{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:14Z","timestamp":1760149754890,"version":"build-2065373602"},"reference-count":61,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T00:00:00Z","timestamp":1694044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12175315","12165008"],"award-info":[{"award-number":["12175315","12165008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Motivated by the recent experiment on bosonic mixtures of atoms and molecules, we investigate pairing superfluid\u2013insulator (SI) transition for bosonic mixtures of atoms and molecules in a one-dimensional optical lattice, which is described by an extended Bose\u2013Hubbard model with atom\u2013molecule conservation (AMC). It is found that AMC can induce an extra pair\u2013superfluid phase though the system does not demonstrate pair-hopping. In particular, the system may undergo several pairing SI or insulator\u2013superfluid transitions as the detuning from the Feshbach resonance is varied from negative to positive, and the larger positive detuning can bifurcate the pair\u2013superfluid phases into mixed superfluid phases consisting of single-atomic and pair-atomic superfluid. The calculation of the second-order R\u00e9nyi entropy reveals that the discontinuity in its first-order derivative corresponds to the phase boundary of the pairing SI transition. This means that the residual entanglement in our mean-field treatment can be used to efficiently capture the signature of the pairing SI transition induced by AMC.<\/jats:p>","DOI":"10.3390\/sym15091715","type":"journal-article","created":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T09:51:37Z","timestamp":1694080297000},"page":"1715","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pairing Superfluid\u2013Insulator Transition Induced by Atom\u2013Molecule Conversion in Bosonic Mixtures in Optical Lattice"],"prefix":"10.3390","volume":"15","author":[{"given":"Haiming","family":"Deng","sequence":"first","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Xiangnan University, Chenzhou 423000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Tan","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha 410004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chao","family":"Kong","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Xiangnan University, Chenzhou 423000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuqiu","family":"Ye","sequence":"additional","affiliation":[{"name":"Department of Physics, Jishou University, Jishou 416000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Honghua","family":"Zhong","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha 410004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1038\/nature09036","article-title":"Time-resolved observation of coherent multi-body interactions in quantum phase revivals","volume":"465","author":"Will","year":"2010","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1038\/nphys2128","article-title":"Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices","volume":"8","author":"Struck","year":"2012","journal-title":"Nat. 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