Abstract
We propose an efficient scheme for the dissipative generation of steady-state entanglement of two negatively charged silicon-vacancy (SiV \(^{-}\)) centers, which are coupled to two separated photonic crystal cavities, respectively. With the external driving fields to tailor the desired interaction between the Zeeman-split lower orbital branches of the ground states of the SiV\(^{-}\) centers and the cavity fields, we show that the heavily damped cavities can induce an effective quantum reservoir coupled to the two SiV\(^{-}\) centers. Based on a form of quantum reservoir engineering, the two SiV\(^{-}\) centers can be cooled down to an entangled state at stationary state. Our scheme has the distinct feature that the decay of the cavities as resource is utilized for producing the steady-state entanglement, which does not need to exactly prepare the initial state of the system. The present work may open up promising perspectives for realizing quantum networks and quantum information processing with solid-state SiV\(^{-}\) centers in nanophotonic structures.
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References
Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)
Kimble, H.J.: The quantum internet. Nature 453, 1023 (2008)
Reiserer, A., Rempe, G.: Cavity-based quantum networks with single atoms and optical photons. Rev. Mod. Phys. 87, 1379 (2015)
Zheng, S.B., Guo, G.C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity QED. Phys. Rev. Lett. 85, 2392 (2000)
Hennessy, K., Badolato, A., Winger, M., Gerace, D., Atatüre, M., Gulde, S., Fält, S., Hu, E.L., Imamoğlu, A.: Quantum nature of a strongly coupled single quantum dot-cavity system. Nature 445, 896–899 (2007)
Carter, S.G., Sweeney, T.M., Kim, M., Kim, C.S., Solenov, D., Economou, S.E., Reinecke, T.L., Yang, L., Bracker, A.S., Gammon, D.: Quantum control of a spin qubit coupled to a photonic crystal cavity. Nat. Photonics 7, 329–334 (2013)
Bai, C.H., Wang, D.Y., Hu, S., Cui, W.X., Jiang, X.X., Wang, H.F.: Scheme for implementing multitarget qubit controlled-not gate of photons and controlled-phase gate of electron spins via quantum dot-microcavity coupled system. Quantum Inf. Process. 15, 1485–1498 (2016)
Chang, C., Lanco, L., Citrin, D.: Quantum stabilization of microcavity excitation in a coupled microcavity-half-cavity system. Phys. Rev. B 101, 024305 (2020)
Borjans, F., Croot, X., Mi, X., Gullans, M., Petta, J.: Resonant microwave-mediated interactions between distant electron spins. Nature 577, 195–198 (2020)
Faraon, A., Santori, C., Huang, Z., Acosta, V.M., Beausoleil, R.G.: Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond. Phys. Rev. Lett. 109, 033604 (2012)
Li, P.B., Gao, S.Y., Li, H.R., Ma, S.L., Li, F.L.: Dissipative preparation of entangled states between two spatially separated nitrogen-vacancy centers. Phys. Rev. A 85, 042306 (2012)
Park, Y.S., Cook, A.K., Wang, H.: Cavity QED with diamond nanocrystals and silica microspheres. Nano Lett. 6, 2075–2079 (2006)
Yu, X.C., Liu, Y.C., Yan, M.Y., Jin, W.L., Xiao, Y.F.: Coupling of diamond nanocrystals to a high-\(q\) whispering-gallery microresonator. Phys. Rev. A 86, 043833 (2012)
Hong, F.Y., Fu, J.L., Wu, Y., Zhu, Z.Y.: Room-temperature spin-photon interface for quantum networks. Quantum Inf. Process 16, 43 (2017)
Lodahl, P., Mahmoodian, S., Stobbe, S.: Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347 (2015)
Laucht, A., Villas-Bôas, J.M., Stobbe, S., Hauke, N., Hofbauer, F., Böhm, G., Lodahl, P., Amann, M.C., Kaniber, M., Finley, J.J.: Mutual coupling of two semiconductor quantum dots via an optical nanocavity. Phys. Rev. B 82, 075305 (2010)
Press, D., Greve, K.D., McMahon, P.L., Ladd, T.D., Friess, B., Schneider, C., Kamp, M., Höfling, S., Forchel, A., Yamamoto, Y.: Ultrafast optical spin echo in a single quantum dot. Nat. Photonics 4, 367–370 (2010)
Balasubramanian, G., et al.: Ultralong spin coherence time in isotopically engineered diamond. Nat. Mater. 8, 383 (2009)
Bernien, H., et al.: Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013)
Shi, F., Rong, X., Xu, N., Wang, Y., Wu, J., Chong, B., Peng, X., Kniepert, J., Schoenfeld, R.S., Harneit, W., Feng, M., Du, J.: Room-temperature implementation of the deutsch-jozsa algorithm with a single electronic spin in diamond. Phys. Rev. Lett. 105, 040504 (2010)
Evans, R.E., Sipahigil, A., Sukachev, D.D., Zibrov, A.S., Lukin, M.D.: Narrow-linewidth homogeneous optical emitters in diamond nanostructures via silicon ion implantation. Phys. Rev. Appl. 5, 044010 (2016)
Sohn, Y.I., Meesala, S., Pingault, B., Atikian, H.A., Holzgrafe, J., Gündoğan, M., Stavrakas, C., Stanley, M.J., Sipahigil, A., Choi, J., Zhang, M., Pacheco, J.L., Abraham, J., Bielejec, E., Lukin, M.D., Atatüre, M., Lončar, M.: Controlling the coherence of a diamond spin qubit through its strain environment. Nat. Commun. 9, 2012 (2018)
Weinzetl, C., Görlitz, J., Becker, J.N., Walmsley, I.A., Poem, E., Nunn, J., Becher, C.: Coherent control and wave mixing in an ensemble of silicon-vacancy centers in diamond. Phys. Rev. Lett. 122, 063601 (2019)
Sun, S., Zhang, J.L., Fischer, K.A., Burek, M.J., Dory, C., Lagoudakis, K.G., Tzeng, Y.K., Radulaski, M., Kelaita, Y., Safavi-Naeini, A., Shen, Z.X., Melosh, N.A., Chu, S., Lončar, J.: Cavity-enhanced raman emission from a single color center in a solid. Phys. Rev. Lett. 121, 083601 (2018)
Maity, S., et al.: Coherent acoustic control of a single silicon vacancy spin in diamond. Nat. Commun. 11, 193 (2020)
Rogers, L.J., Jahnke, K.D., Metsch, M.H., Sipahigil, A., Binder, J.M., Teraji, T., Sumiya, H., Isoya, J., Lukin, M.D., Hemmer, P., Jelezko, F.: All-optical initialization, readout, and coherent preparation of single silicon-vacancy spins in diamond. Phys. Rev. Lett. 113, 263602 (2014)
Becker, J.N., Pingault, B., Groß, D., Gündoğan, M., Kukharchyk, N., Markham, M., Edmonds, A., Atatüre, M., Bushev, P., Becher, C.: All-optical control of the silicon-vacancy spin in diamond at millikelvin temperatures. Phys. Rev. Lett. 120, 053603 (2018)
Pingault, B., Jarausch, D.D., Hepp, C., Klintberg, L., Becker, J.N., Markham, M., Becher, C., Atatüre, M.: Coherent control of the silicon-vacancy spin in diamond. Nat. Commun. 8, 15579 (2017)
Evans, R.E., et al.: Photon-mediated interactions between quantum emitters in a diamond nanocavity. Science 362, 662–665 (2018)
Sipahigil, A., et al.: An integrated diamond nanophotonics platform for quantum optical networks. Science 354, 847–850 (2016)
Kastoryano, M.J., Reiter, F., Sørensen, A.S.: Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)
Wu, Q.C., Ji, X.: Generation of steady three-and four-dimensional entangled states via quantum-jump-based feedback. Quantum Inf. Process. 12, 3167–3178 (2013)
Shao, X.Q., Wu, J.H., Yi, X.X., Long, G.L.: Dissipative preparation of steady greenberger-horne-zeilinger states for rydberg atoms with quantum zeno dynamics. Phys. Rev. A 96, 062315 (2017)
Su, S.L., Shao, X.Q., Wang, H.F., Zhang, S.: Scheme for entanglement generation in an atom-cavity system via dissipation. Phys. Rev. A 90, 054302 (2014)
Rao, D.D.B., Mølmer, K.: Deterministic entanglement of Rydberg ensembles by engineered dissipation. Phys. Rev. A 90, 062319 (2014)
Su, S.L., Tian, Y.Z., Shen, H.Z., Zang, H.P., Liang, E., Zhang, S.: Applications of the modified Rydberg antiblockade regime with simultaneous driving. Phys. Rev. A 96, 042335 (2017)
Jin, Z., Su, S.L., Zhang, S.: Preparation of a steady entangled state of two nitrogen-vacancy centers by simultaneouly utilizing two dissipative factors. Phys. Rev. A 100, 052332 (2019)
Riedrich-Möller, J., Arend, C., Pauly, C., Mücklich, F., Fischer, M., Gsell, S., Schreck, M., Becher, C.: Deterministic coupling of a single silicon-vacancy color center to a photonic crystal cavity in diamond. Nano Lett. 14, 5281–5287 (2014)
Wan, N.H., Mouradian, S., Englund, D.: Two-dimensional photonic crystal slab nanocavities on bulk single-crystal diamond. Appl. Phys. Lett. 112, 141102 (2018)
Englund, D., Shields, B., Rivoire, K., Hatami, F., Vuckovic, J., Park, H., Lukin, M.D.: Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity. Nano lett. 10, 3922–3926 (2010)
Chatzopoulos, I., Martini, F., Cernansky, R., Politi, A.: High-Q/V photonic crystal cavities and QED analysis in 3C-SiC. ACS Photonics 6, 1826–1831 (2019)
Asano, T., Ochi, Y., Takahashi, Y., Kishimoto, K., Noda, S.: Photonic crystal nanocavity with a q factor exceeding eleven million. Opt. Express 25, 1769 (2017)
Riedrich-Möller, J., Kipfstuhl, L., Hepp, C., Neu, E., Pauly, C., Mücklich, F., Baur, A., Wandt, M., Wolff, S., Fischer, M., Gsell, S., Schreck, M., Becher, C.: One- and two-dimensional photonic crystal microcavities in single crystal diamond. Nat. Nanotechnol. 7, 69–74 (2011)
Burek, M.J., Chu, Y., Liddy, M.S.Z., Patel, P., Rochman, J., Meesala, S., Hong, W., Quan, Q., Lukin, M.D., Lončar, M.: High quality-factor optical nanocavities in bulk single-crystal diamond. Nat. Commun. 5, 5718 (2014)
Mouradian, S., Wan, N.H., Schröder, T., Englund, D.: Rectangular photonic crystal nanobeam cavities in bulk diamond. Appl. Phys. Lett. 111, 021103 (2017)
Zhang, J.L., Sun, S., Burek, M.J., Dory, C., Tzeng, Y.K., Fischer, K.A., Kelaita, Y., Lagoudakis, K.G., Radulaski, M., Shen, Z.X., Melosh, N.A., Chu, S., Lončar, M., Vučković, J.: Strongly cavity-enhanced spontaneous emission from silicon-vacancy centers in diamond. Nano Lett. 18, 1360–1365 (2018)
Na, N., Utsunomiya, S., Tian, L., Yamamoto, Y.: Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities. Phys. Rev. A 77, 031803 (2008)
Shen, L.T., Chen, X.Y., Yang, Z.B., Wu, H.Z., Zheng, S.B.: Steady-state entanglement for distant atoms by dissipation in coupled cavities. Phys. Rev. A 84, 064302 (2011)
Notomi, M., Kuramochi, E., Tanabe, T.: Large-scale arrays of ultrahigh-q coupled nanocavities. Nat. Photonics 2, 741 (2008)
Sato, Y., Tanaka, Y., Upham, J., Takahashi, Y., Asano, T., Noda, S.: Strong coupling between distant photonic nanocavities and its dynamic control. Nat. Photonics 6, 56 (2012)
Goss, J.P., Briddon, P.R., Shaw, M.J.: Density functional simulations of silicon-containing point defects in diamond. Phys. Rev. B 76, 075204 (2007)
Pingault, B., Becker, J.N., Schulte, C.H.H., Arend, C., Hepp, C., Godde, T., Tartakovskii, A.I., Markham, M., Becher, C., Atatüre, M.: All-optical formation of coherent dark states of silicon-vacancy spins in diamond. Phys. Rev. Lett. 113, 263601 (2014)
Zhou, Y., Rasmita, A., Li, K., Xiong, Q., Aharonovich, I., Gao, W.B.: Coherent control of a strongly driven silicon vacancy optical transition in diamond. Nat. Commun. 8, 14451 (2017)
Awschalom, D.D., Hanson, R., Wrachtrup, J., Zhou, B.B.: Quantum technologies with optically interfaced solid-state spins. Nat. Photonics 12, 516–527 (2018)
Müller, T., Hepp, C., Pingault, B., Neu, E., Gsell, S., Schreck, M., Sternschulte, H., Steinmüller-Nethl, D., Becher, C., Atatüre, M.: Optical signatures of silicon-vacancy spins in diamond. Nat. Commun. 5, 3328 (2014)
Hepp, C., Müller, T., Waselowski, V., Becker, J.N., Pingault, B., Sternschulte, H., Steinmüller-Nethl, D., Gali, A., Maze, J.R., Atatüre, M., Becher, C.: Electronic structure of the silicon vacancy color center in diamond. Phys. Rev. Lett. 112, 036405 (2014)
Lemonde, M.A., Meesala, S., Sipahigil, A., Schuetz, M.J.A., Lukin, M.D., Loncar, M., Rabl, P.: Phonon networks with silicon-vacancy centers in diamond waveguides. Phys. Rev. Lett. 120, 213603 (2018)
James, D.F.V.: Quantum computation with hot and cold ions: an assessment of proposed schemes. Fortschr. Phys. 48, 823–837 (2000)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)
Nguyen, C.T., Sukachev, D.D., Bhaskar, M.K., Machielse, B., Levonian, D.S., Knall, E.N., Stroganov, P., Riedinger, R., Park, H., Lončar, M., Lukin, M.D.: Quantum network nodes based on diamond qubits with an efficient nanophotonic interface. Phys. Rev. Lett. 123, 183602 (2019)
Nguyen, C.T., Sukachev, D.D., Bhaskar, M.K., Machielse, B., Levonian, D.S., Knall, E.N., Stroganov, P., Chia, C., Burek, M.J., Riedinger, R., Park, H., Lončar, M., Lukin, M.D.: An integrated nanophotonic quantum register based on silicon-vacancy spins in diamond. Phys. Rev. B 100, 165428 (2019)
Metsch, M.H., Senkalla, K., Tratzmiller, B., Scheuer, J., Kern, M., Achard, J., Tallaire, A., Plenio, M.B., Siyushev, P., Jelezko, F.: Initialization and readout of nuclear spins via a negatively charged silicon-vacancy center in diamond. Phys. Rev. Lett. 122, 190503 (2019)
Acknowledgements
The work was partly supported by the National Key R & D Project (Grant No. 2016YFA0301404), the National Nature Science Foundation of China (Grant Nos. 11704306 and 11534008), and the China Postdoctoral Science Foundation (Grant No. 2016M602795)
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Li, X., Ma, S., Xie, J. et al. Dissipative generation of steady-state entanglement of two separated SiV\(^{-}\) centers coupled to photonic crystal cavities. Quantum Inf Process 19, 301 (2020). https://doi.org/10.1007/s11128-020-02797-0
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DOI: https://doi.org/10.1007/s11128-020-02797-0