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Stabilizing a Bell state by engineering collective photon decay

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Abstract

We propose a dissipation-engineering method for generation and stabilization of a Bell state for two superconducting qubits in coupled circuit quantum electrodynamics architecture. In the scheme, the large dispersive qubit–resonator interaction and resonant photon hopping between resonators jointly induce asymmetric energy gaps in the dressed state subspaces for the qubits and the collective resonator photon modes. The target steady state is reached and protected by applying each qubit with two microwave drives, that perturbatively induce the specific dressed state transition, while simultaneously by employing the decay of the collective photon modes. Numerical simulation verifies that high-fidelity and long-lived two-qubit Bell state can be obtained (based on the recently available experimental parameters) and is robust against the potential fluctuation of the system parameters.

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References

  1. Bell, J.: On the Einstein–Podolsky–Rosen paradox. Physics 1(3), 195–200 (1964)

    Google Scholar 

  2. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  Google Scholar 

  3. Bennett, C.H., Divicenzo, D.P.: Quantum information and computation. Nature 404, 247–255 (2000)

    Article  ADS  Google Scholar 

  4. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Communication. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  5. Hua, M., Tao, M.J., Deng, F.G.: Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED. Sci. Rep. 5, 9274 (2015)

    Article  ADS  Google Scholar 

  6. He, X.L., Su, Q.P., Zhang, F.Y., Yang, C.P.: Generating multipartite entangled states of qubits distributed in different cavities. Quantum Inf. Process 13, 1381–1395 (2014)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Hu, Y., Tian, L.: Deterministic generation of entangled photons in superconducting resonator arrays. Phys. Rev. Lett. 106, 257002 (2011)

    Article  ADS  Google Scholar 

  8. Cao, Y., Huo, W.Y., Ai, Q., Long, G.L.: Theory of degenerate three-wave mixing using circuit QED in solid-state circuits. Phys. Rev. A 84, 053846 (2011)

    Article  ADS  Google Scholar 

  9. Sheng, Y.B., Liu, J., Zhao, S.Y., Zhou, L.: Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system. Chin. Sci. Bull. 58, 3507–3513 (2013)

    Article  Google Scholar 

  10. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Aolita, L., de Melo, F., Davidovich, L.: Open-system dynamics of entanglement: a key issues review. Rep. Prog. Phys. 78, 042001 (2015)

    Article  ADS  Google Scholar 

  12. Gardiner, C.W., Zoller, P.: Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Application to Quantum Optics. Springer Series in Synergetics. Springer (2000)

  13. Poyatos, J.F., Cirac, J.I., Zoller, P.: Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728 (1996)

    Article  ADS  Google Scholar 

  14. Barreiro, J.T., Mller, M., Schindler, P., Nigg, D., Monz, T., Chwalla, M., Hennrich, M., Roos, C.F., Zoller, P., Blatt, R.: An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011)

    Article  ADS  Google Scholar 

  15. Mller, M., Diehl, S., Pupillo, G., Zoller, P.: Engineered open systems and quantum simulations with atoms and ions. Adv. At. Mol. Opt. Phys. 61, 1–80 (2012)

    Article  ADS  Google Scholar 

  16. Lin, Y., Gaebler, J.P., Reiter, F., Tan, T.R., Bowler, R., Sørensen, A.S., Leibfried, D., Wineland, D.J.: Dissipative production of a maximally entangled steady state of two quantum bits. Nature 504, 415–418 (2013)

    Article  ADS  Google Scholar 

  17. Kienzler, D., Lo, H.Y., Keitch, B., de Clercq, L., Leupold, F., Lindenfelser, F., Marinelli, M., Negnevitsky, V., Home, J.P.: Quantum harmonic oscillator state synthesis by reservoir engineering. Science 347(6217), 53–56 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  18. Geerlings, K., Leghtas, Z., Pop, I.M., Shankar, S., Frunzio, L., Schoelkopf, R.J., Mirrahimi, M., Devoret, M.H.: Demonstrating a driven reset protocol for a superconducting qubit. Phys. Rev. Lett. 110, 120501 (2013)

    Article  ADS  Google Scholar 

  19. Leghtas, Z., Touzard, S., Pop, I.M., Kou, A., Vlastakis, B., Petrenko, A., Sliwa, K.M., Narla, A., Shankar, S., Hatridge, M.J., Reagor, M., Frunzio, L., Schoelkopf, R.J., Mirrahimi, M., Devoret, M.H.: Confining the state of light to a quantum manifold by engineered two-photon loss. Science 347(6224), 853–857 (2015)

    Article  ADS  Google Scholar 

  20. Mirrahimi, M., Leghtas, Z., Albert, V.V., Touzard, S., Schoelkopf, R.J., Jiang, L., Devoret, M.H.: Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16, 045014 (2014)

    Article  ADS  Google Scholar 

  21. Shankar, S., Hatridge, M., Leghtas, Z., Sliwa, K.M., Narla, A., Vool, U., Girvin, S.M., Frunzio, L., Mirrahimi, M., Devoret, M.H.: Autonomously stabilized entanglement between two superconducting quantum bits. Nature 504, 419–422 (2013)

    Article  ADS  Google Scholar 

  22. Leghtas, Z., Vool, U., Shankar, S., Hatridge, M., Girvin, S.M., Devoret, M.H., Mirrahimi, M.: Stabilizing a Bell state of two superconducting qubits by dissipation engineering. Phys. Rev. A 88, 023849 (2013)

    Article  ADS  Google Scholar 

  23. Raftery, J., Sadri, D., Schmidt, S., Treci, H.E., Houck, A.A.: Observation of a dissipation-induced classical to quantum transition. Phys. Rev. X 4, 031043 (2014)

    Google Scholar 

  24. Schmidt, S., Gerace, D., Houck, A.A., Blatter, G., Treci, H.E.: Nonequilibrium delocalization-localization transition of photons in circuit quantum electrodynamics. Phys. Rev. B 82, 100507(R) (2010)

    Article  ADS  Google Scholar 

  25. Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Huang, R.S., Majer, J., Kumar, S., Girvin, S.M., Schoelkopf, R.J.: Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)

    Article  ADS  Google Scholar 

  26. Zheng, S.B., Shen, L.T.: Generation and stabilization of maximal entanglement between two atomic qubits coupled to a decaying resonator. J. Phys. B 47, 055502 (2014)

    Article  ADS  Google Scholar 

  27. Shen, L.T., Chen, R.X., Yang, Z.B., Wu, H.Z., Zheng, S.B.: Preparation of two-qubit steady entanglement through driving a single qubit. Opt. Lett. 39, 6046–6049 (2014)

    Article  ADS  Google Scholar 

  28. Kimble, H.J.: The quantum internet. Nature 453, 1023–1030 (2008)

    Article  ADS  Google Scholar 

  29. Zhou, J., Hu, Y., Yin, Z.Q., Zhu, S.L., Xue, Z.Y.: High fidelity quantum state transfer in electromechanical systems with intermediate coupling. Sci. Rep. 4, 6237 (2014)

    Article  ADS  Google Scholar 

  30. Su, S.L., Shao, X.Q., Wang, H.F., Zhang, S.: Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay. Sci. Rep. 4, 7566 (2014)

    Article  ADS  Google Scholar 

  31. Kastoryano, M.J., Reiter, F., Sørensen, A.S.: Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)

    Article  ADS  Google Scholar 

  32. Reiter, F., Kastoryano, M.J., Sørensen, A.S.: Driving two atoms in an optical cavity into an entangled steady state using engineered decay. New J. Phys. 14, 053022 (2012)

    Article  ADS  Google Scholar 

  33. Reiter, F., Tornberg, L., Johansson, G., Sørensen, A.S.: Steady-state entanglement of two superconducting qubits engineered by dissipation. Phys. Rev. A 88, 032317 (2013)

    Article  ADS  Google Scholar 

  34. 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)

    Article  ADS  Google Scholar 

  35. Shen, L.T., Chen, X.Y., Yang, Z.B., Wu, H.Z., Zheng, S.B.: Cooling distant atoms into steady entanglement via coupled cavities. Quantum Inf. Comput. 13, 281 (2013)

    Google Scholar 

  36. Carr, A.W., Saffman, M.: Preparation of entangled and antiferromagnetic states by dissipative Rydberg pumping. Phys. Rev. Lett. 111, 033607 (2013)

    Article  ADS  Google Scholar 

  37. Shao, X.Q., You, J.B., Zheng, T.Y., Oh, C.H., Zhang, S.: Stationary three-dimensional entanglement via dissipative Rydberg pumping. Phys. Rev. A 89, 052313 (2014)

    Article  ADS  Google Scholar 

  38. Aron, C., Kulkarni, M., Treci, H.E.: Steady-state entanglement of spatially separated qubits via quantum bath engineering. Phys. Rev. A 90, 062305 (2014)

    Article  ADS  Google Scholar 

  39. Aron, C., Kulkarni, M., Treci, H.E.: Photon-mediated interactions: a scalable tool to create and sustain entangled many-body states. arXiv:1412.8477 (2014)

  40. Schuster, D.I., Houck, A.A., Schreier, J.A., Wallraff, A., Gambetta, J.M., Blais, A., Frunzio, L., Majer, J., Johnson, B., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007)

    Article  ADS  Google Scholar 

  41. Blais, A., Huang, R.S., Wallraff, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

    Article  ADS  Google Scholar 

  42. Sun, L., Petrenko, A., Leghtas, Z., Vlastakis, B., Kirchmair, G., Sliwa, K.M., Narla, A., Hatridge, M., Shankar, S., Blumoff, J., Frunzio, L., Mirrahimi, M., Devoret, M.H., Schoelkopf, R.J.: Tracking photon jumps with repeated quantum non-demolition parity measurements. Nature 511, 444–448 (2014)

    Article  ADS  Google Scholar 

  43. Ye, S.Y., Yang, Z.B., Zheng, S.B., Serafini, A.: Coherent quantum effects through dispersive bosonic media. Phys. Rev. A 82, 012307 (2010)

    Article  ADS  Google Scholar 

  44. Pozniak, M., Zyczkowski, K., Kus, M.: Composed ensembles of random unitary matrices. J. Phys. A 31, 1059 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. Houck, A.A., Treci, H.E., Koch, J.: On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012)

    Article  Google Scholar 

  46. Liu, Z.X., Yang, Z.B., Han, Y.J., Yi, W., Wen, X.G.: Symmetry-protected topological phases in spin ladders with two-body interactions. Phys. Rev. B 86, 195122 (2012)

    Article  ADS  Google Scholar 

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Acknowledgments

This work is supported by the Major State Basic Research Development Program of China under Grant No. 2012CB921601, the National Natural Science Foundation of China under Grant Nos. 11374054, 11305037, and 11405031, the Natural Science Foundation of Fujian Province under Grant No. 2014J05005, and the funds from Fuzhou University.

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Authors and Affiliations

  1. Department of Physics, Fuzhou University, Fuzhou, 350116, China

    Jie Lin, Li-Tuo Shen, Huai-Zhi Wu & Zhen-Biao Yang

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  1. Jie Lin
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Correspondence to Jie Lin.

Appendices

Appendix 1

We introduce the non-local bosonic modes

$$\begin{aligned} c_1= & {} \frac{\sqrt{2}}{2}(a_1+a_2), \end{aligned}$$
(10)
$$\begin{aligned} c_2= & {} \frac{\sqrt{2}}{2}(a_1-a_2), \end{aligned}$$
(11)

to simplify the dynamics of the system. In the interaction picture with respect to \(H_\mathrm{o}+H_{\mathrm{p}{-}\mathrm{p}},\) we obtain the interaction Hamiltonian

$$\begin{aligned} H_{\mathrm{q}{-}\mathrm{p}}^{'}= & {} ge^{i\varDelta t}\frac{\sqrt{2}(e^{-iJt}c_1+e^{iJt}c_2)}{2}\sigma _1^\dag \nonumber \\&\quad +\,ge^{i\varDelta t}\frac{\sqrt{2}(e^{-iJt}c_1-e^{iJt}c_2)}{2}\sigma _2^\dag +H.c. \end{aligned}$$
(12)

Under the condition of \(J=\varDelta \) and \(\varDelta +J \gg g\), the bosonic mode \(c_1\) is resonant with the two qubits, while the bosonic mode \(c_2\) is largely dispersive with the two qubits. Therefore, the interaction Hamiltonian reduces to

$$\begin{aligned} H_{\mathrm{q}{-}\mathrm{p}}^{'}= & {} \frac{\sqrt{2}}{2}g[(\sigma _1^\dag +\sigma _2^\dag )c_1 +H.c. \end{aligned}$$
(13)

Appendix 2

In Fig. 6, we illustrate the dressed states and the corresponding energy levels of the coupled qubit–photon system.

Fig. 6
figure 6

Schematic diagram for the dressed state of the coupled qubit–photon system

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Lin, J., Shen, LT., Wu, HZ. et al. Stabilizing a Bell state by engineering collective photon decay. Quantum Inf Process 15, 185–197 (2016). https://doi.org/10.1007/s11128-015-1169-8

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