doi-asserted-by":"publisher","unstructured":"``Optical sectioning in induced coherence tomography with frequency-entangled photons'', A. Vall\u00e9s, G. Jim\u00e9nez, L.J. Salazar-Serrano, and J.P. Torres, Phys. Rev. A 97, 023824 (2018).","DOI":"10.1103\/PhysRevA.97.023824"},{"key":"32","doi-asserted-by":"publisher","unstructured":"``Quantum-enhanced spectroscopy with entangled multiphoton states'', H.T. Dinani, M.K. Gupta, J.P. Dowling, and D.W. Berry, Phys. Rev. A 93, 063804 (2016).","DOI":"10.1103\/PhysRevA.93.063804"},{"key":"33","doi-asserted-by":"publisher","unstructured":"``Measurement of infrared optical constants with visible photons'', A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New. J. Phys. 20, 043015 (2018).","DOI":"10.1088\/1367-2630\/aab5ce"},{"key":"34","doi-asserted-by":"publisher","unstructured":"``Infrared spectroscopy with visible light'', D.A. Kalashnikov, A.V. Paterova, S.P. Kulik, and L.A. Krivitsky, Nat. Photonics 10, 98 (2016).","DOI":"10.1038\/nphoton.2015.252"},{"key":"35","doi-asserted-by":"publisher","unstructured":"``Absorption spectroscopy at the ultimate quantum limit from single-photon states'', R. Whittaker, C. Erven, A. Neville, M. Berry, J.L. O'Brien, H. Cable, and J.C.F. Matthews, New J. Phys. 19, 023013 (2017).","DOI":"10.1088\/1367-2630\/aa5512"},{"key":"36","doi-asserted-by":"publisher","unstructured":"``Frequency comb single-photon interferometry'', S.K. Lee, N.S. Han, T.H. Yoon, and M. Cho, Comm. Phys. 1, 51 (2018).","DOI":"10.1038\/s42005-018-0051-2"},{"key":"37","doi-asserted-by":"publisher","unstructured":"``Interferometric quantum spectroscopy with undetected photons via distinguishability modulation'', S.K. Lee, T.H. Yoon, and M. Cho, Optics Exp. 27, 14853 (2019).","DOI":"10.1364\/OE.27.014853"},{"key":"38","doi-asserted-by":"publisher","unstructured":"``Frequency-domain optical coherence tomography with undetected mid-infrared photons'', A. Vanselow1, P. Kaufmann, I. Zorin, B. Heise, H.M. Chrzanowski1, and S. Ramelow, Optica 7, 1729 (2020).","DOI":"10.1364\/OPTICA.400128"},{"key":"39","doi-asserted-by":"publisher","unstructured":"``Microscopy with undetected photons in the mid-infrared'', I. Kviatkovsky, H.M. Chrzanowski, E.G. Avery, H. Bartolomaeus, S. Ramelow, Science Advances 6, eabd0264 (2020).","DOI":"10.1126\/sciadv.abd0264"},{"key":"40","doi-asserted-by":"publisher","unstructured":"``Coherence and multimode correlations from vacuum fluctuations in a microwave superconducting cavity'', P. L\u00e4hteenm\u00e4ki1, G.S. Paraoanu, J. Hassel, and P.J. Hakonen, Nat. Comm. 7, 12548 (2016).","DOI":"10.1038\/ncomms12548"},{"key":"41","doi-asserted-by":"publisher","unstructured":"``Entanglement, coherence, and redistribution of quantum resources in double spontaneous down-conversion processes'', D.E. Bruschi, C. Sab\u00edn, and G.S. Paraoanu, Phys. Rev. A 95, 062324 (2017).","DOI":"10.1103\/PhysRevA.95.062324"},{"key":"42","doi-asserted-by":"publisher","unstructured":"``Statistical distance and the geometry of quantum states'' S.L. Braunstein, and C.M. Caves, Phys. Rev. Lett. 72, 3439 (1994).","DOI":"10.1103\/PhysRevLett.72.3439"},{"key":"43","unstructured":"http:\/\/math.ucsd.edu\/$\\sim$ncalg\/."},{"key":"44","doi-asserted-by":"publisher","unstructured":"``Controlling induced coherence for quantum imaging'', M.I. Kolobov, E. Giese, S. Lemieux, R. Fickler, and R.W. Boyd, J. of Optics 19, 054003 (2017).","DOI":"10.1088\/2040-8986\/aa64a2"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-05-26-458\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,5,26]],"date-time":"2021-05-26T09:01:00Z","timestamp":1622019660000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-05-26-458\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,26]]},"references-count":45,"URL":"https:\/\/doi.org\/10.22331\/q-2021-05-26-458","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"type":"electronic","value":"2521-327X"}],"subject":[],"published":{"date-parts":[[2021,5,26]]},"article-number":"458"}}