Controllable and shortcut-based population transfers with a composite system of a nitrogen-vacancy electron spin and microwave photons


Optimal population transfer is of critical importance for quantum information processing. Here an efficient scheme is proposed for implementing controllable and shortcut-based population transfers with a nitrogen-vacancy (NV) electron spin and cavity photons. The electron spin is placed inside a setup of circuit quantum electrodynamics (QED). Under a suitable magnetic field bias, the ground state of electron spin constitutes an effective triplet. By means of the quantized cavity field and classical drivings, we obtain a \(\Delta \)-configuration interaction within a composite three-state system. Based on the adjustable Rabi couplings, the shortcut-based population transfers can be performed controllably. Moreover, compared with the adiabatic counterparts, the operations assisted by counter-diabatic drivings need much shorter times and then are less susceptible to decoherence effects. Our scheme provides a promising avenue toward optimized transfer operations on NV center electron spins in circuit QED.

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  1. 1.

    Togan, E., et al.: Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730 (2010)

    Article  ADS  Google Scholar 

  2. 2.

    Robledo, L., Childress, L., Bernien, H., Hensen, B., Alkemade, P.F.A., Hanson, R.: High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574 (2011)

    Article  ADS  Google Scholar 

  3. 3.

    Doherty, M.W., Manson, N.B., Delaney, P., Jelezko, F., Wrachtrupe, J., Hollenberg, L.C.L.: The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1 (2013)

    Article  ADS  Google Scholar 

  4. 4.

    Zhou, J.-W., et al.: Quantum information processing and metrology with color centers in diamonds. Front. Phys. 9, 587 (2014)

    Article  ADS  Google Scholar 

  5. 5.

    Zhou, Y., Li, B., Li, X.-X., Li, F.-L., Li, P.-B.: Preparing multiparticle entangled states of nitrogen-vacancy centers via adiabatic ground-state transitions. Phys. Rev. A 98, 052346 (2018)

    Article  ADS  Google Scholar 

  6. 6.

    Siyushev, P., et al.: Photoelectrical imaging and coherent spin-state readout of single nitrogen-vacancy centers in diamond. Science 363, 728 (2019)

    Article  ADS  Google Scholar 

  7. 7.

    Ouyang, X.-L., et al.: Experimental demonstration of quantum-enhanced machine learning in a nitrogen-vacancy-center system. Phys. Rev. A 101, 012307 (2020)

    Article  ADS  Google Scholar 

  8. 8.

    Wallraff, A., et al.: Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162 (2004)

    Article  ADS  Google Scholar 

  9. 9.

    Blais, A., Gambetta, J., Wallraff, A., Schuster, D.I., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Quantum-information processing with circuit quantum electrodynamics. Phys. Rev. A 75, 032329 (2007)

    Article  ADS  Google Scholar 

  10. 10.

    Kubo, Y., et al.: Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble. Phys. Rev. Lett. 107, 220501 (2011)

    Article  ADS  Google Scholar 

  11. 11.

    Xiang, Z.-L., Lü, X.-Y., Li, T.-F., You, J.Q., Nori, F.: Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator. Phys. Rev. B 87, 144516 (2013)

    Article  ADS  Google Scholar 

  12. 12.

    Chen, C.-Y., Hou, Q.-Z., Li, S.-H.: Spin Ensembles Coupled to Superconducting Resonators: A Scalable Architecture for Solid-State Quantum Computing. Commun. Theor. Phys. 62, 196 (2014)

    MathSciNet  MATH  Article  ADS  Google Scholar 

  13. 13.

    Tao, M.-J., Hua, M., Ai, Q., Deng, F.-G.: Quantum-information processing on nitrogen-vacancy ensembles with the local resonance assisted by circuit QED. Phys. Rev. A 91, 062325 (2015)

    Article  ADS  Google Scholar 

  14. 14.

    Feng, Z.-B.: Robust quantum state transfer between a Cooper-pair box and diamond nitrogen-vacancy centers. Phys. Rev. A 91, 032307 (2015)

    Article  ADS  Google Scholar 

  15. 15.

    Hu, Y., Song, Y., Duan, L.: Quantum interface between a transmon qubit and spins of nitrogen-vacancy centers. Phys. Rev. A 96, 062301 (2017)

    Article  ADS  Google Scholar 

  16. 16.

    Ma, S.-l., Li, X.-k., Xie, J.-k., Li, F.-l.: Two-mode squeezed states of two separated nitrogen-vacancy-center ensembles coupled via dissipative photons of superconducting resonators. Phys. Rev. A 99, 012325 (2019)

  17. 17.

    Li, P.-B., Gao, S.-Y., Li, F.-L.: Quantum-information transfer with nitrogen-vacancy centers coupled to a whispering-gallery microresonator. Phys. Rev. A 83, 054306 (2011)

    Article  ADS  Google Scholar 

  18. 18.

    Chen, Q., Yang, W.L., Feng, M.: Controllable quantum state transfer and entanglement generation between distant nitrogen-vacancy-center ensembles coupled to superconducting flux qubits. Phys. Rev. A 86, 022327 (2012)

    Article  ADS  Google Scholar 

  19. 19.

    Ali, H., Basit, A., Badshah, F., Ge, G.-Q.: Quantum state transfer between nitrogen vacancy centers coupled to photonic crystal molecule in the off resonant regime. Physica E 104, 261 (2018)

    Article  ADS  Google Scholar 

  20. 20.

    Ali, H., Basit, A., Badshah, F., Qurban, M., Ge, G.-Q.: Quantum state transfer between nitrogen vacancy center ensembles in hybrid quantum system. Europhys. Lett. 127, 30007 (2019)

    Article  ADS  Google Scholar 

  21. 21.

    Wu, S.-H., Amezcua, M., Wang, H.: Adiabatic population transfer of dressed spin states with quantum optimal control. Phys. Rev. A 99, 063812 (2019)

    Article  ADS  Google Scholar 

  22. 22.

    Tian, J., Du, T., Liu, Y., Liu, H., Jin, F., Said, R.S., Cai, J.: Optimal quantum optical control of spin in diamond. Phys. Rev. A 100, 012110 (2019)

    Article  ADS  Google Scholar 

  23. 23.

    Lu, X.-J., Feng, Z.-B.: Error-insensitive population transfer in a qutrit by invariant-based shortcuts with optimized drivings. Europhys. Lett. 127, 64001 (2019)

    Article  ADS  Google Scholar 

  24. 24.

    Torrontegui, E., et al.: Shortcuts to adiabaticity. Adv. At. Mol. Opt. Phys. 62, 117 (2013)

    Article  ADS  Google Scholar 

  25. 25.

    Chen, Y.-H., Shi, Z.-C., Song, J., Xia, Y., Zheng, S.-B.: Optimal shortcut approach based on an easily obtained intermediate Hamiltonian. Phys. Rev. A 95, 062319 (2017)

    Article  ADS  Google Scholar 

  26. 26.

    Mortensen, H. L., S\(\phi \)rensen, J. J. W. H., M\( \phi \)lmer K., Sherson, J. F.: Fast state transfer in a \(\Lambda \)-system: a shortcut-to-adiabaticity approach to robust and resource optimized control. New J. Phys. 20, 025009 (2018)

  27. 27.

    Guéry-Odelin, D., Ruschhaupt, A., Kiely, A., Torrontegui, E., Martinez-Garaot, S., Muga, J.G.: Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys. 91, 045001 (2019)

    MathSciNet  Article  ADS  Google Scholar 

  28. 28.

    Zhang, J., et al.: Experimental Implementation of Assisted Quantum Adiabatic Passage in a Single Spin. Phys. Rev. Lett. 110, 240501 (2013)

    Article  ADS  Google Scholar 

  29. 29.

    Zhou, B.B., et al.: Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system. Nat. Phys. 13, 330 (2017)

    Article  Google Scholar 

  30. 30.

    Feng, Z.-B., Yan, R.-Y., Yan, L.-L., Zhou, Y.-Q.: Tunable photon transmission through a waveguide cavity coupled to an electron spin ensemble. Laser Phys. Lett. 14, 025204 (2017)

    Article  ADS  Google Scholar 

  31. 31.

    Kubo, Y., et al.: Strong Coupling of a Spin Ensemble to a Superconducting Resonator. Phys. Rev. Lett. 105, 140502 (2010)

    Article  ADS  Google Scholar 

  32. 32.

    Sandner, K., et al.: Strong magnetic coupling of an inhomogeneous nitrogen-vacancy ensemble to a cavity. Phys. Rev. A 85, 053806 (2012)

    Article  ADS  Google Scholar 

  33. 33.

    Vepsäläinen, A., Danilin, S., Paladino, E., Falci, G., Paraoanu, G.S.: Quantum Control in Qutrit Systems Using Hybrid Rabi-STIRAP Pulses. Photonics 3, 62 (2016)

    Article  Google Scholar 

  34. 34.

    Yan, R.-Y., Feng, Z.-B., Li, M., Zhang, C.-L., Zhao, Z.-Y.: Speeding up Generation of Entangled State between a Superconducting Qubit and Cavity Photons via Counterdiabatic Driving. Ann. Phys. (Berlin) 1900613, (2020)

  35. 35.

    Premaratne, S.P., Wellstood, F.C., Palmer, B.S.: Microwave photon Fock state generation by stimulated Raman adiabatic passage. Nat. Commun. 8, 14148 (2017)

    Article  ADS  Google Scholar 

  36. 36.

    Vitanov, N.V., Stenholm, S.: Analytic properties and effective two-level problems in stimulated Raman adiabatic passage. Phys. Rev. A 55, 648 (1997)

    Article  ADS  Google Scholar 

  37. 37.

    Lu, X.-J., Li, M., Zhao, Z.Y., Zhang, C.-L., Han, H.-P., Feng, Z.-B., Zhou, Y.-Q.: Nonleaky and accelerated population transfer in a transmon qutrit. Phys. Rev. A 96, 023843 (2017)

    Article  ADS  Google Scholar 

  38. 38.

    Chen, X., Lizuain, I., Ruschhaupt, A., Gué ry-Odelin, D., Muga, J. G.: Shortcut to Adiabatic Passage in Two- and Three-Level Atoms. Phys. Rev. Lett. 105, 123003 (2010)

  39. 39.

    Feng, Z.-B., Lu, X.-J., Li, M., Yan, R.-Y., Zhou, Y.-Q.: Speeding up adiabatic population transfer in a Josephson qutrit via counter-diabatic driving. New J. Phys. 19, 123023 (2017)

    Article  ADS  Google Scholar 

  40. 40.

    Masuda, S., Nakamura, K.: Fast-forward problem in quantum mechanics. Phys. Rev. A 78, 062108 (2008)

    Article  ADS  Google Scholar 

  41. 41.

    Bukova, M., D’Alessioab, L., Polkovnikova, A.: Universal high frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. Adv. Phys. 64, 139 (2015)

    Article  ADS  Google Scholar 

  42. 42.

    Yang, W., Xu, Z., Feng, M., Du, J.: Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity. New J. Phys. 12, 113039 (2010)

    Article  ADS  Google Scholar 

  43. 43.

    Coto, R., Jacques, V., Hetet, G., Maze, J.R.: Stimulated Raman adiabatic control of a nuclear spin in diamond. Phys. Rev. B 96, 085420 (2017)

    Article  ADS  Google Scholar 

  44. 44.

    Wu, Q.-Q., Xu, L., Tan, Q.-S., Yan, L.-L.: Multipartite entanglement transfer in a hybrid circuit-QED system. Int. J. Theor. Phys. 51, 1482 (2012)

    MATH  Article  Google Scholar 

  45. 45.

    Feng, Z.-B., Zhang, X.-D.: Holonomic quantum computation with superconducting charge-phase qubits in a cavity. Phys. Lett. A 372, 1589 (2008)

    MATH  Article  ADS  Google Scholar 

  46. 46.

    Unanyan, R., Fleischhauer, M., Shore, B.W., Bergmann, K.: Robust creation and phase-sensitive probing of superposition states via stimulated Raman adiabatic passage STIRAP with degenerate dark states. Opt. Commun. 155, 144 (1998)

    Article  ADS  Google Scholar 

  47. 47.

    Yang, W.L., Yin, Z.Q., Xu, Z.Y., Feng, M., Oh, C.H.: Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities. Phys. Rev. A 84, 043849 (2011)

    Article  ADS  Google Scholar 

  48. 48.

    Yan, R.-Y., Yang, F., Zhang, N., Feng, Z.-B.: Accelerated and robust population transfer in a transmon qutrit via \(\Delta \) -type driving. Quantum Inf. Process. 17, 237 (2018)

    MathSciNet  MATH  Article  ADS  Google Scholar 

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This work is supported by the Key Research Project in Univesities of Henan Province under Grant No. 19A140016, the “316” Project Plan of Xuchang University, the Research Project of Xuchang University under Grant No. 2020YB009, and the Natural Science Foundation of Henan Province under Grant No. 212300410388.

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Correspondence to Zhi-Bo Feng.

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Zhao, ZY., Feng, ZB., Li, M. et al. Controllable and shortcut-based population transfers with a composite system of a nitrogen-vacancy electron spin and microwave photons. Quantum Inf Process 20, 66 (2021).

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  • Optimized population transfer
  • Counter-diabatic driving
  • Nitrogen-vacancy electron spin
  • Microwave photon