Abstract
We propose a scheme for the realization of a hybrid, strongly entangled system formed of an atomic ensemble surrounded by a quadratically coupled optomechanical cavity with a vibrating mirror. We firstly investigate the steady-state bipartite entanglement between the movable mirror and the cavity mode with the help of an atomic media. It shows that the introduction of the atomic medium can greatly improve the entanglement between the movable mirror and the cavity mode. Secondly, steady-state tripartite entanglement including the movable mirror, the cavity and atom media are investigated. We find the robust tripartite entanglement persists in the present system.
Similar content being viewed by others
References
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Esteve, D., Raimond, J.M., Dalibard, J.: Quantum Entanlement and Information Processing. Elsevier (2004)
Horodecki, R., et al.: Rev. Mod. Phys. 81, 865–942 (2009)
Mancini, S., Giovannetti, V., Vitali, D., Tombesi, P.: Phys. Rev. Lett. 88, 120401 (2002)
Wang, G.L., Huang, L., Lai, Y.C., Grebogi, C.: Phys. Rev. Lett. 112, 110406 (2014)
Bariani, F., Singh, S., Buchmann, L.F., Vengalattore, M., Meystre, P.: Phys. Rev. A 90, 033838 (2014)
Wang, Y.D., Clerk, A.A.: Phys. Rev. Lett. 110, 253601 (2013)
Xu, X.N., Taylor, J.M.: Phys. Rev. A 90, 043848 (2014)
Huang, S.M., Agarwal, G.S.: Phys. Rev. A 83, 043826 (2011)
Huang, S.M., Agarwal, G.S.: Phys. Rev. A 80, 033807 (2009)
Rocheleau, T., Ndukum, T., Macklin, C., Hertzberg, J.B., Clerk, A.A, Achwab, K.C.: Nature 463, 72–75 (2010)
O’Connell, A.D., et al.: Nature 464, 697–703 (2010)
Brown, K.R., et al.: Nature 471, 196–199 (2011)
Khalili, F., et al.: Phys. Rev. Lett. 105, 070403 (2010)
Zhao, C., et al.: Phys. Rev. Lett. 102, 243902 (2009)
Jähne, K., Genes, C., Hammerer, K., et al.: Phys. Rev. A 79, 063819 (2009)
Pinard, M., Dantan, A., Vitali, D., Arcizet, O., Briant, T., Heidmann, A.: Europhys. Lett. 72, 747 (2005)
Vitali, D., Mancini, S., Tombesi, P.J.: Phys. A: Math. Theor. 40, 8055 (2007)
Huang, S.M., Agarwal, G.S.: New J. Phys. 11, 103044 (2009)
Vitali, D., Gigan, S., Ferreira, A., Böhm, H.R., Tombesi, P., Guerreiro, A., Vedral, V., Zeilinger, A., Aspelmeyer, M.: Phys. Rev. Lett. 98, 030405 (2007)
Genes, C., Mari, A., Tombesi, P., Vitali, D.: Phys. Rev. A 78, 032316 (2008)
Ferreira, A., Guerreiro, A., Vedral, V.: Phys. Rev. Lett. 96, 060407 (2006)
Vedral, V.: New. J. Phys. 6, 102 (2004)
Ma, Y.H., Zhou, L.: J. Appl. Phys. 111, 103109 (2012)
Ma, Y.H., Zhou, L.: Chin. Phys. B 2, 024204 (2013)
Ma, Y.H., Zhang, X.F.: Appl. Phys. B 112, 485–489 (2013)
Thompson, J.D., Zwickl, B.M., Jayich, A.M., Marquardt, F., Girvin, S.M., Harris, J.G.E.: Nature (London) 452, 72 (2008)
Braginsky, V.B., Vorontsov, Y.I., Thorne, K.S.: Science 209, 547–557 (1980)
Santamore, D.H., Doherty, A.C., Cross, M.C.: Phys. Rev. B 70, 144301 (2004)
Matin, I., Zurek, W.H.: Phys. Rev. Lett. 98, 120401 (2007)
Jacobs, K., Lougovski, P., Blencowe, M.: Phys. Rev. Lett. 98, 147201 (2007)
Jayich, A.M., et al.: New J. Phys. 10, 095008 (2008)
Sankey, J.C., Yang, C., Zwickl, B.M., Jayich, A.M., Harris, J.G.E.: Nat. Phys. 6, 707–712 (2010)
Bhattacharya, M., Uys, H., Meystre, P.: Phys. Rev. A 77, 033819 (2008)
Nunnenkamp, A., Børkje, K., Harris, J.G.E., Girvin, S.M.: Phys. Rev. A 82, 021806(R) (2010)
Asjad, M., Agarwal, G.S., Kim, M.S., Tombesi, P., Di Giuseppe, G., Vitali, D.: Phys. Rev. A 89, 023849 (2014)
Han, Y., Cheng, J., Zhou, L.: J. Mod. Opt. 15, 1336–1341 (2012)
Xuereb, A., Paternostro, M.: Phys. Rev. A 87, 023830 (2013)
Vanner, M.R.: Phys. Rev. X 1, 021011 (2011)
Shi, H, Bhattacharya, M.: Phys. Rev. A 87, 043829 (2013)
Li, H.K., Liu, Y.C., Yi, X., Zou, C.L., Ren, X.X., Xiao, Y.F.: Phys.Rev. A 85, 053832 (2012)
Deng, Z.J., Li, Y., Gao, M., Wu, C.W.: Phys. Rev. A 85, 025804 (2012)
Liao, J.Q., Nori, F.: Phys. Rev. A 88, 023853 (2013)
Treutlein, P., et al.: arXiv:1210.4151
Genes, C., Ritsch, H., Vitali, D.: Phys. Rev. A 80, 061803(R) (2009)
Hunger, D., Camerer, S., Hänsch, T.W., König, D., Kotthaus, J.P., Reichel, J., Treutlein, P.: Phys. Rev. Lett. 104, 143002 (2010)
Camerer, S., Korppi, M., Jöckel, A., Hunger, D., Hänsch, T.W., Treutlein, P.: Phys. Rev. Lett. 107, 223001 (2011)
Hammerer, K., et al.: Phys. Rev. Lett. 103, 063005 (2009)
Meiser, D., Meystre, P.: Phys. Rev. A 73, 033417 (2006)
Ian, H., Gong, Z.R., Liu, Y.X., Sun, C.P., Nori, F.: Phys. Rev. A 78, 013824 (2008)
Chang, Y., Ian, H., Sun, C.P.: J. Phys. B 42, 215502 (2009)
Han, Y., Cheng, J., Zhou, L.: Eur. Phys. J. D 67, 20 (2013)
Genes, C., Vitali, D., Tombesi, P.: Phys. Rev. A 77(R), 050307 (2008)
De Chiara, G., Paternostro, M., Palma, G.M.: Phys. Rev. A 83, 052324 (2011)
Zhang, J., Zhang, T., Xuereb, A., Vitali, D., Li, J.: Annalen der Physik 527, 147 (2015)
Brennecke, F., Donner, T., Ritter, S., et al.: Nature 450, 268–271 (2007)
Brennecke, F., Ritter, S., Donner, T., et al.: Science 322, 235–238 (2008)
He, L., Liu, Y.X., Yi, S., Sun, C.P., Nori, F.: Phys. Rev. A 75, 063818 (2007)
Song, Z., Zhang, P., Shi, T., Sun, C.P.: Phys. Rev. B 71, 205314 (2005)
Gardiner, C.: Quantum Noise. Springer, Berlin (1991)
DeJesus, E.X., Kaufman, C.: Phys. Rev. A 35, 5288 (1987)
Laurat, J., Keller, G., Augusto Oliveira-Huguenin, J., Fabre, C., Coudreau, T., Serafini, A., Adesso, G., Illuminati, F.: J. Opt. B: Quantum Semiclass. Opt. 7, S577–S587 (2005)
Vidal, G., Werner, R.F.: Pyhs. Rew. A 65, 032314 (2002)
Ma, Y.H., Mu, Q.X., Zhou, L.: J. Phys. B: At. Mol. Opt. Phys. 41, 215502 (2008)
Adesso, G., Serafini, A., Illuminati, F.: Phys. Rev. A 70, 022318 (2004)
Aspelmeyer, M: Rev. Mod. Phys. 86, 1391 (2014)
Vogell, B., Stannigel, K., Zoller, P., Hammerer, K., Rakher, M.T., Korppi, M., Jöckel, A., Treutlein, P.: Phys. Rev. A 87, 023816 (2013)
van Loock, P., Braunstein, S.L.: Phys. Rev. Lett. 84, 3482 (2000)
van Loock, P., Furusawa, A.: Phys. Rev. A 67, 052315 (2003)
Olsen, M.K., Bradley, A.S.: Phys. Rev. A 74, 063809 (2006)
Villar, A.S., Martinelli, M., Fabre, C., Nussenzveig, P.: Phys. Rev. Lett. 97, 140504 (2006)
Li, X.X., Hu, X.M.: Phys. Rev. A 85, 023815 (2009)
Tan, H.T., Huang, H.: Phys. Rev. A 83, 015802 (2011)
Lv, X.Y., Huang, P., Yang, W.X., Yang, X.X.: Phys. Rev. A 80, 032305 (2009)
Tan, A.H., Xie, C.D., Peng, K.C.: Phys. Rev. A 85, 013819 (2012)
Sherson, J., et al.: Nature 443, 557 (2006)
Grimm, R., Weidemüller, M., Ovchinnikov, Y.B.: pp 95–170. Academic Press (2000)
Kerman, A.J., Vuletic, V., Chin, C., Chu, S.: Phys. Rev. Lett. 84, 439 (2000)
Acknowledgments
The project was supported by NSFC (Grants No.11164018 and 11305085) and Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grants No. NJYT-13-B13), the Key Project of Chinese Ministry of Education under Grant No. 212028 and Youth academic backbone of inner university of science and technology special project (No. 2014QNGG04).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that there is no conflict of interests regarding the publication of this article.
Rights and permissions
About this article
Cite this article
Ma, YH., Li, FZ., Han, XG. et al. Generation of Steady-State Entanglement in Quadratically Coupled Optomechanical System Assisted by Two-Level Atoms. Int J Theor Phys 55, 2386–2396 (2016). https://doi.org/10.1007/s10773-015-2876-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-015-2876-8