Skip to main content

Advertisement

Springer Nature Link
Log in

Emergence of multipartite optomechanical entanglement in microdisk cavities coupled to nanostring waveguide

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, we propose a scheme to show signatures of multipartite optomechanical entanglement, which is based on two high quality factor (high-\(Q\)) silicon nitride (\(\text{ Si }_{3}\text{ N }_{4}\)) microdisk cavities coupled to a nanostring waveguide via evanescent field. Genuine tripartite optomechanical entanglement is shared in the subsystem even though the two fields of microdisk cavities do not have direct interaction. In addition, we study the behaviors of the bipartite entanglement between the pairs of the system constituents by numerical simulation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Mancini, S., Vitali, D., Tombesi, P.: Scheme for teleportation of quantum states onto a mechanical resonator. Phys. Rev. Lett. 90, 137901 (2003)

    Article  ADS  Google Scholar 

  2. Eichenfield, M., Camacho, R., Chan, J., Vahala, K.J., Painter, O.: A picogram- and nanometre-scale photonic-crystal optomechanical cavity. Nature (London) 459, 550–555 (2009)

    Article  ADS  Google Scholar 

  3. Pernice, W.H.P., Li, M., Tang, H.X.: Optomechanical coupling in photonic crystal supported nanomechanical waveguides. Opt. Express 17, 12424–12432 (2009)

    Article  ADS  Google Scholar 

  4. Schliesser, A., Arcizet, O., Riviere, R., Anetsberger, G., Kippenberg, T.J.: Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit. Nat. Phys. 5, 509–514 (2009)

    Article  Google Scholar 

  5. Kippenberg, T.J., Rokhsari, H., Carmon, T., Scherer, A., Vahala, K.J.: Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity. Phys. Rev. Lett. 95, 033901 (2005)

    Article  ADS  Google Scholar 

  6. Park, Y.S., Wang, H.: Resolved-sideband and cryogenic cooling of an optomechanical resonator. Nat. Phys. 5, 489–493 (2009)

    Article  Google Scholar 

  7. Pernice, M.L.W.H.P., Tang, X.H.: Harnessing optical forces in integrated photonic circuits. Nature (London) 456, 480–484 (2008)

    Article  ADS  Google Scholar 

  8. Verbridge, S.S., Craighead, H.G., Parpia, J.M.: A megahertz nanomechanical resonator with room temperature quality factor over a million. Appl. Phys. Lett. 92, 013112 (2008)

    Article  ADS  Google Scholar 

  9. Fong, K.Y., Pernice, W.H.P., Li, M., Tang, H.X.: High Q optomechanical resonators in silicon nitride nanophotonic circuits. Appl. Phys. Lett. 97, 073112 (2010)

    Article  ADS  Google Scholar 

  10. Hertzberg, J.B., Rocheleau, T., Ndukum, T., Savva, M., Clerk, A.A., Schwab, K.C.: Back-action-evading measurements of nanomechanical motion. Nat. Phys. 6, 213–217 (2010)

    Article  Google Scholar 

  11. Eichenfield, M., Michael, C.P., Perahia, R., Painter, O.: Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces. Nat. Photonics 1, 416–422 (2007)

    Article  ADS  Google Scholar 

  12. Thompson, J.D., Zwickl, B.M., Jayich, A.M., Marquardt, F., Girvin, S.M., Harris, J.G.E.: Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature (London) 452, 72–75 (2008)

    Article  ADS  Google Scholar 

  13. Metzger, C.H., Karrai, K.: Cavity cooling of a microlever. Nature (London) 432, 1002–1005 (2004)

    Article  ADS  Google Scholar 

  14. Li, T., Kheifets, S., Medellin, D., Raizen, M.G.: Measurement of the instantaneous velocity of a Brownian particle. Science 328, 1673–1675 (2010)

    Article  ADS  Google Scholar 

  15. Mancini, S., Giovannetti, V., Vitali, D., Tombesi, P.: Entangling macroscopic oscillators exploiting radiation pressure. Phys. Rev. Lett. 88, 120401 (2002)

    Article  ADS  Google Scholar 

  16. Pirandola, S., Vitali, D., Tombesi, P., Lloyd, S.: Macroscopic entanglement by entanglement swapping. Phys. Rev. Lett. 97, 150403 (2006)

    Article  ADS  Google Scholar 

  17. Vitali, D., Gigan, S., Ferreira, A., Bohm, H.R., Tombesi, P., Guerreiro, A., Vedral, V., Zeilinger, A., Aspelmeyer, M.: Optomechanical entanglement between a movable mirror and a cavity field. Phys. Rev. Lett. 98, 030405 (2007)

    Article  ADS  Google Scholar 

  18. Genes, C., Vitali, D., Tombesi, P.: Emergence of atom-light-mirror entanglement inside an optical cavity. Phys. Rev. A 77, 050307 (2008)

    Article  ADS  Google Scholar 

  19. Chiara, G.D., Paternostro, M., Palma, G.M.: Entanglement detection in hybrid optomechanical systems. Phys. Rev. A 83, 052324 (2011)

    Article  ADS  Google Scholar 

  20. Zhou, L., Han, Y., Jing, J.T., Zhang, W.P.: Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence. Phys. Rev. A 83, 052117 (2011)

    Article  ADS  Google Scholar 

  21. Huang, S.M., Agarwal, G.S.: Entangling nanomechanical oscillators in a ring cavity by feeding squeezed light. New J. Phys. 11, 103044 (2009)

    Article  ADS  Google Scholar 

  22. Zou, C.L., Zou, X.B., Sun, F.W., Han, Z.F., Guo, G.C.: Room-temperature steady-state optomechanical entanglement on a chip. Phys. Rev. A 84, 032317 (2011)

    Article  ADS  Google Scholar 

  23. Anetsberger, G., Arcizet, O., Unterreithmeier, Q.P., Rivière, R., Schliesser, A., Weig, E.M., Kotthaus, J.P., Kippenberg, T.J.: Near-field cavity optomechanics with nanomechanical oscillators. Nat. Phys. 5, 909–914 (2009)

    Article  Google Scholar 

  24. Anetsberger, G., Gavartin, E., Arcizet, O., Unterreithmeier, Q.P., Weig, E.M., Gorodetsky, M.L., Kotthaus, J.P., Kippenberg, T.J.: Measuring nanomechanical motion with an imprecision below the standard quantum limit. Phys. Rev. A 82, 061804 (2010)

    Article  ADS  Google Scholar 

  25. Paternostro, M., Vitali, D., Gigan, S., Kim, M.S., Brukner, C., Eisert, J., Aspelmeyer, M.: Creating and probing multipartite macroscopic entanglement with light. Phys. Rev. Lett. 99, 250401 (2007)

    Article  ADS  Google Scholar 

  26. Miao, H., Danilishin, S., Chen, Y.: Universal quantum entanglement between an oscillator and continuous fields. Phys. Rev. A 81, 052307 (2010)

    Article  ADS  Google Scholar 

  27. Miao, H., Danilishin, S., Müller-Ebhardt, H., Chen, Y.: Achieving ground state and enhancing optomechanical entanglement by recovering information. New J. Phys. 12, 083032 (2010)

    Article  ADS  Google Scholar 

  28. Simon, R.: Peres–Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726–2729 (2000)

    Article  ADS  Google Scholar 

  29. Miao, H., Zhao, C., Ju, L., Blair, D.G.: Quantum ground-state cooling and tripartite entanglement with three-mode optoacoustic interactions. Phys. Rev. A 79, 063801 (2009)

    Article  ADS  Google Scholar 

  30. Gorodetsky, M.L., Ilchenko, V.S.: Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes. J. Opt. Soc. Am. B 16, 147–154 (1999)

    Article  ADS  Google Scholar 

  31. Cai, M., Painter, O., Vahala, K.J.: Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system. Phys. Rev. Lett. 85, 74–77 (2000)

    Article  ADS  Google Scholar 

  32. Walls, D.F., Milburn, G.J.: Quantum Optics. Springer, Berlin (1994)

    MATH  Google Scholar 

  33. Giovannetti, V., Vitali, D.: Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion. Phys. Rev. A 63, 023812 (2001)

    Article  ADS  Google Scholar 

  34. Li, M., Pernice, W.H.P., Tang, H.X.: Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides. Phys. Rev. Lett. 103, 223901 (2009)

    Article  ADS  Google Scholar 

  35. Huang, S.M., Agarwal, G.S.: Reactive-coupling-induced normal mode splittings in microdisk resonators coupled to waveguides. Phys. Rev. A 81, 053810 (2010)

    Article  ADS  Google Scholar 

  36. DeJesus, E.X., Kaufman, C.: Routh–Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Phys. Rev. A 35, 5288–5290 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  37. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  38. Eisert, J., Plenio, M.B.: Quantum and classical correlations in quantum Brownian motion. Phys. Rev. Lett. 89, 137902 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  39. Adesso, G., Serafini, A., Illuminati, F.: Extremal entanglement and mixedness in continuous variable systems. Phys. Rev. A 70, 022318 (2004)

    Article  ADS  Google Scholar 

  40. Tien, M.C., Bauters, J.F., Heck, M.J.R., Spencer, D.T., Blumenthal, D.J., Bowers, J.E.: Ultra-high quality factor planar Si3N4 ring resonators on Si substrates. Opt. Express 19, 13551–13556 (2011)

    Article  ADS  Google Scholar 

  41. Barclay, P.E., Srinivasan, K., Painter, O., Lev, B., Mabuchi, H.: Integration of fiber-coupled high-Q SiNx microdisks with atom chips. Appl. Phys. Lett. 89, 131108 (2006)

    Article  ADS  Google Scholar 

  42. Hosseini, E.S., Yegnanarayanan, S., Atabaki, A.H., Soltani, M., Adibi, A.: High quality planar silicon nitride microdisk resonators for integrated photonics in the visible wavelength range. Opt. Express 17, 14543–14551 (2009)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China under grant no. 11047122 and no. 11105030, the Natural Science Foundation of Fuzhou University of China under grant no. XRC-0976 and no.2010-XQ-28, the SRTP Foundation of Fuzhou University of China under grant no. 16118, the funds from Education Department of Fujian Province of China under grant no. JA11005, no. JA10009 and no. JA10039, the National Natural Science Foundation of Fujian Province of China under grant no. 2010J01006 and 2012J01269, the Foundation of Ministry of Education of China under grant no. 212085.

Author information

Authors and Affiliations

  1. Department of Physics, Fuzhou University, Fuzhou, 350002, China

    Zhi-Cheng Shi & Yan Xia

  2. School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian, 116024, China

    Yan Xia

  3. Department of Physics, Harbin Institute of Technology, Harbin, 150001, China

    Jie Song

Authors
  1. Zhi-Cheng Shi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yan Xia
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Jie Song
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yan Xia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi, ZC., Xia, Y. & Song, J. Emergence of multipartite optomechanical entanglement in microdisk cavities coupled to nanostring waveguide. Quantum Inf Process 12, 3179–3190 (2013). https://doi.org/10.1007/s11128-013-0590-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-013-0590-0

Keywords