{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T12:30:45Z","timestamp":1761395445435,"version":"build-2065373602"},"reference-count":82,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,13]],"date-time":"2019-03-13T00:00:00Z","timestamp":1552435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We propose a method to generate nonclassical states of light in multimode microwave cavities. Our approach considers two-photon processes that take place in a system composed of N extended cavities and an ultrastrongly coupled light\u2013matter system. Under specific resonance conditions, our method generates, in a deterministic manner, product states of uncorrelated photon pairs, Bell states, and W states in different modes on the extended cavities. Furthermore, the numerical simulations show that the generation scheme exhibits a collective effect which decreases the generation time in the same proportion as the number of extended cavity increases. Moreover, the entanglement encoded in the photonic states can be transferred towards ancillary two-level systems to generate genuine multipartite entanglement. Finally, we discuss the feasibility of our proposal in circuit quantum electrodynamics. This proposal could be of interest in the context of quantum random number generator, due to the quadratic scaling of the output state.<\/jats:p>","DOI":"10.3390\/sym11030372","type":"journal-article","created":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T04:15:29Z","timestamp":1552536929000},"page":"372","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Parity-Assisted Generation of Nonclassical States of Light in Circuit Quantum Electrodynamics"],"prefix":"10.3390","volume":"11","author":[{"given":"Francisco","family":"C\u00e1rdenas-L\u00f3pez","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Santiago de Chile (USACH), Avenida Ecuador 3493, Santiago 9170124, Chile"},{"name":"Center for the Development of Nanoscience and Nanotechnology, Estaci\u00f3n Central, Santiago 9170124, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2917-7814","authenticated-orcid":false,"given":"Guillermo","family":"Romero","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Santiago de Chile (USACH), Avenida Ecuador 3493, Santiago 9170124, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9504-8685","authenticated-orcid":false,"given":"Lucas","family":"Lamata","sequence":"additional","affiliation":[{"name":"Department of Physical Chemistry, University of the Basque Country UPV\/EHU, Apartado 644, 48080 Bilbao, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8602-1181","authenticated-orcid":false,"given":"Enrique","family":"Solano","sequence":"additional","affiliation":[{"name":"Department of Physical Chemistry, University of the Basque Country UPV\/EHU, Apartado 644, 48080 Bilbao, Spain"},{"name":"IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain"},{"name":"Department of Physics, Shanghai University, Shanghai 200444, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7174-7879","authenticated-orcid":false,"given":"Juan","family":"Retamal","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Santiago de Chile (USACH), Avenida Ecuador 3493, Santiago 9170124, Chile"},{"name":"Center for the Development of Nanoscience and Nanotechnology, Estaci\u00f3n Central, Santiago 9170124, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1038\/nature10122","article-title":"Atomic physics and quantum optics using superconducting circuits","volume":"474","author":"You","year":"2011","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1038\/nphys2251","article-title":"On-chip quantum simulation with superconducting circuits","volume":"8","author":"Houck","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1126\/science.1231930","article-title":"Superconducting circuits for quantum information: An outlook","volume":"339","author":"Devoret","year":"2013","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1038\/nature02851","article-title":"Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics","volume":"431","author":"Wallraff","year":"2004","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"062320","DOI":"10.1103\/PhysRevA.69.062320","article-title":"Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation","volume":"69","author":"Blais","year":"2004","journal-title":"Phys. Rev. A"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Nakamura, Y. (2012, January 23\u201327). Microwave quantum photonics in superconducting circuits. Proceedings of the IEEE Photonics Conference 2012, Burlingame, CA, USA.","DOI":"10.1109\/IPCon.2012.6358734"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.10.002","article-title":"Microwave photonics with superconducting quantum circuits","volume":"718\u2013719","author":"Gu","year":"2017","journal-title":"Phys. Rep."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"15398","DOI":"10.1103\/PhysRevB.60.15398","article-title":"Superconducting persistent-current qubit","volume":"60","author":"Orlando","year":"1999","journal-title":"Phys. Rev. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"042319","DOI":"10.1103\/PhysRevA.76.042319","article-title":"Charge-insensitive qubit design derived from the Cooper pair box","volume":"76","author":"Koch","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113904","DOI":"10.1063\/1.3010859","article-title":"Coplanar waveguide resonators for circuit quantum electrodynamics","volume":"104","author":"Fragner","year":"2008","journal-title":"J. Appl. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"193601","DOI":"10.1103\/PhysRevLett.104.193601","article-title":"Electromagnetically induced transparency on a single artificial atom","volume":"104","author":"Abdumalikov","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"243601","DOI":"10.1103\/PhysRevLett.106.243601","article-title":"Observation of resonant photon blockade at microwave frequencies using correlation function measurements","volume":"106","author":"Lang","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"060503","DOI":"10.1103\/PhysRevLett.121.060503","article-title":"Parity-Engineered Light-Matter Interaction","volume":"121","author":"Goetz","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1038\/nphys1516","article-title":"Analog information processing at the quantum limit with a Josephson ring modulator","volume":"6","author":"Bergeal","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"100504","DOI":"10.1103\/PhysRevLett.105.100504","article-title":"Improved superconducting qubit readout by qubit-induced nonlinearities","volume":"105","author":"Boissonneault","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"013814","DOI":"10.1103\/PhysRevA.86.013814","article-title":"Josephson-junction-embedded transmission-line resonators: From Kerr medium to in-line transmon","volume":"86","author":"Bourassa","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"075024","DOI":"10.1088\/1367-2630\/14\/7\/075024","article-title":"Networks of nonlinear superconducting transmission line resonators","volume":"14","author":"Leib","year":"2012","journal-title":"New J. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"053601","DOI":"10.1103\/PhysRevLett.111.053601","article-title":"Giant Cross\u2013Kerr Effect for Propagating Microwaves Induced by an Artificial Atom","volume":"111","author":"Hoi","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"205416","DOI":"10.1103\/PhysRevB.76.205416","article-title":"Efficient on-chip source of microwave photon pairs in superconducting circuit QED","volume":"76","author":"Marquardt","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"013804","DOI":"10.1103\/PhysRevA.79.013804","article-title":"Down-conversion of a single photon with unit efficiency","volume":"79","author":"Koshino","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7289","DOI":"10.1038\/srep07289","article-title":"Controllable microwave three-wave mixing via a single three-level superconducting quantum circuit","volume":"4","author":"Liu","year":"2014","journal-title":"Sci. Rep."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"053814","DOI":"10.1103\/PhysRevA.94.053814","article-title":"Full two-photon down-conversion of a single photon","volume":"94","author":"Zueco","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2519","DOI":"10.1103\/PhysRevA.39.2519","article-title":"Observation of parametric amplification and deamplification in a Josephson parametric amplifier","volume":"39","author":"Yurke","year":"1989","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"043804","DOI":"10.1103\/PhysRevA.69.043804","article-title":"Superconducting analogs of quantum optical phenomena: Macroscopic quantum superpositions and squeezing in a superconducting quantum-interference device ring","volume":"69","author":"Everitt","year":"2004","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"253602","DOI":"10.1103\/PhysRevLett.101.253602","article-title":"Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit","volume":"101","author":"Zagoskin","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"140504","DOI":"10.1103\/PhysRevLett.95.140504","article-title":"Theory of microwave parametric down-conversion and squeezing using circuit QED","volume":"95","author":"Moon","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"013820","DOI":"10.1103\/PhysRevA.89.013820","article-title":"Perfect squeezing by damping modulation in circuit quantum electrodynamics","volume":"89","author":"Didier","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"210501","DOI":"10.1103\/PhysRevLett.109.210501","article-title":"All-resonant control of superconducting resonators","volume":"109","author":"Strauch","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"23646","DOI":"10.1038\/srep23646","article-title":"Engineering entangled microwave photon states through multiphoton interactions between two cavity fields and a superconducting qubit","volume":"6","author":"Zhao","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"093036","DOI":"10.1088\/1367-2630\/12\/9\/093036","article-title":"Generation and detection of NOON states in superconducting circuits","volume":"12","author":"Merkel","year":"2010","journal-title":"New J. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"050501","DOI":"10.1103\/PhysRevLett.105.050501","article-title":"Arbitrary Control of Entanglement between two Superconducting Resonators","volume":"105","author":"Strauch","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"060401","DOI":"10.1103\/PhysRevLett.106.060401","article-title":"Deterministic Entanglement of Photons in Two Superconducting Microwave Resonators","volume":"106","author":"Wang","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"140504","DOI":"10.1103\/PhysRevLett.119.140504","article-title":"Correlations and entanglement of microwave photons emitted in a cascade decay","volume":"119","author":"Gasparinetti","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"200501","DOI":"10.1103\/PhysRevLett.120.200501","article-title":"Deterministic remote entanglement of superconducting circuits through microwave two-photon transitions","volume":"120","author":"Narla","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1038\/s41467-018-03059-5","article-title":"A CNOT gate between multiphoton qubits encoded in two cavities","volume":"9","author":"Rosenblum","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_36","first-page":"031036","article-title":"Robust concurrent remote entanglement between two superconducting qubits","volume":"6","author":"Narla","year":"2016","journal-title":"Phys. Rev. X"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1038\/s41586-018-0195-y","article-title":"Deterministic Quantum State Transfer and Generation of Remote Entanglement using Microwave Photons","volume":"558","author":"Kurpiers","year":"2018","journal-title":"Nature"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"032109","DOI":"10.1103\/PhysRevA.80.032109","article-title":"Ultrastrong coupling regime of cavity QED with phase-biased flux qubits","volume":"80","author":"Bourassa","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1038\/nphys1730","article-title":"Circuit quantum electrodynamics in the ultrastrong-coupling regime","volume":"6","author":"Niemczyk","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"237001","DOI":"10.1103\/PhysRevLett.105.237001","article-title":"Observation of the Bloch-Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime","volume":"105","author":"Lisenfeld","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"023022","DOI":"10.1088\/1367-2630\/aa5941","article-title":"Ultrastrong coupling dynamics with a transmon qubit","volume":"19","author":"Andersen","year":"2017","journal-title":"New J. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1038\/nphys3905","article-title":"Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime","volume":"13","author":"Peropadre","year":"2017","journal-title":"Nat. Phys."},{"key":"ref_43","unstructured":"Mart\u00ednez, J.P., L\u00e9ger, S., Gheeraert, N., Dassonneville, R., Planat, L., Foroughi, F., Krupko, Y., Buisson, O., Naud, C., and Hasch-Guichard, W. (arXiv, 2018). A tunable Josephson platform to explore many-body quantum optics in circuit-QED, arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"263603","DOI":"10.1103\/PhysRevLett.105.263603","article-title":"Deep Strong Coupling Regime of the Jaynes-Cummings Model","volume":"105","author":"Casanova","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1038\/nphys3906","article-title":"Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime","volume":"13","author":"Yoshihara","year":"2017","journal-title":"Nat. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Forn-D\u00edaz, P., Lamata, L., Rico, E., Kono, J., and Solano, E. (arXiv, 2018). Ultrastrong coupling regimes of light\u2013matter interaction, arXiv.","DOI":"10.1103\/RevModPhys.91.025005"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1038\/s42254-018-0006-2","article-title":"Ultrastrong coupling between light and matter","volume":"1","author":"Kockum","year":"2019","journal-title":"Nat. Rev. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1103\/PhysRev.49.324","article-title":"On the Process of Space Quantization","volume":"49","author":"Rabi","year":"1936","journal-title":"Phys. Rev."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"100401","DOI":"10.1103\/PhysRevLett.107.100401","article-title":"Integrability of the Rabi Model","volume":"107","author":"Braak","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"190402","DOI":"10.1103\/PhysRevLett.107.190402","article-title":"Protected Quantum Computation with Multiple Resonators in Ultrastrong Coupling Circuit QED","volume":"107","author":"Nataf","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"120501","DOI":"10.1103\/PhysRevLett.108.120501","article-title":"Ultrafast Quantum Gates in Circuit QED","volume":"108","author":"Romero","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"8621","DOI":"10.1038\/srep08621","article-title":"Scalable quantum memory in the ultrastrong coupling regime","volume":"5","author":"Kyaw","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"11818","DOI":"10.1038\/srep11818","article-title":"Parity-dependent state engineering and tomography in the ultrastrong coupling regime","volume":"5","author":"Felicetti","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"064503","DOI":"10.1103\/PhysRevB.91.064503","article-title":"Creation of quantum error correcting codes in the ultrastrong coupling regime","volume":"91","author":"Kyaw","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"012328","DOI":"10.1103\/PhysRevA.94.012328","article-title":"Holonomic quantum computation in the ultrastrong-coupling regime of circuit QED","volume":"94","author":"Wang","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"022306","DOI":"10.1103\/PhysRevA.97.022306","article-title":"Spin-1 models in the ultrastrong-coupling regime of circuit QED","volume":"97","author":"Lamata","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"063830","DOI":"10.1103\/PhysRevA.92.063830","article-title":"Multiphoton quantum Rabi oscillations in ultrastrong cavity QED","volume":"92","author":"Garziano","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"063849","DOI":"10.1103\/PhysRevA.95.063849","article-title":"Deterministic quantum nonlinear optics with single atoms and virtual photons","volume":"95","author":"Kockum","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"5313","DOI":"10.1038\/s41598-017-04225-3","article-title":"Frequency conversion in ultrastrong cavity QED","volume":"7","author":"Kockum","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"023818","DOI":"10.1103\/PhysRevA.96.023818","article-title":"Quantum nonlinear optics without photons","volume":"96","author":"Stassi","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"053838","DOI":"10.1103\/PhysRevA.86.053838","article-title":"Demonstrating W-type entanglement of Dicke states in resonant cavity quantum electrodynamics","volume":"86","author":"Mlynek","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2419","DOI":"10.1007\/s11128-015-0973-5","article-title":"Preparation of multi-qubit W states in multiple resonators coupled by a superconducting qubit via adiabatic passage","volume":"14","author":"Wei","year":"2013","journal-title":"Quantum Inf. Process."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.optcom.2015.10.012","article-title":"One-step schemes for multiqubit GHZ states and W-class states in circuit QED","volume":"359","author":"Liu","year":"2016","journal-title":"Opt. Commun."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"012319","DOI":"10.1103\/PhysRevA.99.012319","article-title":"Robust multipartite entanglement generation via a collision model","volume":"99","author":"Campbell","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1007\/s10773-014-2274-7","article-title":"Generation of N-Qubit W State in N Separated Resonators via Resonant Interaction","volume":"54","author":"Wei","year":"2014","journal-title":"Int. J. Theor. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"163601","DOI":"10.1103\/PhysRevLett.111.163601","article-title":"Multimode Circuit Quantum Electrodynamics with Hybrid Metamaterial Transmission Lines","volume":"111","author":"Egger","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"023837","DOI":"10.1103\/PhysRevA.86.023837","article-title":"Low-disorder microwave cavity lattices for quantum simulation with photons","volume":"86","author":"Underwood","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"013601","DOI":"10.1103\/PhysRevLett.98.013601","article-title":"Strong-coupling theory of periodically driven two-level systems","volume":"98","author":"Wu","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1103\/PhysRevA.35.154","article-title":"Theory of the Rydberg-atom two-photon micromaser","volume":"35","author":"Brune","year":"1987","journal-title":"Phys. Rev. A"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1899","DOI":"10.1103\/PhysRevLett.59.1899","article-title":"Realization of a two-photon maser oscillator","volume":"59","author":"Brune","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"062314","DOI":"10.1103\/PhysRevA.62.062314","article-title":"Three qubits can be entangled in two inequivalent ways","volume":"62","author":"Vidal","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"062327","DOI":"10.1103\/PhysRevA.98.062327","article-title":"Simple preparation of Bell and GHZ states using ultrastrong-coupling circuit QED","volume":"98","author":"Macri","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"043832","DOI":"10.1103\/PhysRevA.84.043832","article-title":"Dissipation and ultrastrong coupling in circuit QED","volume":"84","author":"Beaudoin","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"193602","DOI":"10.1103\/PhysRevLett.109.193602","article-title":"Photon Blockade in the Ultrastrong Coupling Regime","volume":"109","author":"Ridolfo","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"053834","DOI":"10.1103\/PhysRevA.98.053834","article-title":"Dissipation and Thermal Noise in Hybrid Quantum Systems in the Ultrastrong Coupling Regime","volume":"98","author":"Settineri","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"144510","DOI":"10.1103\/PhysRevB.81.144510","article-title":"Two-resonator circuit quantum electrodynamics: Dissipative theory","volume":"81","author":"Reuther","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"26720","DOI":"10.1038\/srep26720","article-title":"Broken selection rule in the quantum Rabi model","volume":"6","author":"Romero","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"013819","DOI":"10.1103\/PhysRevA.79.013819","article-title":"Dispersive regime of circuit QED: Photon-dependent qubit dephasing and relaxation rates","volume":"79","author":"Boissonneault","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_79","unstructured":"Masluk, N.A. (2013). Reducing the Losses of the Fluxonium Artificial Atom. [Ph.D. Thesis, Yale University]."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1103\/PhysRevA.29.1419","article-title":"Quantum network theory","volume":"29","author":"Yurke","year":"1984","journal-title":"Phys. Rev. A"},{"key":"ref_81","unstructured":"Reynaud, S., Giacobino, E., and Zinn-Justin, J. (1997). Quantum Fluctuations in electrical circuits. Les Houches Session LXIII, Elsevier."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"063414","DOI":"10.1103\/PhysRevA.75.063414","article-title":"Two-level systems driven by large-amplitude fields","volume":"75","author":"Ashhab","year":"2007","journal-title":"Phys. Rev. A"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/372\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:38:32Z","timestamp":1760186312000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/372"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,13]]},"references-count":82,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["sym11030372"],"URL":"https:\/\/doi.org\/10.3390\/sym11030372","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,3,13]]}}}