{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:18:57Z","timestamp":1760231937528,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T00:00:00Z","timestamp":1652400000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation (NSF) of China","award":["1137405","11774054","12075036"],"award-info":[{"award-number":["1137405","11774054","12075036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Interesting coherence and correlations appear between superpositions of two bosonic modes when the modes are parametrically coupled to a third intermediate mode and are also coupled to external modes which are in thermal states of unequal mean photon numbers. Under such conditions, it is found that one of linear superpositions of the modes, which is effectively decoupled from the other modes, can be perfectly coherent with the other orthogonal superposition of the modes and can simultaneously exhibit anticoherence with the intermediate mode, which can give rise to entanglement between the modes. It is shown that the coherence effects have a substantial effect on the population distribution between the modes, which may result in lowering the population of the intermediate mode. This shows that the system can be employed to cool modes to lower temperatures. Furthermore, for appropriate thermal photon numbers and coupling strengths between the modes, it is found that entanglement between the directly coupled superposition and the intermediate modes may occur in a less restricted range of the number of the thermal photons such that the modes could be strongly entangled, even at large numbers of the thermal photons.<\/jats:p>","DOI":"10.3390\/e24050692","type":"journal-article","created":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T09:27:56Z","timestamp":1652520476000},"page":"692","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coherence and Anticoherence Induced by Thermal Fields"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0425-7431","authenticated-orcid":false,"given":"Lihui","family":"Sun","sequence":"first","affiliation":[{"name":"Institute of Quantum Optics and Information Photonics, School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China"}]},{"given":"Ya","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Quantum Optics and Information Photonics, School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China"}]},{"given":"Chen","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Quantum Optics and Information Photonics, School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China"}]},{"given":"Kaikai","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Quantum Optics and Information Photonics, School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China"}]},{"given":"Wenxing","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Quantum Optics and Information Photonics, School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China"},{"name":"Department of Physics, Southeast University, Nanjing 211189, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5260-0169","authenticated-orcid":false,"given":"Zbigniew","family":"Ficek","sequence":"additional","affiliation":[{"name":"Quantum Optics and Engineering Division, Institute of Physics, University of Zielona G\u00f3ra, Szafrana 4a, 65-516 Zielona G\u00f3ra, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1103\/PhysRevLett.10.84","article-title":"Photon correlations","volume":"10","author":"Glauber","year":"1963","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1103\/PhysRev.130.2529","article-title":"The quantum theory of optical coherence","volume":"130","author":"Glauber","year":"1963","journal-title":"Phys. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mandel, L., and Wolf, E. (1995). Optical Coherence and Quantum Optics, Cambridge University Press.","DOI":"10.1017\/CBO9781139644105"},{"key":"ref_4","unstructured":"Ficek, Z., and Swain, S. (2004). Quantum Interference and Coherence: Theory and Experiments, Springer."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11584","DOI":"10.1103\/PhysRevA.33.2472","article-title":"Anomalous coherence functions of the radiation fields","volume":"33","author":"Agarwal","year":"1986","journal-title":"Phys. Rev. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1080\/09500348714550841","article-title":"Squeezing and antibunching in phase-matched many-atom resonance fluorescence","volume":"34","author":"Heidmann","year":"1987","journal-title":"J. Mod. Opt."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"183002","DOI":"10.1103\/PhysRevLett.116.183002","article-title":"Visibility of Young\u2019s interference fringes: Scattered light from small ion crystals","volume":"116","author":"Wolf","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"093039","DOI":"10.1088\/1367-2630\/ab4081","article-title":"Multipath interference from large trapped ion chains","volume":"21","author":"Obsil","year":"2019","journal-title":"New J. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1103\/PhysRevA.28.929","article-title":"Photon interference and correlation effects produced by independent quantum sources","volume":"28","author":"Mandel","year":"1983","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3962","DOI":"10.1103\/PhysRevA.34.3962","article-title":"Interference of two photons in parametric down conversion","volume":"34","author":"Ghosh","year":"1986","journal-title":"Phys. Rev. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1038\/nphoton.2013.339","article-title":"On-chip quantum interference between silicon photon-pair sources","volume":"8","author":"Silverstone","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"021001","DOI":"10.1103\/PhysRevApplied.4.021001","article-title":"On-chip quantum interference from a single silicon ring-resonator source","volume":"4","author":"Preble","year":"2015","journal-title":"Phys. Rev. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1080\/09500348714550781","article-title":"Squeezing in correlated quantum systems","volume":"34","author":"Barnett","year":"1987","journal-title":"J. Mod. Opt."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ficek, Z., and Tana\u015b, R. (2017). Quantum-Limit Spectroscopy, Springer.","DOI":"10.1007\/978-1-4939-3740-0"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4614","DOI":"10.1103\/PhysRevA.44.4614","article-title":"Induced coherence without induced emission","volume":"44","author":"Wang","year":"1991","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"053601","DOI":"10.1103\/PhysRevLett.114.053601","article-title":"Induced coherence, vacumm fields, and complementatity in biphoton generation","volume":"114","author":"Heuer","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2941","DOI":"10.1103\/PhysRevLett.62.2941","article-title":"Further evidence of nonclassical behavior in optical interference","volume":"62","author":"Ou","year":"1989","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5122","DOI":"10.1103\/PhysRevA.50.5122","article-title":"Theory of two-photon entanglement in type-II optical parametric down-conversion","volume":"50","author":"Rubin","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1088\/0963-9659\/7\/5\/002","article-title":"Anticoherence","volume":"7","author":"Mandel","year":"1998","journal-title":"Pure Appl. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1038\/nphys3202","article-title":"Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks","volume":"11","author":"Armstrong","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"053602","DOI":"10.1103\/PhysRevLett.96.053602","article-title":"Unconditional two-mode squeezing of separated atomic ensembles","volume":"96","author":"Parkins","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"093019","DOI":"10.1088\/1367-2630\/13\/9\/093019","article-title":"Generating coherence and entanglement with a finite-size atomic ensemble in a ring cavity","volume":"13","author":"Sun","year":"2011","journal-title":"New J. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"250401","DOI":"10.1103\/PhysRevLett.99.250401","article-title":"Creating and probing multipartite macroscopic entanglement with light","volume":"99","author":"Paternostro","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"013602","DOI":"10.1103\/PhysRevLett.112.013602","article-title":"Optically mediated hybridization between two mechanical modes","volume":"112","author":"Shkarin","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1038\/s41586-019-1061-2","article-title":"Nonreciprocal control and cooling of phonon modes in an optomechanical system","volume":"568","author":"Xu","year":"2019","journal-title":"Nature"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1016\/j.crhy.2011.02.004","article-title":"Dynamics of coupled multimode and hybrid optomechanical systems","volume":"12","author":"Heinrich","year":"2011","journal-title":"C. R. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S1049-250X(09)57002-4","article-title":"Quantum effects in optomechanical systems","volume":"57","author":"Genes","year":"2009","journal-title":"Adv. At. Mol. Opt. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1002\/andp.201200226","article-title":"A short walk through quantum optomechanics","volume":"525","author":"Meystre","year":"2013","journal-title":"Ann. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1103\/RevModPhys.86.1391","article-title":"Cavity optomechanics","volume":"86","author":"Aspelmeyer","year":"2014","journal-title":"Rev. Mod. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"042336","DOI":"10.1103\/PhysRevA.76.042336","article-title":"Entangling a nanomechanical resonator and a superconducting microwave cavity","volume":"76","author":"Vitali","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"A189","DOI":"10.1364\/JOSAB.27.00A189","article-title":"Quantum optomechanics\u2014Throwing a glance","volume":"27","author":"Aspelmeyer","year":"2010","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"052327","DOI":"10.1103\/PhysRevA.84.052327","article-title":"Quantum entanglement and teleportation in pulsed cavity optomechanics","volume":"84","author":"Hofer","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"022327","DOI":"10.1103\/PhysRevA.85.022327","article-title":"First-order coherence versus entanglement in a nanomechanical cavity","volume":"85","author":"Sun","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"123039","DOI":"10.1088\/1367-2630\/aa9c9a","article-title":"Phase control of entanglement and quantum steering in a three-mode optomechanical system","volume":"19","author":"Sun","year":"2017","journal-title":"New J. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1126\/science.abf5389","article-title":"Quantum mechanics\u2013free subsystem with mechanical oscillators","volume":"372","author":"Woolley","year":"2021","journal-title":"Science"},{"key":"ref_36","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (1980). Table of Integrals, Series and Products, Academic Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"033834","DOI":"10.1103\/PhysRevA.92.033834","article-title":"Complementarity in biphoton generation with stimulated or induced coherence","volume":"92","author":"Heuer","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Menzel, R., Heuer, A., and Milonni, P.W. (2019). Entanglement, complementarity, and vacuum fields in spontaneous parametric down-conversion. Atoms, 7.","DOI":"10.3390\/atoms7010027"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"053839","DOI":"10.1103\/PhysRevA.100.053839","article-title":"Nonclassicality of induced coherence without induced emission","volume":"100","author":"Lahiri","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/S0375-9601(00)00314-5","article-title":"Induced coherence with and without induced emission","volume":"270","author":"Wiseman","year":"2000","journal-title":"Phys. Lett. A"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Gardiner, C.W., and Zoller, P. (2000). Quantum Noise, Springer.","DOI":"10.1007\/978-3-662-04103-1"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/692\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:10:36Z","timestamp":1760137836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/692"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,13]]},"references-count":41,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["e24050692"],"URL":"https:\/\/doi.org\/10.3390\/e24050692","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,5,13]]}}}