Online optimization for optical readout of a single electron spin in diamond

doi:10.1007/s11467-022-1235-5

Front. Phys.

2023, Vol. 18

Issue (2) : 21301 https://doi.org/10.1007/s11467-022-1235-5

RESEARCH ARTICLE

Online optimization for optical readout of a single electron spin in diamond

Xue Lin^1,², Jingwei Fan¹, Runchuan Ye^1,², Mingti Zhou², Yumeng Song^1,², Dawei Lu³(

), Nanyang Xu²(

)

¹. School of Microelectronics and School of Physics, Hefei University of Technology, Hefei 230009, China
². Research Center for Quantum Sensing, Zhejiang Laboratory, Hangzhou 311000, China
³. Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China

Download: PDF(3350 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

The nitrogen-vacancy (NV) center in diamond has been developed as a promising platform for quantum sensing, especially for magnetic field measurements in the nano-tesla range with a nano-meter resolution. Optical spin readout performance has a direct effect on the signal-to-noise ratio (SNR) of experiments. In this work, we introduce an online optimization method to customize the laser waveform for readout. Both simulations and experiments reveal that our new scheme optimizes the optically detected magnetic resonance in NV center. The SNR of optical spin readout has been witnessed a 44.1% increase in experiments. In addition, we applied the scheme to the Rabi oscillation experiment, which shows an improvement of 46.0% in contrast and a reduction of 12.1% in mean deviation compared to traditional constant laser power SNR optimization. This scheme is promising to improve sensitivities for a wide range of NV-based applications in the future.

Keywords NV center readout signal-to-noise ratio online optimization

Corresponding Author(s): Dawei Lu,Nanyang Xu

Issue Date: 11 January 2023

Cite this article:

Xue Lin,Jingwei Fan,Runchuan Ye, et al. Online optimization for optical readout of a single electron spin in diamond[J]. Front. Phys. , 2023, 18(2): 21301.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1235-5
https://academic.hep.com.cn/fop/EN/Y2023/V18/I2/21301

Fig.1 Illustration of algorithm-assisted OLO method for NV-based metrology. On the left is a schematic of the experimental setup, which mainly includes an AOM driven by the AWG and a 532 nm continuous-wave laser modulated by the AOM. The modulated laser is used for optical pumping of the electron spin in diamond. A detector records the fluorescences emitted by the spin system and feeds the photon time traces to the classical computer on the right. SNR is extracted from the feedback information, and subsequently utilized to generate a new set of laser parameters

u = [u 1, u 2, . . ., u n]

by the algorithm. These parameters are then performed in new experiments for the next-round feedback information.

Fig.2 Analysis of optical pumping for the electron spin in diamond. (a) Pulse sequence of the electron-spin initialization and readout. The microwave operation only acts on the preparation of spin states other than

m s = 0

. (b) Photon time traces of spin states initialized at

m s = 0

(dark green and dark red dotted lines) and

m s = 1

(light green and light red dotted lines), measured with

108

repetitions. The red and green lines covered by the shadow are their differential signals, namely, signal photons. The inset plot shows the detailed comparison between signal photons at different time and power of laser. (c, e) Theoretical SNR of the traditional scheme as a function of the pumping rate and duration for global optical pumping (including initialization and readout) and initialization, respectively. (d, f) SNR of the traditional scheme as a function of pumping rate in simulations or power in experiments under optimal duration conditions for global optical pumping and initialization, respectively.

Fig.3 Simulation and experimental results of the OLO scheme for readout. (a) and (b) show the optimization process for simulations and experiments, respectively. The dotted lines represent the optimal SNR achieved at each iteration. (c) and (d) plot the final optimal laser waveform (shaded area) and photon time traces of the

m s = 0

and

m s = 1

for simulations and experiments, respectively.

Fig.4 Rabi oscillation measurements (left axis) and their deviation (right axis) with different optimizations. The fitted contrast of the OLO scheme (green, solid line), the traditional scheme optimized by SNR (orange, dashed line), and the traditional scheme optimized by contrast (purple, dash-dot line) are 16.5%, 11.3%, and 15.2%, respectively. Columns are deviations of Rabi measurements, defined by differences between the data points and the best fitted lines. The means of deviations on each Rabi oscillation, are 0.00538 (OLO scheme by SNR), 0.00612 (traditional scheme by SNR), and 0.04794 (traditional scheme by contrast), respectively. Both contrast and deviation are improved by our OLO scheme.

1	Balasubramanian G. , Y. Chan I. , Kolesov R. , Al-Hmoud M. , Tisler J. , Shin C. , Kim C. , Wojcik A. , R. Hemmer P. , Krueger A. , Hanke T. , Leitenstorfer A. , Bratschitsch R. , Jelezko F. , Wrachtrup J. . Nanoscale imaging magnetometry with diamond spins under ambient conditions. Nature, 2008, 455(7213): 648 https://doi.org/10.1038/nature07278
2	Jakobi I. , Neumann P. , Wang Y. , B. R. Dasari D. , El Hallak F. , A. Bashir M. , Markham M. , Edmonds A. , Twitchen D. , Wrachtrup J. . Measuring broadband magnetic fields on the nanoscale using a hybrid quantum register. Nat. Nanotechnol., 2017, 12(1): 67 https://doi.org/10.1038/nnano.2016.163
3	R. Maze J. , L. Stanwix P. , S. Hodges J. , Hong S. , M. Taylor J. , Cappellaro P. , Jiang L. , V. G. Dutt M. , Togan E. , S. Zibrov A. , Yacoby A. , L. Walsworth R. , D. Lukin M. . Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature, 2008, 455(7213): 644 https://doi.org/10.1038/nature07279
4	Zaiser S. , Rendler T. , Jakobi I. , Wolf T. , Y. Lee S. , Wagner S. , Bergholm V. , Schulte-Herbrggen T. , Neumann P. , Wrachtrup J. . Enhancing quantum sensing sensitivity by a quantum memory. Nat. Commun., 2016, 7(1): 12279 https://doi.org/10.1038/ncomms12279
5	Unden T. , Balasubramanian P. , Louzon D. , Vinkler Y. , Plenio M. , Markham M. , Twitchen D. , Stacey A. , Lovchinsky I. , Sushkov A. , Lukin M. , Retzker A. , Naydenov B. , McGuinness L. , Jelezko F. . Quantum metrology enhanced by repetitive quantum error correction. Phys. Rev. Lett., 2016, 116(23): 230502 https://doi.org/10.1103/PhysRevLett.116.230502
6	L. Degen C. . Scanning magnetic field microscope with a diamond single-spin sensor. Appl. Phys. Lett., 2008, 92(24): 243111 https://doi.org/10.1063/1.2943282
7	Zhou J. , Wang P. , Shi F. , Huang P. , Kong X. , Xu X. , Zhang Q. , Wang Z. , Rong X. , Du J. . Quantum information processing and metrology with color centers in diamonds. Front. Phys., 2014, 9(5): 587 https://doi.org/10.1007/s11467-014-0421-5
8	Dolde F. , Fedder H. , W. Doherty M. , Nbauer T. , Rempp F. , Balasubramanian G. , Wolf T. , Reinhard F. , C. L. Hollenberg L. , Jelezko F. , Wrachtrup J. . Electric-field sensing using single diamond spins. Nat. Phys., 2011, 7(6): 459 https://doi.org/10.1038/nphys1969
9	Kucsko G. , C. Maurer P. , Y. Yao N. , Kubo M. , J. Noh H. , K. Lo P. , Park H. , D. Lukin M. . Nanometre-scale thermometry in a living cell. Nature, 2013, 500(7460): 54 https://doi.org/10.1038/nature12373
10	M. Toyli D. , F. de las Casas C. , J. Christle D. , V. Dobrovitski V. , D. Awschalom D. . Fluorescence thermometry enhanced by the quantum coherence of single spins in diamond. Proc. Natl. Acad. Sci. USA, 2013, 110(21): 8417 https://doi.org/10.1073/pnas.1306825110
11	Hsieh S. , Bhattacharyya P. , Zu C. , Mittiga T. , J. Smart T. , Machado F. , Kobrin B. , O. Hhn T. , Z. Rui N. , Kamrani M. , Chatterjee S. , Choi S. , Zaletel M. , V. Struzhkin V. , E. Moore J. , I. Levitas V. , Jeanloz R. , Y. Yao N. . Imaging stress and magnetism at high pressures using a nanoscale quantum sensor. Science, 2019, 366(6471): 1349 https://doi.org/10.1126/science.aaw4352
12	Staudacher T. , Shi F. , Pezzagna S. , Meijer J. , Du J. , A. Meriles C. , Reinhard F. , Wrachtrup J. . Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume. Science, 2013, 339(6119): 561 https://doi.org/10.1126/science.1231675
13	Shi F. , Zhang Q. , Wang P. , Sun H. , Wang J. , Rong X. , Chen M. , Ju C. , Reinhard F. , Chen H. , Wrachtrup J. , Wang J. , Du J. . Single-protein spin resonance spectroscopy under ambient conditions. Science, 2015, 347(6226): 1135 https://doi.org/10.1126/science.aaa2253
14	P. Tetienne J. , Hingant T. , V. Kim J. , H. Diez L. , P. Adam J. , Garcia K. , F. Roch J. , Rohart S. , Thiaville A. , Ravelosona D. , Jacques V. . Nanoscale imaging and control of domain-wall hopping with a nitrogen-vacancy center microscope. Science, 2014, 344(6190): 1366 https://doi.org/10.1126/science.1250113
15	L. Degen C. , Poggio M. , J. Mamin H. , T. Rettner C. , Rugar D. . Nanoscale magnetic resonance imaging. Proc. Natl. Acad. Sci. USA, 2009, 106(5): 1313 https://doi.org/10.1073/pnas.0812068106
16	L. Degen C.Reinhard F.Cappellaro P., Quantum sensing, Rev. Mod. Phys. 89(3), 035002 (2017) (rMP.)
17	F. Barry J. , M. Schloss J. , Bauch E. , J. Turner M. , A. Hart C. , M. Pham L. , L. Walsworth R. . Sensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys., 2020, 92(1): 015004 https://doi.org/10.1103/RevModPhys.92.015004
18	F. Barry J. , J. Turner M. , M. Schloss J. , R. Glenn D. , Song Y. , D. Lukin M. , Park H. , L. Walsworth R. . Optical magnetic detection of single-neuron action potentials using quantum defects in diamond. Proc. Natl. Acad. Sci. USA, 2016, 113(49): 14133 https://doi.org/10.1073/pnas.1601513113
19	C. Davis H. , Ramesh P. , Bhatnagar A. , Lee-Gosselin A. , F. Barry J. , R. Glenn D. , L. Walsworth R. , G. Shapiro M. . Mapping the microscale origins of magnetic resonance image contrast with subcellular diamond magnetometry. Nat. Commun., 2018, 9(1): 131 https://doi.org/10.1038/s41467-017-02471-7
20	A. Hopper D.R. Grote R.L. Exarhos A.C. Bassett L., Near-infrared-assisted charge control and spin readout of the nitrogen-vacancy center in diamond, Phys. Rev. B 94(24), 241201 (2016) (pRB.)
21	Neumann P. , Beck J. , Steiner M. , Rempp F. , Fedder H. , R. Hemmer P. , Wrachtrup J. , Jelezko F. . Single-shot readout of a single nuclear spin. Science, 2010, 329(5991): 542 https://doi.org/10.1126/science.1189075
22	Qian P. , Lin X. , Zhou F. , Ye R. , Ji Y. , Chen B. , Xie G. , Xu N. . Machine-learning-assisted electron-spin readout of nitrogen-vacancy center in diamond. Appl. Phys. Lett., 2021, 118(8): 084001 https://doi.org/10.1063/5.0038590
23	Song Y. , Tian Y. , Hu Z. , Zhou F. , Xing T. , Lu D. , Chen B. , Wang Y. , Xu N. , Du J. . Pulse-width-induced polarization enhancement of optically pumped N-V electron spin in diamond. Photon. Res., 2020, 8(8): 1289 https://doi.org/10.1364/PRJ.386983
24	Liu T. , Zhang J. , Yuan H. , Xu L. , Bian G. , Fan P. , Li M. , Liu Y. , Xia S. , Xu C. , Xiao X. . A pulsed time-varying method for improving the spin readout efficiency of nitrogen vacancy centers. J. Phys. D, 2021, 54(39): 395002 https://doi.org/10.1088/1361-6463/ac1191
25	Oshnik N. , Rembold P. , Calarco T. , Montangero S. , Neu E. , M. Müller M. . Robust magnetometry with single nitrogen-vacancy centers via two-step optimization. Phys. Rev. A, 2022, 106(1): 013107 https://doi.org/10.1103/PhysRevA.106.013107
26	Bauer B. , Wecker D. , J. Millis A. , B. Hastings M. , Troyer M. . Hybrid quantum-classical approach to correlated materials. Phys. Rev. X, 2016, 6(3): 031045 https://doi.org/10.1103/PhysRevX.6.031045
27	Bravyi S. , Smith G. , A. Smolin J. . Trading classical and quantum computational resources. Phys. Rev. X, 2016, 6(2): 021043 https://doi.org/10.1103/PhysRevX.6.021043
28	R. McClean J. , Romero J. , Babbush R. , Aspuru-Guzik A. . The theory of variational hybrid quantum-classical algorithms. New J. Phys., 2016, 18(2): 023023 https://doi.org/10.1088/1367-2630/18/2/023023
29	Suter D. , Jelezko F. . Single-spin magnetic resonance in the nitrogen-vacancy center of diamond. Prog. Nucl. Magn. Reson. Spectrosc., 2017, 98–99, 50 https://doi.org/10.1016/j.pnmrs.2016.12.001
30	W. Doherty M. , B. Manson N. , Delaney P. , Jelezko F. , Wrachtrup J. , C. L. Hollenberg L. . The nitrogen-vacancy colour centre in diamond. Phys. Rep., 2013, 528(1): 1 https://doi.org/10.1016/j.physrep.2013.02.001
31	W. Doherty M. , B. Manson N. , Delaney P. , C. L. Hollenberg L. . The negatively charged nitrogen-vacancy centre in diamond: The electronic solution. New J. Phys., 2011, 13(2): 025019 https://doi.org/10.1088/1367-2630/13/2/025019
32	Chen B. , Hou X. , Zhou F. , Qian P. , Shen H. , Xu N. . Detecting the out-of-time-order correlations of dynamical quantum phase transitions in a solid-state quantum simulator. Appl. Phys. Lett., 2020, 116(19): 194002 https://doi.org/10.1063/5.0004152
33	D. Fuchs G. , V. Dobrovitski V. , M. Toyli D. , J. Heremans F. , D. Weis C. , Schenkel T. , D. Awschalom D. . Excited-state spin coherence of a single nitrogen–vacancy centre in diamond. Nat. Phys., 2010, 6(9): 668 https://doi.org/10.1038/nphys1716
34	L. Goldman M.Sipahigil A.W. Doherty M.Y. Yao N.D. Bennett S.Markham M.J. Twitchen D.B. Manson N.Kubanek A.D. Lukin M., Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers, Phys. Rev. Lett. 114(14), 145502 (2015)
35	B. Manson N. , P. Harrison J. , J. Sellars M. . Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics. Phys. Rev. B, 2006, 74(10): 104303 https://doi.org/10.1103/PhysRevB.74.104303
36	Steiner M.Neumann P.Beck J.Jelezko F.Wrachtrup J., Universal enhancement of the optical readout fidelity of single electron spins at nitrogen-vacancy centers in diamond, Phys. Rev. B 81(3), 035205 (2010)
37	A. Wolf S.Rosenberg I.Rapaport R.Bar-Gill N., Purcell-enhanced optical spin readout of nitrogen-vacancy centers in diamond, Phys. Rev. B 92(23), 235410 (2015)
38	G. Skellam J. . The frequency distribution of the difference between two poisson variates belonging to different populations. J. R. Stat. Soc., 1946, 109(3): 296 https://doi.org/10.2307/2981372
39	Yang X. , Chen X. , Li J. , Peng X. , Laamme R. . Hybrid quantum-classical approach to enhanced quantum metrology. Sci. Rep., 2021, 11: 672 https://doi.org/10.1038/s41598-020-80070-1
40	Li J. , Yang X. , Peng X. , P. Sun C. . Hybrid quantum-classical approach to quantum optimal control. Phys. Rev. Lett., 2017, 118(15): 150503 https://doi.org/10.1103/PhysRevLett.118.150503
41	Lu D. , Li K. , Li J. , Katiyar H. , J. Park A. , Feng G. , Xin T. , Li H. , Long G. , Brodutch A. , Baugh J. , Zeng B. , Laamme R. . Enhancing quantum control by bootstrapping a quantum processor of 12 qubits. npj Quantum Inform., 2017, 3: 45 https://doi.org/10.1038/s41534-017-0045-z
42	Xin T. , Nie X. , Kong X. , Wen J. , Lu D. , Li J. . Quantum pure state tomography via variational hybrid quantum-classical method. Phys. Rev. Appl., 2020, 13(2): 024013 https://doi.org/10.1103/PhysRevApplied.13.024013
43	Bhole G. , A. Jones J. . Practical pulse engineering: Gradient ascent without matrix exponentiation. Front. Phys., 2018, 13(3): 130312 https://doi.org/10.1007/s11467-018-0791-1
44	Ouyang Y. , Yu C. , Yan G. , Chen J. . Machine learning approach for the prediction and optimization of thermal transport properties. Front. Phys., 2021, 16(4): 43200 https://doi.org/10.1007/s11467-020-1041-x
45	Li X. , Yu W. , Fan X. , J. Babu G. . Some optimizations on detecting gravitational wave using convolutional neural network. Front. Phys., 2020, 15(5): 54501 https://doi.org/10.1007/s11467-020-0966-4
46	M. Lewis R. , Torczon V. , W. Trosset M. . Direct search methods: Then and now. J. Comput. Appl. Math., 2000, 124(1-2): 191 https://doi.org/10.1016/S0377-0427(00)00423-4
47	E. Eiben A. , Smith J. . From evolutionary computation to the evolution of things. Nature, 2015, 521(7553): 476 https://doi.org/10.1038/nature14544
48	Hooke R. , A. Jeeves T. . “Direct search” solution of numerical and statistical problems. J. Assoc. Comput. Mach., 1961, 8(2): 212 https://doi.org/10.1145/321062.321069
49	A. Golter D. , Wang H. . Optically driven rabi oscillations and adiabatic passage of single electron spins in diamond. Phys. Rev. Lett., 2014, 112(11): 116403 https://doi.org/10.1103/PhysRevLett.112.116403
50	Robledo L.Bernien H.van Weperen I.Hanson R., Control and coherence of the optical transition of single nitrogen vacancy centers in diamond, Phys. Rev. Lett. 105(17), 177403 (2010)
51	A. Hopper D. , J. Shulevitz H. , C. Bassett L. . Spin readout techniques of the nitrogen-vacancy center in diamond. Micromachines (Basel), 2018, 9(9): 437 https://doi.org/10.3390/mi9090437
52	M. Pham L. , Bar-Gill N. , Belthangady C. , Le Sage D. , Cappellaro P. , D. Lukin M. , Yacoby A. , L. Walsworth R. . Enhanced solid-state multispin metrology using dynamical decoupling. Phys. Rev. B, 2012, 86(4): 045214 https://doi.org/10.1103/PhysRevB.86.045214
53	V. G. Dutt M. , Childress L. , Jiang L. , Togan E. , Maze J. , Jelezko F. , S. Zibrov A. , R. Hemmer P. , D. Lukin M. . Quantum register based on individual electronic and nuclear spin qubits in diamond. Science, 2007, 316(5829): 1312 https://doi.org/10.1126/science.1139831
54	M. Pham L. , L. Sage D. , L. Stanwix P. , K. Yeung T. , Glenn D. , Trifonov A. , Cappellaro P. , R. Hemmer P. , D. Lukin M. , Park H. , Yacoby A. , L. Walsworth R. . Magnetic field imaging with nitrogen-vacancy ensembles. New J. Phys., 2011, 13(4): 045021 https://doi.org/10.1088/1367-2630/13/4/045021

[1]

fop-21235-OF-linxue_suppl_1

Download

Viewed

Full text

Abstract

Cited

Shared

Discussed