{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T06:35:04Z","timestamp":1775198104216,"version":"3.50.1"},"reference-count":66,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s11128-021-03338-z","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T09:03:02Z","timestamp":1637658182000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Two-photon Jaynes\u2013Cummings model: a two-level atom interacting with the para-Bose field"],"prefix":"10.1007","volume":"20","author":[{"given":"H.","family":"Fakhri","sequence":"first","affiliation":[]},{"given":"S.","family":"Mirzaei","sequence":"additional","affiliation":[]},{"given":"M.","family":"Sayyah-Fard","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"3338_CR1","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1103\/PhysRev.93.99","volume":"93","author":"RH Dicke","year":"1954","unstructured":"Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93, 99 (1954). https:\/\/doi.org\/10.1103\/PhysRev.93.99","journal-title":"Phys. Rev."},{"key":"3338_CR2","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1103\/PhysRev.51.652","volume":"51","author":"II Rabi","year":"1937","unstructured":"Rabi, I.I.: Space quantization in a gyrating magnetic field. Phys. Rev. 51, 652 (1937). https:\/\/doi.org\/10.1103\/PhysRev.51.652","journal-title":"Phys. Rev."},{"key":"3338_CR3","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1109\/PROC.1963.1664","volume":"51","author":"ET Jaynes","year":"1963","unstructured":"Jaynes, E.T., Cummings, F.W.: Comparison of quantum and semi-classical radiation theories with application to beam maser. Proc. Inst. Elect. Eng. 51, 89 (1963). https:\/\/doi.org\/10.1109\/PROC.1963.1664","journal-title":"Proc. Inst. Elect. Eng."},{"key":"3338_CR4","volume-title":"Optical Resonance and Two-Level Atoms","author":"L Allen","year":"1975","unstructured":"Allen, L., Eberly, J.H.: Optical Resonance and Two-Level Atoms. Wiley, New York (1975)"},{"key":"3338_CR5","doi-asserted-by":"publisher","first-page":"6023","DOI":"10.1103\/physreva.44.6023","volume":"44","author":"S Phoenix","year":"1991","unstructured":"Phoenix, S., Knight, P.L.: Establishment of an entangled atom-field state in the Jaynes-Cummings model. Phys. Rev. A 44, 6023 (1991). https:\/\/doi.org\/10.1103\/physreva.44.6023","journal-title":"Phys. Rev. A"},{"key":"3338_CR6","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1080\/09500349314551321","volume":"40","author":"BW Shore","year":"1993","unstructured":"Shore, B.W., Knight, P.L.: The Jaynes-Cummings model. J. Mod. Opt. 40, 1195 (1993). https:\/\/doi.org\/10.1080\/09500349314551321","journal-title":"J. Mod. Opt."},{"key":"3338_CR7","doi-asserted-by":"publisher","first-page":"3900","DOI":"10.1103\/PhysRevA.48.3900","volume":"48","author":"H Moya-Cessa","year":"1993","unstructured":"Moya-Cessa, H., Buzek, V., Kim, M.S., Knight, P.L.: Intrinsic decoherence in the atom-field interaction. Phys. Rev. A 48, 3900 (1993). https:\/\/doi.org\/10.1103\/PhysRevA.48.3900","journal-title":"Phys. Rev. A"},{"key":"3338_CR8","doi-asserted-by":"publisher","first-page":"1685","DOI":"10.1364\/JOSAB.21.001685","volume":"21","author":"A Joshi","year":"2004","unstructured":"Joshi, A., Xiao, M.: Atomic-coherence effect on the Jaynes-Cummings model with atomic motion. J. Opt. Soc. Am. B 21, 1685 (2004). https:\/\/doi.org\/10.1364\/JOSAB.21.001685","journal-title":"J. Opt. Soc. Am. B"},{"key":"3338_CR9","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198509141.001.0001","volume-title":"Exploring the Quantum: Atoms","author":"S Haroche","year":"2006","unstructured":"Haroche, S., Raimond, J.M.: Exploring the Quantum: Atoms. Cavities and Photons. Oxford University Press, Oxford (2006)"},{"key":"3338_CR10","volume-title":"Elements of Quantum Optics","author":"P Meystre","year":"1998","unstructured":"Meystre, P.: Elements of Quantum Optics. Springer, Berlin (1998)"},{"key":"3338_CR11","doi-asserted-by":"publisher","first-page":"3385","DOI":"10.1103\/PhysRevLett.65.3385","volume":"65","author":"J Gea-Banacloche","year":"1990","unstructured":"Gea-Banacloche, J.: Collapse and revival of the state vector in the Jaynes-Cummings model: an example of state preparation by a quantum apparatus. Phys. Rev. Lett. 65, 3385 (1990). https:\/\/doi.org\/10.1103\/PhysRevLett.65.3385","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR12","doi-asserted-by":"publisher","first-page":"2833","DOI":"10.1103\/PhysRevLett.66.2833","volume":"66","author":"S Phoenix","year":"1991","unstructured":"Phoenix, S., Knight, P.L.: Comment on \u201cCollapse and revival of the state vector in the Jaynes-Cummings model: an example of state preparation by a quantum apparatus\u2019\u2019. Phys. Rev. Let. 66, 2833 (1991). https:\/\/doi.org\/10.1103\/PhysRevLett.66.2833","journal-title":"Phys. Rev. Let."},{"key":"3338_CR13","doi-asserted-by":"publisher","first-page":"6092","DOI":"10.1103\/PhysRevA.44.6092","volume":"44","author":"T Quang","year":"1991","unstructured":"Quang, T., Knight, P.L., Bue, V.: Quantum collapses and revivals in an optical cavity. Phys. Rev. A 44, 6092 (1991). https:\/\/doi.org\/10.1103\/PhysRevA.44.6092","journal-title":"Phys. Rev. A"},{"key":"3338_CR14","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/s11128-020-02963-4","volume":"20","author":"S Fu","year":"2021","unstructured":"Fu, S., Luo, S., Zhang, Y.: Dynamics of field nonclassicality in the Jaynes-Cummings model. Quant. Inf. Proc. 20, 88 (2021). https:\/\/doi.org\/10.1007\/s11128-020-02963-4","journal-title":"Quant. Inf. Proc."},{"key":"3338_CR15","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1103\/PhysRevLett.51.550","volume":"51","author":"JJ Sanchez","year":"1983","unstructured":"Sanchez, J.J., Narozhny, N.B., Eberly, J.H.: Theory of spontaneous-emission line shape in an ideal cavity. Phys. Rev. Lett. 51, 550 (1983). https:\/\/doi.org\/10.1103\/PhysRevLett.51.550","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR16","doi-asserted-by":"publisher","first-page":"1323","DOI":"10.1103\/PhysRevLett.44.1323","volume":"44","author":"JH Eberly","year":"1980","unstructured":"Eberly, J.H., Narozhny, N.B., Sanchez-Mondragon, J.J.: Periodic spontaneuous collapse and revival in a simple quantum model. Phys. Rev. Lett. 44, 1323 (1980). https:\/\/doi.org\/10.1103\/PhysRevLett.44.1323","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR17","doi-asserted-by":"publisher","first-page":"3610(R)","DOI":"10.1103\/PhysRevA.33.3610","volume":"33","author":"RR Puri","year":"1986","unstructured":"Puri, R.R., Agarwal, G.S.: Collapse and revival phenomena in the Jaynes-Cummings model with cavity damping. Phys. Rev. A 33, 3610(R) (1986). https:\/\/doi.org\/10.1103\/PhysRevA.33.3610","journal-title":"Phys. Rev. A"},{"key":"3338_CR18","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1364\/JOSAB.4.000177","volume":"4","author":"P Alsing","year":"1987","unstructured":"Alsing, P., Zubairy, M.S.: Collapse and revivals in a two-photon absorption process. J. Opt. Soc. Am. B 4, 177 (1987). https:\/\/doi.org\/10.1364\/JOSAB.4.000177","journal-title":"J. Opt. Soc. Am. B"},{"key":"3338_CR19","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/S0378-4371(96)00295-6","volume":"234","author":"MF Fang","year":"1996","unstructured":"Fang, M.F., Zhou, P.: Quantum entropy and entanglement in the Jaynes-Cummings model without the rotating-wave approximation. Phys. A: Stat. Mech. Appl. 234, 571 (1996). https:\/\/doi.org\/10.1016\/S0378-4371(96)00295-6","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"3338_CR20","doi-asserted-by":"publisher","first-page":"2021","DOI":"10.1364\/JOSAB.5.002021","volume":"5","author":"RR Puri","year":"1987","unstructured":"Puri, R.R., Bullough, R.K.: Quantum electrodynamics of an atom making two-photon transitions in an ideal cavity. J. Opt. Soc. Am. B 5, 2021 (1987). https:\/\/doi.org\/10.1364\/JOSAB.5.002021","journal-title":"J. Opt. Soc. Am. B"},{"key":"3338_CR21","doi-asserted-by":"publisher","first-page":"5665","DOI":"10.1103\/physreva.38.5665","volume":"38","author":"CC Gerry","year":"1998","unstructured":"Gerry, C.C., Moyer, P.J.: Squeezing and higher-order squeezing in one-and two-photon Jaynes-Cummings models. Phys. Rev. A 38, 5665 (1998). https:\/\/doi.org\/10.1103\/physreva.38.5665","journal-title":"Phys. Rev. A"},{"key":"3338_CR22","doi-asserted-by":"publisher","first-page":"1559","DOI":"10.1080\/09500349114551721","volume":"38","author":"V Buzek","year":"1991","unstructured":"Buzek, V., Quang, T.: Squeezing of spectral components in the Jaynes-Cummings model. J. Mod. Opt. 38, 1559 (1991). https:\/\/doi.org\/10.1080\/09500349114551721","journal-title":"J. Mod. Opt."},{"key":"3338_CR23","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1103\/PhysRevLett.54.551","volume":"54","author":"D Meschede","year":"1985","unstructured":"Meschede, D., Walther, H., Muller, G.: One-atom maser. Phys. Rev. Lett. 54, 551 (1985). https:\/\/doi.org\/10.1103\/PhysRevLett.54.551","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR24","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1103\/PhysRevLett.58.353","volume":"58","author":"G Rempe","year":"1987","unstructured":"Rempe, G., Walther, H., Klein, N.: Observation of quantum collapse and revival in a one-atom maser. Phys. Rev. Lett. 58, 353 (1987). https:\/\/doi.org\/10.1103\/PhysRevLett.58.353","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR25","doi-asserted-by":"publisher","first-page":"1800","DOI":"10.1103\/PhysRevLett.76.1800","volume":"76","author":"M Brune","year":"1996","unstructured":"Brune, M., Schmidt-Kaler, F., Maali, A., Dreyer, J., Hagley, E., Raimond, J.M., Haroche, S.: Quantum Rabi oscillation: a direct test of field quantization in a cavity. Phys. Rev. Lett. 76, 1800 (1996). https:\/\/doi.org\/10.1103\/PhysRevLett.76.1800","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR26","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0370-1573(80)90119-2","volume":"66","author":"PL Knight","year":"1980","unstructured":"Knight, P.L., Milonni, P.W.: The Rabi frequency in optical spectra. Phys. Rep. 66, 21 (1980). https:\/\/doi.org\/10.1016\/0370-1573(80)90119-2","journal-title":"Phys. Rep."},{"key":"3338_CR27","doi-asserted-by":"publisher","first-page":"980","DOI":"10.1103\/PhysRevLett.65.980","volume":"65","author":"M Chaichian","year":"1990","unstructured":"Chaichian, M., Ellinas, D., Kulish, P.: Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model. Phys. Rev. Lett. 65, 980 (1990). https:\/\/doi.org\/10.1103\/PhysRevLett.65.980","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR28","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1080\/09500349214550981","volume":"39","author":"V Buzek","year":"1992","unstructured":"Buzek, V.: The Jaynes-Cummings model with a $$q$$ analogue of a coherent state. J. Mod. Opt. 39, 949 (1992). https:\/\/doi.org\/10.1080\/09500349214550981","journal-title":"J. Mod. Opt."},{"key":"3338_CR29","doi-asserted-by":"publisher","unstructured":"de los Santos-Sanchez, O., Recamier, J.: The $$f$$-deformed Jaynes\u2013Cummings model and its nonlinear coherent states. J. Phys. B 45 015502 (2012). https:\/\/doi.org\/10.1088\/0953-4075\/45\/1\/015502","DOI":"10.1088\/0953-4075\/45\/1\/015502"},{"key":"3338_CR30","doi-asserted-by":"publisher","first-page":"38069","DOI":"10.1038\/srep38069","volume":"6","author":"A Dehghani","year":"2016","unstructured":"Dehghani, A., Mojaveri, B., Shirin, S., Faseghandis, S.A.: Parity deformed Jaynes-Cummings model: robust maximally entangled states. Sci. Rep. 6, 38069 (2016). https:\/\/doi.org\/10.1038\/srep38069","journal-title":"Sci. Rep."},{"key":"3338_CR31","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/0375-9601(81)90042-6","volume":"83","author":"B Buck","year":"1981","unstructured":"Buck, B., Sukumar, C.V.: Exactly soluble model of atom-phonon coupling showing periodic decay and revival. Phys. Lett. A 83, 132 (1981). https:\/\/doi.org\/10.1016\/0375-9601(81)90042-6","journal-title":"Phys. Lett. A"},{"key":"3338_CR32","doi-asserted-by":"publisher","first-page":"3206","DOI":"10.1103\/PhysRevA.25.3206","volume":"25","author":"S Singh","year":"1982","unstructured":"Singh, S.: Field statistics in some generalized Jaynes-Cummings models. Phys. Rev. A 25, 3206 (1982). https:\/\/doi.org\/10.1103\/PhysRevA.25.3206","journal-title":"Phys. Rev. A"},{"key":"3338_CR33","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1088\/0305-4470\/17\/4\/029","volume":"17","author":"CV Sukumar","year":"1984","unstructured":"Sukumar, C.V., Buck, B.: Some soluble models for periodic decay and revival. J. Phys. A: Math. Gen. 17, 885 (1984). https:\/\/doi.org\/10.1088\/0305-4470\/17\/4\/029","journal-title":"J. Phys. A: Math. Gen."},{"key":"3338_CR34","doi-asserted-by":"publisher","first-page":"2683","DOI":"10.1103\/PhysRevA.37.2683","volume":"37","author":"CC Gerry","year":"1988","unstructured":"Gerry, C.C.: Two-photon Jaynes-Cummings model interacting with the squeezed vacuum. Phys. Rev. A 37, 2683 (1988). https:\/\/doi.org\/10.1103\/PhysRevA.37.2683","journal-title":"Phys. Rev. A"},{"key":"3338_CR35","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1103\/PhysRevLett.62.137","volume":"62","author":"C Buzano","year":"1989","unstructured":"Buzano, C., Rasetti, M.G., Rastello, M.L.: Dynamical superalgebra of the \u201cdressed\u2019\u2019 Jaynes-Cummings model. Phys. Rev. Lett. 62, 137 (1989). https:\/\/doi.org\/10.1103\/PhysRevLett.62.137","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR36","doi-asserted-by":"publisher","first-page":"3196","DOI":"10.1103\/PhysRevA.39.3196","volume":"39","author":"V Buzek","year":"1989","unstructured":"Buzek, V.: Jaynes-Cummings model with intensity-dependent coupling interacting with Holstein-Primakoff $${\\rm SU}(1,1)$$ coherent state. Phys. Rev. A 39, 3196 (1989). https:\/\/doi.org\/10.1103\/PhysRevA.39.3196","journal-title":"Phys. Rev. A"},{"key":"3338_CR37","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1088\/0954-8998\/2\/2\/005","volume":"2","author":"V Buzek","year":"1990","unstructured":"Buzek, V., Jex, I.: Emission spectra for the Jaynes-Cummings model with intensity-dependent coupling. Quantum Opt. 2, 14 (1990). https:\/\/doi.org\/10.1088\/0954-8998\/2\/2\/005","journal-title":"Quantum Opt."},{"key":"3338_CR38","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1080\/09500349014550371","volume":"37","author":"V Buzek","year":"1990","unstructured":"Buzek, V.: SU(1,1) squeezing of SU(1,1) generalized coherent states. J. Mod. Opt. 37, 303 (1990). https:\/\/doi.org\/10.1080\/09500349014550371","journal-title":"J. Mod. Opt."},{"key":"3338_CR39","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/0375-9601(90)90762-D","volume":"151","author":"V Buzek","year":"1990","unstructured":"Buzek, V.: Light squeezing in the two-photon Jaynes-Cummings model: far-off-resonant limit. Phys. Let. A 151, 234 (1990). https:\/\/doi.org\/10.1016\/0375-9601(90)90762-D","journal-title":"Phys. Let. A"},{"key":"3338_CR40","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1364\/JOSAB.9.000290","volume":"9","author":"CC Gerry","year":"1992","unstructured":"Gerry, C.C., Welc, R.F.: Dynamics of a two-mode two-photon Jaynes-Cummings model interacting with correlated SU(1,1) coherent states. J. Opt. Soc. Am. B 9, 290 (1992). https:\/\/doi.org\/10.1364\/JOSAB.9.000290","journal-title":"J. Opt. Soc. Am. B"},{"key":"3338_CR41","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/0375-9601(81)90825-2","volume":"83","author":"CV Sukumar","year":"1981","unstructured":"Sukumar, C.V., Buck, B.: Multi-phonon generalization of the Jaynes-Cummings model. Phys. Lett. A 83, 211 (1981). https:\/\/doi.org\/10.1016\/0375-9601(81)90825-2","journal-title":"Phys. Lett. A"},{"key":"3338_CR42","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1038\/nphys466","volume":"2","author":"AD Greentree","year":"2006","unstructured":"Greentree, A.D., Tahan, C., Cole, J.H., Hollenberg, L.C.L.: Quantum phase transitions of light. Nat. Phys. 2, 856 (2006). https:\/\/doi.org\/10.1038\/nphys466","journal-title":"Nat. Phys."},{"key":"3338_CR43","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1038\/nphys462","volume":"2","author":"MJ Hartmann","year":"2006","unstructured":"Hartmann, M.J., Brandao, F.G.S.L., Plenio, M.B.: Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2, 849 (2006). https:\/\/doi.org\/10.1038\/nphys462","journal-title":"Nat. Phys."},{"key":"3338_CR44","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1103\/PhysRev.170.379","volume":"170","author":"M Tavis","year":"1968","unstructured":"Tavis, M., Cummings, F.W.: Exact solution for an $$N$$-molecule-radiation-field Hamiltonian. Phys. Rev. 170, 379 (1968). https:\/\/doi.org\/10.1103\/PhysRev.170.379","journal-title":"Phys. Rev."},{"key":"3338_CR45","doi-asserted-by":"publisher","first-page":"1993","DOI":"10.1103\/PhysRevA.49.1993","volume":"49","author":"SM Dutra","year":"1994","unstructured":"Dutra, S.M., Knight, P.L., Moya-Cessa, H.: Large-scale fluctuations in the driven Jaynes-Cummings model. Phys. Rev. A 49, 1993 (1994). https:\/\/doi.org\/10.1103\/PhysRevA.49.1993","journal-title":"Phys. Rev. A"},{"key":"3338_CR46","doi-asserted-by":"publisher","first-page":"2089","DOI":"10.1063\/1.523564","volume":"19","author":"JK Sharma","year":"1978","unstructured":"Sharma, J.K., Mehta, C.L., Sudarshan, E.C.G.: Para-Bose coherent states. J. Math. Phys. 19, 2089 (1978). https:\/\/doi.org\/10.1063\/1.523564","journal-title":"J. Math. Phys."},{"key":"3338_CR47","doi-asserted-by":"publisher","unstructured":"Sharma, J.K., Mehta, C.L., Mukunda, N., Sudarshan, E.C.G.: Representations and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states. J. Math. Phys. 22, 78 (1981). https:\/\/doi.org\/10.1063\/1.524756","DOI":"10.1063\/1.524756"},{"key":"3338_CR48","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.013820","volume":"95","author":"CH Alderete","year":"2017","unstructured":"Alderete, C.H., Rodriguez-Lara, B.M.: Quantum simulation of driven para-Bose oscillators. Phys. Rev. A 95, 013820 (2017). https:\/\/doi.org\/10.1103\/PhysRevA.95.013820","journal-title":"Phys. Rev. A"},{"key":"3338_CR49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.043835","volume":"95","author":"CH Alderete","year":"2017","unstructured":"Alderete, C.H., Vergara, L.V., Rodriguez-Lara, B.M.: Nonclassical and semiclassical para-Bose states. Phy. Rev. A 95, 043835 (2017). https:\/\/doi.org\/10.1103\/PhysRevA.95.043835","journal-title":"Phy. Rev. A"},{"key":"3338_CR50","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1140\/epjp\/i2018-12163-2","volume":"133","author":"B Mojaveri","year":"2018","unstructured":"Mojaveri, B., Dehghani, A., Jafarzadeh-Bahrbeig, R.: Excitation on the para-Bose states: nonclassical properties. Eur. Phys. J. Plus 133, 346 (2018). https:\/\/doi.org\/10.1140\/epjp\/i2018-12163-2","journal-title":"Eur. Phys. J. Plus"},{"key":"3338_CR51","doi-asserted-by":"publisher","first-page":"2191","DOI":"10.1063\/1.1664820","volume":"10","author":"F Calogero","year":"1969","unstructured":"Calogero, F.: Solution of a three-body problem in one dimension. J. Math. Phys. 10, 2191 (1969). https:\/\/doi.org\/10.1063\/1.1664820","journal-title":"J. Math. Phys."},{"key":"3338_CR52","doi-asserted-by":"publisher","first-page":"2019","DOI":"10.1103\/PhysRevA.4.2019","volume":"4","author":"B Sutherland","year":"1971","unstructured":"Sutherland, B.: Exact results for a quantum many-body problem in one dimension. Phys. Rev. A 4, 2019 (1971). https:\/\/doi.org\/10.1103\/PhysRevA.4.2019","journal-title":"Phys. Rev. A"},{"key":"3338_CR53","doi-asserted-by":"publisher","first-page":"1228","DOI":"10.1002\/qua.21944","volume":"109","author":"H Fakhri","year":"2009","unstructured":"Fakhri, H., Dehghani, A., Mojaveri, B.: Approach of the associated Laguerre functions to the $${\\rm SU}(1,1)$$ coherent states for some quantum solvable models. Int. J. Quantum Chem. 109, 1228 (2009). https:\/\/doi.org\/10.1002\/qua.21944","journal-title":"Int. J. Quantum Chem."},{"key":"3338_CR54","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1016\/j.aop.2015.08.031","volume":"362","author":"A Dehghani","year":"2015","unstructured":"Dehghani, A., Mojaveri, B., Shirin, S., Saedi, M.: Cat-states in the framework of Wigner-Heisenberg algebra. Ann. Phys. 362, 659 (2015). https:\/\/doi.org\/10.1016\/j.aop.2015.08.031","journal-title":"Ann. Phys."},{"key":"3338_CR55","doi-asserted-by":"publisher","first-page":"5873","DOI":"10.1088\/0305-4470\/29\/18\/017","volume":"29","author":"C Brif","year":"1996","unstructured":"Brif, C., Vourdas, A., Mann, A.: Analytic representations based on $${\\rm SU}(1,1)$$ coherent states and their applications. J. Phys. A: Math. Gen. 29, 5873 (1996). https:\/\/doi.org\/10.1088\/0305-4470\/29\/18\/017","journal-title":"J. Phys. A: Math. Gen."},{"key":"3338_CR56","doi-asserted-by":"publisher","DOI":"10.1063\/1.4963171","volume":"57","author":"H Fakhri","year":"2016","unstructured":"Fakhri, H., Sayyah-Fard, M.: $$sl(2)$$-modules by $$sl(2)$$-coherent states. J. Math. Phys. 57, 091704 (2016). https:\/\/doi.org\/10.1063\/1.4963171","journal-title":"J. Math. Phys."},{"key":"3338_CR57","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.ijleo.2018.05.057","volume":"169","author":"JM Wanga","year":"2018","unstructured":"Wanga, J.M., Fang, H.H., Xu, X.X.: Two-photon Jaynes-Cummings model interacting with the squeezed vacuum state solved by dressed-state method. Optik 169, 180 (2018). https:\/\/doi.org\/10.1016\/j.ijleo.2018.05.057","journal-title":"Optik"},{"key":"3338_CR58","doi-asserted-by":"publisher","first-page":"12888","DOI":"10.1364\/OE.21.012888","volume":"21","author":"BM Rodriguez-Lara","year":"2013","unstructured":"Rodriguez-Lara, B.M., Soto-Eguibar, F., Cardenas, A.Z., Moya-Cessa, H.M.: A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices. Opt. Express 21, 12888 (2013). https:\/\/doi.org\/10.1364\/OE.21.012888","journal-title":"Opt. Express"},{"key":"3338_CR59","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1364\/JOSAB.31.001719","volume":"31","author":"BM Rodriguez-Lara","year":"2014","unstructured":"Rodriguez-Lara, B.M.: Intensity-dependent quantum Rabi model: spectrum, supersymmetric partner, and optical simulation. J. Opt. Soc. Am. B 31, 1719 (2014). https:\/\/doi.org\/10.1364\/JOSAB.31.001719","journal-title":"J. Opt. Soc. Am. B"},{"key":"3338_CR60","volume-title":"Table of Integrals, Series, and Products","author":"IS Gradshteyn","year":"2000","unstructured":"Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic, San Diego (2000)"},{"key":"3338_CR61","doi-asserted-by":"publisher","first-page":"2315","DOI":"10.1080\/09500349414552171","volume":"41","author":"R Jozsa","year":"1994","unstructured":"Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41, 2315 (1994). https:\/\/doi.org\/10.1080\/09500349414552171","journal-title":"J. Mod. Opt."},{"key":"3338_CR62","doi-asserted-by":"publisher","first-page":"1903","DOI":"10.1103\/PhysRevLett.50.1903","volume":"50","author":"P Goy","year":"1983","unstructured":"Goy, P., Raimond, J.M., Gross, M., Haroche, S.: Observation of cavity-enhanced single-atom spontaneous emission. Phys. Rev. Lett. 50, 1903 (1983). https:\/\/doi.org\/10.1103\/PhysRevLett.50.1903","journal-title":"Phys. Rev. Lett."},{"key":"3338_CR63","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198501770.001.0001","volume-title":"The Quantum Theory of Light","author":"R Loudon","year":"2000","unstructured":"Loudon, R.: The Quantum Theory of Light. Oxford University Press, New York (2000)"},{"key":"3338_CR64","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1143\/PTP.24.1135","volume":"24","author":"IDA Masakuni","year":"1960","unstructured":"Masakuni, I.D.A.: Space-time description of collision and decay processes. Prog. Theor. Phys. 24, 1135 (1960). https:\/\/doi.org\/10.1143\/PTP.24.1135","journal-title":"Prog. Theor. Phys."},{"key":"3338_CR65","doi-asserted-by":"publisher","DOI":"10.1142\/9915","volume-title":"Particles and Quantum Fields","author":"H Kleinert","year":"2016","unstructured":"Kleinert, H.: Particles and Quantum Fields. World scientific, Singapore (2016)"},{"key":"3338_CR66","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1038\/306141a0","volume":"306","author":"DF Walls","year":"1983","unstructured":"Walls, D.F.: Squeezed states of light. Nature (London) 306, 141 (1983). https:\/\/doi.org\/10.1038\/306141a0","journal-title":"Nature (London)"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03338-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03338-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03338-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:25:34Z","timestamp":1699835134000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03338-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,23]]},"references-count":66,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["3338"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03338-z","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,23]]},"assertion":[{"value":"14 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"398"}}