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An ultra-fast C-NOT gate based on electric dipole coupling between nitrogen-vacancy color centers

  • 1.

    Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

  • 2.

    Hefei National Laboratory for Physical Sciences at the Microscale, Hefei 230026, China

  • 3.

    CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China

  • 4.

    Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.52396/JUST-2020-0039
  • Received Date: 12 January 2021
  • Rev Recd Date: 05 March 2021
  • Publish Date: 31 March 2021
    Abstract

  • Abstract

    Our research proposes a new scheme to build a controlled-NOT(C-NOT) gate between two adjacent nitrogen-vacancy (NV) color centers in diamond, using electric dipole coupling between adjacent NVs and selective resonant laser excitation.The electric dipole coupling between two NVs causes the state dependent energy shift.This allows to apply resonant laser excitation to realize the C-phase gate.Combined with a single qubit operation, C-NOT gate can be implemented quickly.Between two adjacent 10 nm NVs, the C-NOT gate can operate up to 120 ns faster than the traditional magnetic dipole coupling method by 2 magnitudes.In order to reduce the effect of a spontaneous emission,we propose to use a non-resonant cavity to suppress the spontaneous emission.The simulation results show that the C-phase gate fidelity can reach 98.88%.Finally, the scheme is extended to a one-dimensional NV spin chain.

    Abstract

    Our research proposes a new scheme to build a controlled-NOT(C-NOT) gate between two adjacent nitrogen-vacancy (NV) color centers in diamond, using electric dipole coupling between adjacent NVs and selective resonant laser excitation.The electric dipole coupling between two NVs causes the state dependent energy shift.This allows to apply resonant laser excitation to realize the C-phase gate.Combined with a single qubit operation, C-NOT gate can be implemented quickly.Between two adjacent 10 nm NVs, the C-NOT gate can operate up to 120 ns faster than the traditional magnetic dipole coupling method by 2 magnitudes.In order to reduce the effect of a spontaneous emission,we propose to use a non-resonant cavity to suppress the spontaneous emission.The simulation results show that the C-phase gate fidelity can reach 98.88%.Finally, the scheme is extended to a one-dimensional NV spin chain.
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    • References(36)
  • [1]
    Nielsen M A , Chuang I L. Quantum Computation and Quantum Information. Beijing: Tsinghua University Press, 2015.
    [2]
    Bar-Gill N, Pham L M, Jarmola A, et al. Solid-state electronic spin coherence time approaching one second. Nature Communications, 2013, 4: Article number 1743.
    [3]
    Neumann P, Beck J, Steiner M, et al. Single-shot readout of a single nuclear spin. Science, 2010, 329(5991): 542-544.
    [4]
    Rong X, Geng J P, Wang Z X, et al. Implementation of dynamically corrected gates on a single electron spin in diamond. Phys. Rev. Lett., 2014, 112: 050503.
    [5]
    Mamin H J, Kim M, Sherwood M H, et al. Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor. Science, 2013, 339(6119): 557-560.
    [6]
    Said R S, Twamley J. Robust control of entanglement in a nitrogen-vacancy center coupled to a C13 nuclear spin in diamond. Physical Review A, 2009, 80(3): 032303.
    [7]
    Dolde F, Jakobi I, Naydenov B, et al. Room-temperature entanglement between single defect spins in diamond. Nature Physics, 2013, 9(3): 139-143.
    [8]
    Dolde F, Bergholm V, Wang Y, et al. High-fidelity spin entanglement using optimal control. Nature Communications, 2014, 5: Article number 3371.
    [9]
    Sekiguchi Y, Niikura N, Kuroiwa R, et al. Optical holonomic single quantum gates with a geometric spin under a zero field. Nature Photonics, 2017, 11: 309-314.
    [10]
    Humphreys P C, Kalb N, Morits J P J, et al. Deterministic delivery of remote entanglement on a quantum network. Nature, 2018, 558(7709): 268-273.
    [11]
    Beterov I I, Khamzina N G, Tret’yakov B D, et al. Resonant dipole-dipole interaction of Rydberg atoms for realisation of quantum computations. Quantum Electronics, 2018, 48(5): 453-459.
    [12]
    King B E. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett., 1995, 75(25): 4714-4717.
    [13]
    Jaksch D, Cirac J I, Zoller P, et al. Fast quantum gates for neutral atoms. Phys. Rev. Lett., 2000, 85(10): 2208-2211.
    [14]
    Lim J, Lee H G, Ahn J. Review of cold Rydberg atoms and their applications. Journal of the Korean Physical Society, 2013, 63(4): 867-876.
    [15]
    Goldman M L, Sipahigil A, Doherty M W, et al. Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers. Phys. Rev. Lett., 2015, 114: 145502.
    [16]
    Hettich C. Coherent optical dipole coupling of two individual molecules at nanometre separation. Konstanz, Germany: University of Konstanz, 2002.
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    Varada G V, Agarwal G S. Two photon resonance induced by the dipole-dipole interaction. Physical Review A, 1992, 45(9): 6721-6729.
    [18]
    Doherty M W, Manson N B, Delaney P, et al. The nitrogenvacancy colour centre in diamond. Physics Reports, 2013, 528(1): 1-45.
    [19]
    Lee K W, Lee D, Ovartchaiyapong P, et al. Strain coupling of a mechanical resonator to a single quantum emitter in diamond. Phys. Rev. Applied, 2016, 6: 034005.
    [20]
    Tamarat Ph, Gaebel T, Rabeau J R, et al. Stark shift control of single optical centers in diamond. Phys. Rev. Lett., 2006, 97: 083002.
    [21]
    Xu Z J, Yin Z Q, Han Q K, et al. Quantum information processing with closely-spaced diamond color centers in strain and magnetic fields. Optical Materials Express, 2019, 9: 4654-4668.
    [22]
    Schirhagl R, Chang K, Loretz M, et al. Nitrogen-vacancy centers in diamond: Nanoscale sensors for physics and biology. Annual Review of Physical Chemistry, 2014, 65(1): 83-105.
    [23]
    Zablotskii V, Polyakova T, Dejneka A. Cells in the nonuniform magnetic world: How cells respond to high-gradient magnetic fields. BioEssays, 2018, 40(8): e1800017.
    [24]
    Batalov A, Zierl C, Gaebel T, et al. Temporal coherence of photons emitted by single nitrogen-vacancy defect centers in diamond using optical Rabi-oscillations. Phys. Rev. Lett., 2008, 100(7): 077401.
    [25]
    Bienfait A, Pla J J, Kubo Y, et al. Controlling spin relaxation with a cavity. Nature, 2016,531(7592): 74-77.
    [26]
    Goy P, Raimond J M, Gross M, et al. Observation of cavity-enhanced single-atom spontaneous emission. Phys. Rev. Lett., 1983, 50(24): 1903-1906.
    [27]
    Hoang T H C, Durán-Valdeiglesias E, Alonso-Ramos C, et al. Narrow-linewidth carbon nanotube emission in silicon hollow-core photonic crystal cavity. Optics Letters, 2017, 42(11): 2228-2231.
    [28]
    Takiguchi M, Sumikura H, Birowosuto M D, et al. Enhanced and suppressed spontaneous emission from a buried heterostructure photonic crystal cavity. In: 2013 Conference on Lasers and Electro-Optics Pacific Rim. Washington DC: Optical Society of America, 2013.
    [29]
    Heinzen D J, Childs J J, Thomas J E, et al. Enhanced and inhibited visible spontaneous emission by atoms in a confocal resonator. Phys. Rev. Lett., 1987, 58(13): 1320-1323.
    [30]
    Yamamoto Y, Machida S, Horikoshi Y, et al. Enhanced and inhibited spontaneous emission of free excitons in GaAs quantum wells in a microcavity. Optics Communications, 1991, 80: 337-342.
    [31]
    Storteboom J, Dolan P, Castelletto S, et al. Lifetime investigation of single nitrogen vacancy centres in nanodiamonds. Optics Express, 2015, 23(9): 11327-11333.
    [32]
    Scully M O, Suhail Zubairy M. Quantum Optics. Beijing: World Publishing, 2000.
    [33]
    Wilmott C, Wild P. A construction of a generalized quantum SWAP gate. https://arxiv.org/abs/0811.1684v1.
    [34]
    Toyli D M, Weis C D, Fuchs G D, et al. Chip-scale nanofabrication of single spins and spin arrays in diamond. Nano Letters, 2010, 10(8): 3168-3172.
    [35]
    Tamura1 S, Koike1 G, Komatsubara1 A, et al. Array of bright silicon-vacancy centers in diamond fabricated by low-energy focused ion beam implantation. Applied Physics Express, 2014, 7(11): 115201.
    [36]
    Scarabelli D, Trusheim M, Gaathon O, et al. Nanoscale engineering of closely-spaced electronic spins in diamond. Nano Letters, 2016, 16(8): 4982-4990.
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    [1]
    Nielsen M A , Chuang I L. Quantum Computation and Quantum Information. Beijing: Tsinghua University Press, 2015.
    [2]
    Bar-Gill N, Pham L M, Jarmola A, et al. Solid-state electronic spin coherence time approaching one second. Nature Communications, 2013, 4: Article number 1743.
    [3]
    Neumann P, Beck J, Steiner M, et al. Single-shot readout of a single nuclear spin. Science, 2010, 329(5991): 542-544.
    [4]
    Rong X, Geng J P, Wang Z X, et al. Implementation of dynamically corrected gates on a single electron spin in diamond. Phys. Rev. Lett., 2014, 112: 050503.
    [5]
    Mamin H J, Kim M, Sherwood M H, et al. Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor. Science, 2013, 339(6119): 557-560.
    [6]
    Said R S, Twamley J. Robust control of entanglement in a nitrogen-vacancy center coupled to a C13 nuclear spin in diamond. Physical Review A, 2009, 80(3): 032303.
    [7]
    Dolde F, Jakobi I, Naydenov B, et al. Room-temperature entanglement between single defect spins in diamond. Nature Physics, 2013, 9(3): 139-143.
    [8]
    Dolde F, Bergholm V, Wang Y, et al. High-fidelity spin entanglement using optimal control. Nature Communications, 2014, 5: Article number 3371.
    [9]
    Sekiguchi Y, Niikura N, Kuroiwa R, et al. Optical holonomic single quantum gates with a geometric spin under a zero field. Nature Photonics, 2017, 11: 309-314.
    [10]
    Humphreys P C, Kalb N, Morits J P J, et al. Deterministic delivery of remote entanglement on a quantum network. Nature, 2018, 558(7709): 268-273.
    [11]
    Beterov I I, Khamzina N G, Tret’yakov B D, et al. Resonant dipole-dipole interaction of Rydberg atoms for realisation of quantum computations. Quantum Electronics, 2018, 48(5): 453-459.
    [12]
    King B E. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett., 1995, 75(25): 4714-4717.
    [13]
    Jaksch D, Cirac J I, Zoller P, et al. Fast quantum gates for neutral atoms. Phys. Rev. Lett., 2000, 85(10): 2208-2211.
    [14]
    Lim J, Lee H G, Ahn J. Review of cold Rydberg atoms and their applications. Journal of the Korean Physical Society, 2013, 63(4): 867-876.
    [15]
    Goldman M L, Sipahigil A, Doherty M W, et al. Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers. Phys. Rev. Lett., 2015, 114: 145502.
    [16]
    Hettich C. Coherent optical dipole coupling of two individual molecules at nanometre separation. Konstanz, Germany: University of Konstanz, 2002.
    [17]
    Varada G V, Agarwal G S. Two photon resonance induced by the dipole-dipole interaction. Physical Review A, 1992, 45(9): 6721-6729.
    [18]
    Doherty M W, Manson N B, Delaney P, et al. The nitrogenvacancy colour centre in diamond. Physics Reports, 2013, 528(1): 1-45.
    [19]
    Lee K W, Lee D, Ovartchaiyapong P, et al. Strain coupling of a mechanical resonator to a single quantum emitter in diamond. Phys. Rev. Applied, 2016, 6: 034005.
    [20]
    Tamarat Ph, Gaebel T, Rabeau J R, et al. Stark shift control of single optical centers in diamond. Phys. Rev. Lett., 2006, 97: 083002.
    [21]
    Xu Z J, Yin Z Q, Han Q K, et al. Quantum information processing with closely-spaced diamond color centers in strain and magnetic fields. Optical Materials Express, 2019, 9: 4654-4668.
    [22]
    Schirhagl R, Chang K, Loretz M, et al. Nitrogen-vacancy centers in diamond: Nanoscale sensors for physics and biology. Annual Review of Physical Chemistry, 2014, 65(1): 83-105.
    [23]
    Zablotskii V, Polyakova T, Dejneka A. Cells in the nonuniform magnetic world: How cells respond to high-gradient magnetic fields. BioEssays, 2018, 40(8): e1800017.
    [24]
    Batalov A, Zierl C, Gaebel T, et al. Temporal coherence of photons emitted by single nitrogen-vacancy defect centers in diamond using optical Rabi-oscillations. Phys. Rev. Lett., 2008, 100(7): 077401.
    [25]
    Bienfait A, Pla J J, Kubo Y, et al. Controlling spin relaxation with a cavity. Nature, 2016,531(7592): 74-77.
    [26]
    Goy P, Raimond J M, Gross M, et al. Observation of cavity-enhanced single-atom spontaneous emission. Phys. Rev. Lett., 1983, 50(24): 1903-1906.
    [27]
    Hoang T H C, Durán-Valdeiglesias E, Alonso-Ramos C, et al. Narrow-linewidth carbon nanotube emission in silicon hollow-core photonic crystal cavity. Optics Letters, 2017, 42(11): 2228-2231.
    [28]
    Takiguchi M, Sumikura H, Birowosuto M D, et al. Enhanced and suppressed spontaneous emission from a buried heterostructure photonic crystal cavity. In: 2013 Conference on Lasers and Electro-Optics Pacific Rim. Washington DC: Optical Society of America, 2013.
    [29]
    Heinzen D J, Childs J J, Thomas J E, et al. Enhanced and inhibited visible spontaneous emission by atoms in a confocal resonator. Phys. Rev. Lett., 1987, 58(13): 1320-1323.
    [30]
    Yamamoto Y, Machida S, Horikoshi Y, et al. Enhanced and inhibited spontaneous emission of free excitons in GaAs quantum wells in a microcavity. Optics Communications, 1991, 80: 337-342.
    [31]
    Storteboom J, Dolan P, Castelletto S, et al. Lifetime investigation of single nitrogen vacancy centres in nanodiamonds. Optics Express, 2015, 23(9): 11327-11333.
    [32]
    Scully M O, Suhail Zubairy M. Quantum Optics. Beijing: World Publishing, 2000.
    [33]
    Wilmott C, Wild P. A construction of a generalized quantum SWAP gate. https://arxiv.org/abs/0811.1684v1.
    [34]
    Toyli D M, Weis C D, Fuchs G D, et al. Chip-scale nanofabrication of single spins and spin arrays in diamond. Nano Letters, 2010, 10(8): 3168-3172.
    [35]
    Tamura1 S, Koike1 G, Komatsubara1 A, et al. Array of bright silicon-vacancy centers in diamond fabricated by low-energy focused ion beam implantation. Applied Physics Express, 2014, 7(11): 115201.
    [36]
    Scarabelli D, Trusheim M, Gaathon O, et al. Nanoscale engineering of closely-spaced electronic spins in diamond. Nano Letters, 2016, 16(8): 4982-4990.
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