{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T01:23:22Z","timestamp":1782350602257,"version":"3.54.5"},"reference-count":75,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,2,23]],"date-time":"2016-02-23T00:00:00Z","timestamp":1456185600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2016,2,23]],"date-time":"2016-02-23T00:00:00Z","timestamp":1456185600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Exploration of macroscopic quantum entanglement is of great interest in both fundamental science and practical application. We investigate a hybrid quantum system that consists of two nitrogen-vacancy centers ensembles (NVE) coupled to a superconducting coplanar waveguide resonator (CPWR). The collective magnetic coupling between the NVE and the CPWR is employed to generate macroscopic entanglement between the NVEs, where the CPWR acts as the quantum bus. We find that, this NVE-CPWR hybrid system behaves as a system of three coupled harmonic oscillators and the excitation prepared initially in the CPWR can be distributed into these two NVEs. In the nondissipative case, the entanglement of NVEs oscillates periodically and the maximal entanglement always keeps unity if the CPWR is initially prepared in the odd coherent state. Considering the dissipative effect from the CPWR and NVEs, the amount of entanglement between these two NVEs strongly depends on the initial state of the CPWR and the maximal entanglement can be tuned by adjusting the initial states of the total system. The experimental feasibility and challenge with currently available technology are discussed.<\/jats:p>","DOI":"10.1038\/srep21775","type":"journal-article","created":{"date-parts":[[2016,2,23]],"date-time":"2016-02-23T10:48:25Z","timestamp":1456224505000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Entanglement dynamics of Nitrogen-vacancy centers spin ensembles coupled to a superconducting resonator"],"prefix":"10.1038","volume":"6","author":[{"given":"Yimin","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiabin","family":"You","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qizhe","family":"Hou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,2,23]]},"reference":[{"key":"BFsrep21775_CR1","doi-asserted-by":"crossref","first-page":"140502","DOI":"10.1103\/PhysRevLett.105.140502","volume":"105","author":"Y Kubo","year":"2010","unstructured":"Kubo, Y. et al. Strong Coupling of a Spin Ensemble to a Superconducting Resonator. Phys. Rev. Lett. 105, 140502 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR2","doi-asserted-by":"crossref","first-page":"060502","DOI":"10.1103\/PhysRevLett.107.060502","volume":"107","author":"R Ams\u00fcss","year":"2011","unstructured":"Ams\u00fcss, R. et al. Cavity QED with Magnetically Coupled Collective Spin States. Phys. Rev. Lett. 107, 060502 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR3","doi-asserted-by":"crossref","first-page":"083601","DOI":"10.1103\/PhysRevLett.103.083601","volume":"103","author":"JM Fink","year":"2009","unstructured":"Fink, J. M. et al. Dressed Collective Qubit States and the Tavis\u2013Cummings Model in Circuit QED. Phys. Rev. Lett. 103, 083601 (2009).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR4","doi-asserted-by":"crossref","first-page":"067004","DOI":"10.1103\/PhysRevLett.110.067004","volume":"110","author":"V Ranjan","year":"2013","unstructured":"Ranjan, V. et al. Probing Dynamics of an Electron\u2013Spin Ensemble via a Superconducting Resonator. Phys. Rev. Lett. 110, 067004 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR5","first-page":"021049","volume":"4","author":"C Grezes","year":"2014","unstructured":"Grezes, C. et al. Multimode Storage and Retrieval of Microwave Fields in a Spin Ensemble. Phys. Rev. X 4, 021049 (2014)","journal-title":"Phys. Rev. X"},{"key":"BFsrep21775_CR6","doi-asserted-by":"crossref","first-page":"140501","DOI":"10.1103\/PhysRevLett.105.140501","volume":"105","author":"DI Schuster","year":"2010","unstructured":"Schuster, D. I. et al. High\u2013Cooperativity Coupling of Electron\u2013Spin Ensembles to Superconducting Cavities. Phys. Rev. Lett. 105, 140501 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR7","doi-asserted-by":"crossref","first-page":"127003","DOI":"10.1103\/PhysRevLett.111.127003","volume":"111","author":"H Huebl","year":"2013","unstructured":"Huebl, H. et al. High Cooperativity in Coupled Microwave Resonator Ferrimagnetic Insulator Hybrids. Phys. Rev. Lett. 111, 127003 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR8","doi-asserted-by":"crossref","first-page":"120501","DOI":"10.1103\/PhysRevLett.112.120501","volume":"112","author":"AW Eddins","year":"2014","unstructured":"Eddins A. W., Beedle C. C., Hendrickson D. N. & Friedman J. R. Collective Coupling of a Macroscopic Number of Single-Molecule Magnets with a Microwave Cavity Mode. Phys. Rev. Lett. 112, 120501 (2014).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR9","doi-asserted-by":"crossref","first-page":"014421","DOI":"10.1103\/PhysRevB.92.014421","volume":"92","author":"S Probst.","year":"2015","unstructured":"Probst. S., Rotzinger, H., Ustinov, A. V. & Bushev, P. A. Microwave multimode memory with an erbium spin ensemble. Phys. Rev. B 92, 014421 (2015).","journal-title":"Phys. Rev. B"},{"key":"BFsrep21775_CR10","doi-asserted-by":"crossref","first-page":"033601","DOI":"10.1103\/PhysRevLett.115.033601","volume":"115","author":"DO Krimer.","year":"2015","unstructured":"Krimer. D. O., Hartl, B. & Rotter, S. Hybrid Quantum Systems with Collectively Coupled Spin States: Suppression of Decoherence through Spectral Hole Burning. Phys. Rev. Lett. 115, 033601 (2015).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR11","doi-asserted-by":"crossref","unstructured":"Grezes, C. et al. Towards a spin-ensemble quantum memory for superconducting qubits. arxiv: 1510.06565 (2015)","DOI":"10.1007\/978-3-319-21572-3"},{"key":"BFsrep21775_CR12","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1103\/RevModPhys.85.623","volume":"85","author":"ZL Xiang","year":"2013","unstructured":"Xiang, Z. L., Ashhab, S., You, J. Q. & Nori, F. Hybrid quantum circuits: Superconducting circuits interacting with other quantum system. Rev. Mod. Phys. 85, 623 (2013).","journal-title":"Rev. Mod. Phys."},{"key":"BFsrep21775_CR13","doi-asserted-by":"crossref","first-page":"076401","DOI":"10.1103\/PhysRevLett.92.076401","volume":"92","author":"F Jelezko","year":"2004","unstructured":"Jelezko, F., Gaebel, T., Popa, I. Gruber, A. & Wrachtrup, J. Observation of Coherent Oscillations in a Single Electron Spin. Phys. Rev. Lett. 92, 076401 (2004).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR14","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1038\/nature10462","volume":"478","author":"X Zhu","year":"2011","unstructured":"Zhu, X. et al. Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond. Nature 478, 221\u2013224 (2011).","journal-title":"Nature"},{"key":"BFsrep21775_CR15","doi-asserted-by":"crossref","first-page":"3424","DOI":"10.1038\/ncomms4424","volume":"5","author":"X Zhu","year":"2014","unstructured":"Zhu, X. et al. Observation of dark states in asuperconductor diamond quantum hybrid system. Nature Commun. 5, 3424 (2014).","journal-title":"Nature Commun."},{"key":"BFsrep21775_CR16","doi-asserted-by":"crossref","first-page":"130501","DOI":"10.1103\/PhysRevLett.93.130501","volume":"93","author":"F Jelezko","year":"2004","unstructured":"Jelezko, F. et al. Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two\u2013Qubit Conditional Quantum Gate. Phys. Rev. Lett. 93, 130501 (2004).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR17","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1126\/science.1176496","volume":"326","author":"L Jiang","year":"2009","unstructured":"Jiang, L. et al. Repective Readout of a single Electronic Spin via Quantum Logic with Nuclear Spin Ancillae. Science 326, 267\u2013271 (2009).","journal-title":"Science"},{"key":"BFsrep21775_CR18","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1038\/nphys1679","volume":"6","author":"P Rabl","year":"2010","unstructured":"Rabl, P. et al. A quantum spin transducer based on nanoelectromechanical. Nature Phys. 6, 602\u2013608 (2010).","journal-title":"Nature Phys."},{"key":"BFsrep21775_CR19","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1038\/nature09256","volume":"466","author":"E Togan","year":"2010","unstructured":"Togan, E. et al. Quantum entanglement between an optical photon and a solid\u2013state spin qubit. Nature 466, 730\u2013734 (2010).","journal-title":"Nature"},{"key":"BFsrep21775_CR20","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1126\/science.1220513","volume":"336","author":"PC Maurer","year":"2012","unstructured":"Maurer, P. C. et al. Room\u2013Temperature Quantum Bit Memory Exceeding One Second. Science 336, 1283\u20131286 (2012).","journal-title":"Science"},{"key":"BFsrep21775_CR21","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1038\/nphys1536","volume":"6","author":"P Neumman","year":"2010","unstructured":"Neumman, P. et al. Quantum register based on coupled electron spins in a room\u2013temperature solid. Nature Phys. 6, 249\u2013253 (2010).","journal-title":"Nature Phys."},{"key":"BFsrep21775_CR22","doi-asserted-by":"crossref","first-page":"011805","DOI":"10.1103\/PhysRevA.84.011805","volume":"84","author":"YC Liu","year":"2011","unstructured":"Liu, Y. C. et al. Coupling of a single diamond nanocrystal to a whispering\u2013gallery microvavity: Photon transport benefitting from Rayleigh scattering. Phys. Rev. A 84, 011805 (2011).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR23","doi-asserted-by":"crossref","first-page":"043833","DOI":"10.1103\/PhysRevA.86.043833","volume":"86","author":"XC Yu","year":"2012","unstructured":"Yu, X. C. et al. Coupling of diamond nanocrystals to a high\u2013Q whispering\u2013gallery microresonator. Phys. Rev. A 86, 043833 (2012).","journal-title":"Rev. A"},{"key":"BFsrep21775_CR24","doi-asserted-by":"crossref","first-page":"042306","DOI":"10.1103\/PhysRevA.85.042306","volume":"85","author":"PB Li","year":"2012","unstructured":"Li, P. B. et al. Dissipative preparation of entangled states between two spatially separated nitrogen\u2013vacancy centers. Phys. Rev. A 85, 042306 (2012).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR25","doi-asserted-by":"crossref","first-page":"241113","DOI":"10.1063\/1.3455891","volume":"96","author":"WL Yang","year":"2010","unstructured":"Yang, W. L., Yin, Z. Q., Xu, Z. Y., Feng, M. & Du, J. F. One\u2013step implementation of multiqubit conditional phase gating with nitrogen\u2013vacancy center coupled to a high\u2013Q silica microsphere cavity. Appl. Phys. Lett. 96, 241113 (2010).","journal-title":"Appl. Phys. Lett."},{"key":"BFsrep21775_CR26","doi-asserted-by":"crossref","first-page":"042118","DOI":"10.1103\/PhysRevA.90.042118","volume":"90","author":"N Zhao","year":"2014","unstructured":"Zhao, N. & Yin, Z. Q. Room-temperature ultrasensitive mass spectrometer via dynamical decoupling. Phys. Rev. A 90, 042118 (2014).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR27","doi-asserted-by":"crossref","first-page":"033614","DOI":"10.1103\/PhysRevA.88.033614","volume":"88","author":"ZQ Yin","year":"2013","unstructured":"Yin, Z. Q., Li, T. C., Zhang, X. & Duan, L. M. Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling. Phys. Rev. A 88, 033614 (2013).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR28","doi-asserted-by":"crossref","first-page":"057403","DOI":"10.1103\/PhysRevLett.102.057403","volume":"102","author":"V Jacques","year":"2009","unstructured":"Jacques, V., Dynamic Polarization of Single Nuclear Spins by Optical Pumping of Nitrogen\u2013Vacancy Color Centers in Diamond at Room Temperature. Phys. Rev. Lett. 102, 057403 (2009).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR29","doi-asserted-by":"crossref","first-page":"087601","DOI":"10.1103\/PhysRevLett.97.087601","volume":"97","author":"R Hanson","year":"2006","unstructured":"Hanson, R., Mendoza, F. M., Epstein, R. J. & Awschalom, D. D. Polarization and Readout of Coupled Single Spins in Damond. Phys. Rev. Lett. 97, 087601 (2006).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR30","doi-asserted-by":"crossref","first-page":"180502","DOI":"10.1103\/PhysRevB.78.180502","volume":"78","author":"AA Abdumalikov","year":"2008","unstructured":"Abdumalikov, A. A., Astafiev, O., Nakamura, Y., Pashkin, Y. A. & Tsai, J. Vacuum Rabi splitting due to strong coupling of a flux qubit and a coplanar\u2013waveguide reasonator. Phys. Rev. B 78, 180502 (2008).","journal-title":"Phys. Rev. B"},{"key":"BFsrep21775_CR31","doi-asserted-by":"crossref","first-page":"241202","DOI":"10.1103\/PhysRevB.81.241202","volume":"81","author":"J Twamley","year":"2010","unstructured":"Twamley, J. & Barrett, S. D. Superconducting cavity bus for single nitrogen\u2013vacancy defect center in diamond. Phys. Rev. B 81, 241202 (2010).","journal-title":"Rev. B"},{"key":"BFsrep21775_CR32","doi-asserted-by":"crossref","first-page":"083602","DOI":"10.1103\/PhysRevLett.102.083602","volume":"102","author":"A Imamo\u011flu","year":"2009","unstructured":"Imamo\u011flu, A. Cavity QED Based on Collective Magnetic Dipole Coupling: Spin Ensembles as Hybrid Two\u2013Level\u2013Systems. Phys. Rev. Lett. 102, 083602 (2009).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR33","doi-asserted-by":"crossref","first-page":"070502","DOI":"10.1103\/PhysRevLett.103.070502","volume":"103","author":"JH Wesenberg","year":"2009","unstructured":"Wesenberg, J. H. et al. Quantum Computing with an Electron Spin Ensemble. Phys. Rev. Lett. 103, 070502 (2009).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR34","doi-asserted-by":"crossref","first-page":"014001","DOI":"10.1088\/0031-8949\/2009\/T137\/014001","volume":"T137","author":"M Wallquist","year":"2009","unstructured":"Wallquist M., Hammerer K., Rabl P., Lukin M. & Zoller P. Hybrid quantum devices and quantum engineering. Phys. Scr. T137 014001 (2009).","journal-title":"Phys. Scr."},{"key":"BFsrep21775_CR35","doi-asserted-by":"crossref","first-page":"220501","DOI":"10.1103\/PhysRevLett.107.220501","volume":"107","author":"Y Kubo","year":"2011","unstructured":"Kubo, Y. et al. Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble. Phys. Rev. Lett. 107, 220501 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR36","doi-asserted-by":"crossref","first-page":"250503","DOI":"10.1103\/PhysRevLett.110.250503","volume":"110","author":"B Julsgaard","year":"2013","unstructured":"Julsgaard, B., Grezes, C., Bertet, P. & M\u00f8mer, K. Quantum Memory for Microwave Photons in an Inhomogeneously Broadened Spin Ensemble. Phys. Rev. Lett. 110, 250503 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR37","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1038\/nphys3050","volume":"10","author":"S Putz","year":"2014","unstructured":"Putz, S. Protecting a spin ensemble against decoherence in the strong\u2013coupling regime of cavity QED. Nature Phys. 10, 720\u2013724 (2014).","journal-title":"Nature Phys."},{"key":"BFsrep21775_CR38","doi-asserted-by":"crossref","first-page":"012307","DOI":"10.1103\/PhysRevA.86.012307","volume":"86","author":"WL Yang","year":"2012","unstructured":"Yang, W. L. et al. Quantum simulation of an artificial Abelian gauge field using nitrogen\u2013vacancy\u2013center ensembles coupled to superconducting. Phys. Rev. A 86, 012307 (2012).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR39","doi-asserted-by":"crossref","first-page":"010301","DOI":"10.1103\/PhysRevA.84.010301","volume":"84","author":"WL Yang","year":"2011","unstructured":"Yang, W. L., Yin, Z. Q., Hu, Y., Feng, M. & Du, J. F. High\u2013fidelity quantum memory using nitrogen\u2013vacancy center ensemble for hybrid quantum computation. Phys. Rev. A 84, 010301 (2011).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR40","doi-asserted-by":"crossref","first-page":"7755","DOI":"10.1038\/srep07755","volume":"5","author":"WL Song","year":"2015","unstructured":"Song, W. L. et al. One-step generation of multipartite entanglement among nitrogen\u2013vacancy center ensembles. Sci. Rep. 5, 7755 (2015).","journal-title":"Sci. Rep."},{"key":"BFsrep21775_CR41","doi-asserted-by":"crossref","first-page":"195112","DOI":"10.1103\/PhysRevB.90.195112","volume":"90","author":"JB You","year":"2014","unstructured":"You, J. B., Yang, W. L., Xu, Z. Y., Chan, A. H. & Oh, C. H. Phase transition of light in circuit-QED lattices coupled to nitrogen-vacancy centers in diamond. Phys. Rev. B 90, 195112 (2014).","journal-title":"Phys. Rev. B"},{"key":"BFsrep21775_CR42","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1103\/Physics.2.34","volume":"2","author":"M Stoneham","year":"2009","unstructured":"Stoneham, M. Trend: Is a room\u2013temperature, solid\u2013state quantum computer mere fantasy? Physics 2, 34 (2009).","journal-title":"Physics"},{"key":"BFsrep21775_CR43","doi-asserted-by":"crossref","first-page":"170402","DOI":"10.1103\/PhysRevLett.88.170402","volume":"88","author":"LM Duan","year":"2002","unstructured":"Duan, L. M. Entangling Many Atomic Ensembles through Laser Manipulation. Phys. Rev. Lett. 88, 170402 (2002).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR44","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1038\/nature12227","volume":"498","author":"L Li","year":"2013","unstructured":"Li, L., Dudin, Y. O. & Kuzmich, A. Entanglement between light and an optical atomic excitation. Nature 498, 466\u2013469 (2013).","journal-title":"Nature"},{"key":"BFsrep21775_CR45","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1038\/35096524","volume":"413","author":"B Julsgaard","year":"2001","unstructured":"Julsgaard, B., Kozhekin, A. & Polzik, E. S. Experimental long\u2013lived entanglement of two macroscopic objects. Nature 413, 400\u2013403 (2001).","journal-title":"Nature"},{"key":"BFsrep21775_CR46","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1038\/35051038","volume":"409","author":"A S\u00f8rensen","year":"2001","unstructured":"S\u00f8rensen, A., Duan, L. M., Cirac, J. I. & Zoller, P. Many\u2013particle entanglement with Bose\u2013Einstein condensates. Nature 409, 63\u201366 (2001).","journal-title":"Nature"},{"key":"BFsrep21775_CR47","doi-asserted-by":"crossref","first-page":"2731","DOI":"10.1103\/PhysRevLett.60.2731","volume":"60","author":"MD Reid","year":"1988","unstructured":"Reid, M. D. & Drummond, P. D. Quantum Correlations of Phase in Nondegenerate Parametric Oscillation. Phys. Rev. Lett. 60, 2731 (1988).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR48","doi-asserted-by":"crossref","first-page":"4232","DOI":"10.1103\/PhysRevLett.84.4232","volume":"84","author":"MD Lukin","year":"2000","unstructured":"Lukin, M. D., Yelin, S. F. & Fleischhauer, M. Entangle of Atomic Ensembles by Trapping Correlated Photon States. Phys. Rev. Lett. 84, 4232 (2000).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR49","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1038\/35106500","volume":"414","author":"LM Duan","year":"2001","unstructured":"Duan, L. M., Lukin, M. D., Cirac, J. I. & Zoller, P. Long\u2013distance quantum communication with atomic ensembles and linear optics. Nature 414, 413\u2013418 (2001).","journal-title":"Nature"},{"key":"BFsrep21775_CR50","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1038\/nature04353","volume":"438","author":"CW Chou","year":"2005","unstructured":"Chou, C. W. et al. Measurement\u2013induced entanglement for excitation stored in remote atomic ensembles. Nature 438, 828\u2013832 (2005).","journal-title":"Nature"},{"key":"BFsrep21775_CR51","doi-asserted-by":"crossref","first-page":"080503","DOI":"10.1103\/PhysRevLett.107.080503","volume":"107","author":"H Krauter","year":"2011","unstructured":"Krauter, H. et al. Entanglement Generated by Dissipation and Steady State Entanglement of two Macroscopic Objects. Phys. Rev. Lett. 107, 080503 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR52","doi-asserted-by":"crossref","first-page":"052312","DOI":"10.1103\/PhysRevA.83.052312","volume":"83","author":"CA Muschik","year":"2011","unstructured":"Muschik, C. A., Polzik, E. S. & Cirac, J. I. Dissipatively driven entanglement of two macroscopic atomic ensembles. Phys. Rev. A 83, 052312 (2011).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR53","doi-asserted-by":"crossref","first-page":"030405","DOI":"10.1103\/PhysRevLett.96.030405","volume":"96","author":"DN Matsukevich","year":"2006","unstructured":"Matsukevich, D. N. et al. Entanglement of Remote Atomic Qubits. Phys. Rev. Lett. 96, 030405 (2006).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR54","doi-asserted-by":"crossref","first-page":"052305","DOI":"10.1103\/PhysRevA.75.052305","volume":"75","author":"W Ji","year":"2007","unstructured":"Ji, W., Wu, C., van Enk, S. J. & Raymer, M. G. Mesoscopic entanglement of atomic ensembles through nonreasonant stimulated Raman scattering. Phys. Rev. A 75, 052305 (2007).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR55","doi-asserted-by":"crossref","first-page":"032328","DOI":"10.1103\/PhysRevA.72.032328","volume":"72","author":"AD Lisi","year":"2005","unstructured":"Lisi, A. D., Siena, S. D., Illuminati, F. & Vitali, D. Quasideterministic generation of maximally entangled states of two mesoscopic atomic ensembles by adiabatic quantum feedback. Phys. Rev. A 72, 032328 (2005).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR56","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1103\/RevModPhys.70.101","volume":"70","author":"MB Plenio","year":"1998","unstructured":"Plenio, M. B. & Knight, P. L. The quantum\u2013jump approach to dissipative dynamics in quantum. Rev. Mod. Phys. 70, 101 (1998).","journal-title":"Rev. Mod. Phys."},{"key":"BFsrep21775_CR57","doi-asserted-by":"crossref","first-page":"1762","DOI":"10.1103\/PhysRevLett.85.1762","volume":"85","author":"A Beige","year":"2000","unstructured":"Beige, A., Braun, D., Tregenna, B. & Knight, P. L. Quantum Computing Using Dissipation to Remain in a Decoherence\u2013Free Subspace. Phys. Rev. Lett. 85, 1762 (2000).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR58","doi-asserted-by":"crossref","first-page":"067901","DOI":"10.1103\/PhysRevLett.91.067901","volume":"91","author":"DE Browne","year":"2003","unstructured":"Browne, D. E., Plenio, M. B. & Huelga, S. F. Robust Creation of Entanglement between Ions in Spatially Separate Cavities. Phys. Rev. Lett. 91, 067901 (2003).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR59","doi-asserted-by":"crossref","first-page":"062335","DOI":"10.1103\/PhysRevA.71.062335","volume":"71","author":"SB Zheng","year":"2005","unstructured":"Zheng, S. B. Quantum logic gates for two atoms with a single reasonant interaction. Phys. Rev. A 71, 062335 (2005).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR60","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1103\/RevModPhys.82.1041","volume":"82","author":"K Hammerer","year":"2010","unstructured":"Hammerer, K., S\u00f8ensen, A. S. & Polzik, E. S. Quantum interface between light and atomic ensemble. Rev. Mod. Phys. 82, 1041 (2010).","journal-title":"Rev. Mod. Phys."},{"key":"BFsrep21775_CR61","doi-asserted-by":"crossref","first-page":"013601","DOI":"10.1103\/PhysRevA.82.013601","volume":"82","author":"G Chen","year":"2010","unstructured":"Chen, G. et al. Qubit\u2013induced high\u2013order nonliner interaction of the polar molecules in a stripline cavity. Phys. Rev. A 82, 013601 (2010).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR62","doi-asserted-by":"crossref","first-page":"148301","DOI":"10.1103\/PhysRevLett.88.148301","volume":"88","author":"AD Armour","year":"2002","unstructured":"Armour, A. D., Blencowe, M. P. & Schwab, K. C. Entangelement and Decoherence of a Micromechanical Resonator via Coupling to a Cooper\u2013Pair Box. Phys. Rev. Lett. 88, 148301 (2002).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR63","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1088\/1751-8113\/46\/48\/485305","volume":"46","author":"L Garcia","year":"2013","unstructured":"Garcia, L., Chhajlany, R. W., Li, Y. & Wu, L. A. Driving a mechanical reasonator into coherent states via random measurement. J. Phys. A: Math. Theor. 46, 852\u2013859 (2013).","journal-title":"J. Phys. A: Math. Theor."},{"key":"BFsrep21775_CR64","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1126\/science.1157233","volume":"320","author":"P Neumann","year":"2008","unstructured":"Neumann, P. Multipartite Entanglement Among Single Spins in Diamond. Science 320, 1326\u20131329 (2008).","journal-title":"Science"},{"key":"BFsrep21775_CR65","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.diamond.2005.12.027","volume":"15","author":"J Harrison","year":"2006","unstructured":"Harrison, J., Sellars, M. J. & Manson, N. B. Measurement of the optically induced spin polarisation of N-V centres in diamond. Diam. Relat. Mater. 15, 586\u2013588 (2006).","journal-title":"Diam. Relat. Mater."},{"key":"BFsrep21775_CR66","doi-asserted-by":"crossref","first-page":"201201","DOI":"10.1103\/PhysRevB.82.201201","volume":"82","author":"PL Stanwix","year":"2010","unstructured":"Stanwix, P. L. et al. Coherence of nitrogen\u2013vacancy electronic spin ensembles in diamond. Phys. Rev. B 82, 201201 (2010).","journal-title":"Rev. B"},{"key":"BFsrep21775_CR67","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1038\/nmat2420","volume":"8","author":"G Balasubramanian","year":"2009","unstructured":"Balasubramanian, G. et al. Ultralong spin coherence time in isotopically engineered diamond. Nat. Materials 8, 383\u2013387 (2009).","journal-title":"Nat. Materials"},{"key":"BFsrep21775_CR68","doi-asserted-by":"crossref","first-page":"210501","DOI":"10.1103\/PhysRevLett.105.210501","volume":"105","author":"D Marcos","year":"2010","unstructured":"Marcos, D. et al. Coupling Nitrogen\u2013Vacancy Centers in Diamond to Superconducting Flux Qubits. Phys. Rev. Lett. 105, 210501 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR69","doi-asserted-by":"crossref","first-page":"060501","DOI":"10.1103\/PhysRevLett.108.060501","volume":"108","author":"JI de Vicente","year":"2012","unstructured":"de Vicente, J. I., Carle, T., Streitberger, C. & Kraus, B. Complete Set of Operational Measures for the Characterization of Three\u2013Qubit Entanglement. Phys. Rev. Lett. 108, 060501 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"BFsrep21775_CR70","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1038\/nphys3202","volume":"11","author":"S Armstrong","year":"2015","unstructured":"Armstrong, S. et al. Multipartite Einstein\u2013Podolsky\u2013Rosen steering and genuine tripartite entanglement with optical networks. Nature Phys. 11, 167 (2015).","journal-title":"Nature Phys."},{"key":"BFsrep21775_CR71","doi-asserted-by":"crossref","first-page":"13734","DOI":"10.1364\/OE.23.013734","volume":"23","author":"WL Song","year":"2015","unstructured":"Song, W. L. et al. Entanglement dynamics for three nitrogen\u2013vavancy centers coupled to a whispering\u2013gallery\u2013mode microcavity. Opt. Express 23, 13734\u201313751 (2015).","journal-title":"Opt. Express"},{"key":"BFsrep21775_CR72","doi-asserted-by":"crossref","first-page":"033813","DOI":"10.1103\/PhysRevA.90.033813","volume":"90","author":"F Badshah.","year":"2014","unstructured":"Badshah. F., Qamar, S. & Paternostro, M. Dynamics of interacting Dicke model in a coupled\u2013cavity array. Phys. Rev. A 90, 033813 (2014).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR73","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1088\/0305-4470\/35\/1\/313","volume":"35","author":"X Wang","year":"2002","unstructured":"Wang, X. Bipartite entangled non\u2013orthogonal states. J. Phys. A: Math. Gen. 35, 165\u2013173 (2002).","journal-title":"J. Phys. A: Math. Gen."},{"key":"BFsrep21775_CR74","doi-asserted-by":"crossref","first-page":"052308","DOI":"10.1103\/PhysRevA.64.052308","volume":"64","author":"H Jeong","year":"2001","unstructured":"Jeong, H., Kim, M. S. & Lee, J. Quantum\u2013information processing for a coherent superposition state via a mixedentangled coherent channel. Phys. Rev. A 64, 052308 (2001).","journal-title":"Phys. Rev. A"},{"key":"BFsrep21775_CR75","doi-asserted-by":"crossref","first-page":"2140","DOI":"10.1103\/PhysRevA.53.2140","volume":"53","author":"F Mertins","year":"1996","unstructured":"Mertins, F. & Schirmer, J. Algebraic propagator approaches and intermediate\u2013state representations. I. The biorthogonal and unitary coupled\u2013cluster methods. Phys. Rev. A 53, 2140 (1996).","journal-title":"Phys. Rev. A"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/srep21775","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep21775.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep21775.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T14:28:13Z","timestamp":1672842493000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/srep21775"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,23]]},"references-count":75,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,4,20]]}},"alternative-id":["BFsrep21775"],"URL":"https:\/\/doi.org\/10.1038\/srep21775","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,23]]},"assertion":[{"value":"15 December 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing financial interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"21775"}}