Quantum sensing based on strongly interacting nuclear spin systems

LI Qing; JI Yunlan; LIU Ran; Suter Dieter; JIANG Min; PENG Xinhua

doi:10.7498/aps.74.20250271

Abstract

Quantum sensing utilizes the quantum resources of well-controlled quantum systems to measure small signals with high sensitivity, and has great potential in both fundamental science and concrete applications. Interacting quantum systems have attracted increasing interest in the field of precise measurements, owing to their potential to generate quantum-correlated states and exhibit rich many-body dynamics. These features provide a novel avenue for exploiting quantum resources in sensing applications. Although previous studies have shown that using such systems can improve sensitivity, they mainly focused on measuring individual physical quantities. In experiment, the challenge of using interacting quantum systems to achieve high-precision measurements of multiple physical parameters simultaneously has not been explored to a large extent. In this study, we demonstrate a first realisation of interaction-based multiparameter sensing by using strongly interacting nuclear spins under ultra-low magnetic field conditions. We find that, as the interaction strength among nuclear spins becomes significantly larger than their Larmor frequencies, a different regime emerges where the strongly interacting spins can be simultaneously sensitive to all components of a multidimensional field, such as a three-dimensional magnetic field. Moreover, we observe that the strong interactions between nuclear spins can increase their quantum coherence times to as long as several seconds, thereby improving measurement precision. Our sensor successfully achieves precision measurement of three-dimensional vector magnetic fields with a field sensitivity reaching the order of 10^–11 T and an angular resolution as high as 0.2 rad. Importantly, this approach eliminates the need for external reference fields, thereby avoiding calibration errors and technical noise commonly encountered in traditional magnetometry. Experimentally optimized protocol further enhances the sensitivity of the interacting spin-based sensor by up to five orders of magnitude compared with non-interacting or classical schemes. These results demonstrate the enormous potential of interacting spin systems as a powerful platform for high-precision multi-parameter quantum sensing. The techniques developed here pave the way for a new generation of quantum sensors that use intrinsic spin interactions to exceed the traditional sensitivity limits, presenting a promising route toward ultra-sensitive, calibration-free magnetometry in complex environments.

Keywords:

Authors and contacts

1.
CAS Key Laboratory of Microscale Magnetic Resonance, Department of Modern Physics,University of Science and Technology of China, Hefei 230026, China
2.
CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
3.
Hefei National Laboratory, Hefei 230088, China
4.
School of Physics, Hefei University of Technology, Hefei 230009, China
5.
College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
6.
Fakultät Physik, Technische Universität Dortmund, Dortmund D-44221, Germany

Corresponding author: JIANG Min, dxjm@ustc.edu.cn ; PENG Xinhua, xhpeng@ustc.edu.cn

Funds: Project supported by the Innovation Program for Quantum Science and Technology, China (Grant No. 2021ZD0303205), the National Natural Science Foundation of China (Grant Nos. T2388102, 11927811, 92476204, 12150014, 12205296, 12274395, 12261160569), and the Youth Innovation Promotion Association, China (Grant No. 2023474).

FullText HTML

References

[1]	Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photonics 5 222 Google Scholar
[2]	Degen C L, Reinhard F, Cappellaro P 2017 Rev. Mod. Phys. 89 035002 Google Scholar
[3]	Pezze L, Smerzi A, Oberthaler M K, Schmied R, Treutlein P 2018 Rev. Mod. Phys. 90 035005 Google Scholar
[4]	Braun D, Adesso G, Benatti F, Floreanini R, Marzolino U, Mitchell M W, Pirandola S 2018 Rev. Mod. Phys. 90 035006 Google Scholar
[5]	Aasi J, Abadie J, Abbott B, et al. 2013 Nat. Photonics 7 613 Google Scholar
[6]	Budker D, Romalis M 2007 Nat. Phys. 3 227 Google Scholar
[7]	Safronova M, Budker D, DeMille D, Kimball D F J, Derevianko A, Clark C W 2018 Rev. Mod. Phys. 90 025008 Google Scholar
[8]	彭世杰, 刘颖, 马文超, 石发展, 杜江峰 2018 物理学报 67 167601 Google Scholar Peng S J, Liu Y, Ma W C, Shi F Z, Du J F 2018 Acta Phys. Sin. 67 167601 Google Scholar
[9]	Álvarez G A, Suter D, Kaiser R 2015 Science 349 846 Google Scholar
[10]	Lucchesi L, Chiofalo M L 2019 Phys. Rev. Lett. 123 060406 Google Scholar
[11]	Kong J, Jiménez-Martínez R, Troullinou C, Lucivero V G, Tóth G, Mitchell M W 2020 Nat. Commun. 11 1 Google Scholar
[12]	Peyronel T, Firstenberg O, Liang Q Y, Hofferberth S, Gorshkov A V, Pohl T, Lukin M D, Vuletić V 2012 Nature 488 57 Google Scholar
[13]	Dooley S, Hanks M, Nakayama S, Munro W J, Nemoto K 2018 NPJ Quant. Inf. 4 1 Google Scholar
[14]	Nolan S P, Szigeti S S, Haine S A 2017 Phys. Rev. Lett. 119 193601 Google Scholar
[15]	Zhou H, Choi J, Choi S, et al. 2020 Phys. Rev. X 10 031003
[16]	Frérot I, Roscilde T 2018 Phys. Rev. Lett. 121 020402 Google Scholar
[17]	Roy S, Braunstein S L 2008 Phys. Rev. Lett. 100 220501 Google Scholar
[18]	Napolitano M, Koschorreck M, Dubost B, Behbood N, Sewell R, Mitchell M W 2011 Nature 471 486 Google Scholar
[19]	Boixo S, Flammia S T, Caves C M, Geremia J M 2007 Phys. Rev. Lett. 98 090401 Google Scholar
[20]	Chu Y, Zhang S, Yu B, Cai J 2021 Phys. Rev. Lett. 126 010502 Google Scholar
[21]	Rams M M, Sierant P, Dutta O, Horodecki P, Zakrzewski J 2018 Phys. Rev. X 8 021022
[22]	Rovny J, Blum R L, Barrett S E 2018 Phys. Rev. Lett. 120 180603 Google Scholar
[23]	Kominis I, Kornack T, Allred J, Romalis M V 2003 Nature 422 596 Google Scholar
[24]	Boixo S, Datta A, Davis M J, Flammia S T, Shaji A, Caves C M 2008 Phys. Rev. Lett. 101 040403 Google Scholar
[25]	李辉, 江敏, 朱振南, 徐文杰, 徐翔, 彭新华 2019 物理学报 68 160701 Google Scholar Li H, Jiang M, Zhu Z N, Xu W J, Xu M X, Peng X H 2019 Acta Phys. Sin. 68 160701 Google Scholar
[26]	张语珊, 许廷发 2016 地球物理学进展 31 2346 Google Scholar Zhang Y S, Xu T F 2016 Prog. Geophys 31 2346 Google Scholar
[27]	Wang X, Zhu M, Xiao K, Guo J, Wang L 2019 J. Magn. Reson. 307 106580 Google Scholar
[28]	Szczykulska M, Baumgratz T, Datta A 2016 Adv. Phys.: X 1 621
[29]	Vidrighin M D, Donati G, Genoni M G, et al. 2014 Nat. Commun. 5 1
[30]	Hou Z, Tang J F, Chen H, Yuan H, Xiang G Y, Li C F, Guo G C 2021 Sci. Adv. 7 eabd2986
[31]	Roccia E, Cimini V, Sbroscia M, et al. 2018 Optica 5 1171 Google Scholar
[32]	Hou Z, Zhang Z, Xiang G Y, Li C F, Guo G C, Chen H, Liu L, Yuan H 2020 Phys. Rev. Lett. 125 020501 Google Scholar
[33]	Seltzer S, Romalis M 2004 Appl. Phys. Lett. 85 4804 Google Scholar
[34]	Patton B, Zhivun E, Hovde D, Budker D 2014 Phys. Rev. Lett. 113 013001 Google Scholar
[35]	Thiele T, Lin Y, Brown M O, Regal C A 2018 Phys. Rev. Lett. 121 153202 Google Scholar
[36]	Li R, Quan W, Fan W, Xing L, Wang Z, Zhai Y, Fang J 2017 Chin. Phys. B 26 120702 Google Scholar
[37]	Liu J, Yuan H 2017 Phys. Rev. A 96 042114 Google Scholar
[38]	Legchenko A, Baltassat J M, Beauce A, Bernard J 2002 J. Appl. Geophys. 50 21 Google Scholar
[39]	Gross S, Barmet C, Dietrich B E, Brunner D O, Schmid T, Pruessmann K P 2016 Nat. Commun. 7 1
[40]	Genovese M 2016 J. Optics 18 073002 Google Scholar
[41]	王宁, 金贻荣, 邓辉, 吴玉林, 郑国林, 李绍, 田野, 任育峰, 陈莺飞, 郑东宁 2012 物理学报 61 213302 Google Scholar Wang N, Jin Y R, Deng H, Wu Y L, Zheng G L, Li S, Ye T, Ren Y F, Chen Y F, Zheng D N 2012 Acta Phys. Sin. 61 213302 Google Scholar
[42]	Komar P, Kessler E M, Bishof M, Jiang L, Sørensen A S, Ye J, Lukin M D 2014 Nat. Phys. 10 582 Google Scholar
[43]	Donley E A 2010 IEEE Sensors Waikoloa, HI, USA, November 01–04, 2010 p17–22
[44]	Walker T G, Happer W 1997 Rev. Mod. Phys. 69 629 Google Scholar
[45]	Kornack T, Ghosh R, Romalis M 2005 Phys. Rev. Lett. 95 230801 Google Scholar
[46]	Hurwitz L, Nelson J 1960 J. Geophys. Res. 65 1759 Google Scholar
[47]	Wu T, Blanchard J W, Kimball D F J, Jiang M, Budker D 2018 Phys. Rev. Lett. 121 023202 Google Scholar
[48]	Garcon A, Blanchard J W, Centers G P, et al. 2019 Sci. Adv. 5 eaax4539 Google Scholar
[49]	Jiang M, Su H, Garcon A, Peng X, Budker D 2021 arXiv: 2102.01448
[50]	Farooq M, Chupp T, Grange J, et al. 2020 Phys. Rev. Lett. 124 223001 Google Scholar
[51]	Adams R W, Aguilar J A, Atkinson K D, et al. 2009 Science 323 1708 Google Scholar
[52]	Theis T, Ganssle P, Kervern G, Knappe S, Kitching J, Ledbetter M, Budker D, Pines A 2011 Nat. Phys. 7 571 Google Scholar
[53]	Maly T, Debelouchina G T, Bajaj V S, et al. 2008 J. Chem. Phys. 128 02B611
[54]	Spagnolo N, Aparo L, Vitelli C, Crespi A, Ramponi R, Osellame R, Mataloni P, Sciarrino F 2012 Sci. Rep. 2 1
[55]	Jiang M, Wu T, Blanchard J W, Feng G, Peng X, Budker D 2018 Sci. Adv. 4 eaar6327
[56]	Jiang M, Frutos R P, Wu T, Blanchard J W, Peng X, Budker D 2019 Phys. Rev. Appl. 11 024005 Google Scholar
[57]	Tayler M C, Theis T, Sjolander T F, Blanchard J W, Kentner A, Pustelny S, Pines A, Budker D 2017 Rev. Sci. Instrum. 88 091101 Google Scholar
[58]	Jiang M, Xu W, Li Q, Wu Z, Suter D, Peng X 2020 Adv. Quantum Technol. 3 2000078 Google Scholar
[59]	Ledbetter M, Theis T, Blanchard J, et al. 2011 Phys. Rev. Lett. 107 107601 Google Scholar
[60]	Appelt S, Häsing F, Sieling U, Gordji-Nejad A, Glöggler S, Blümich B 2010 Phys. Rev. A 81 023420 Google Scholar
[61]	Gemmel C, Heil W, Karpuk S, et al. 2010 Eur. Phys. J. D 57 303 Google Scholar
[62]	Sjolander T F, Tayler M C, King J P, Budker D, Pines A 2016 J. Phys. Chem. A 120 4343 Google Scholar
[63]	Alcicek S, Put P, Kubrak A, Alcicek F C, Barskiy D, Gloeggler S, Dybas J, Pustelny S 2023 Commun. Chem. 6 165 Google Scholar
[64]	Picazo-Frutos R, Sheberstov K F, Blanchard J W, et al. 2024 Nat. Commun. 15 4487 Google Scholar
[65]	Zeeman P 1897 Nature 55 347
[66]	Condon E U, Condon E, Shortley G 1935 The Theory of Atomic Spectra (Cambridge: Cambridge University Press) pp378–380
[67]	Hou Z, Jin Y, Chen H, Tang J F, Huang C J, Yuan H, Xiang G Y, Li C F, Guo G C 2021 Phys. Rev. Lett. 126 070503 Google Scholar
[68]	Bao G, Wickenbrock A, Rochester S, Zhang W, Budker D 2018 Phys. Rev. Lett. 120 033202 Google Scholar
[69]	王忻昌, 江文龙, 黄程达, 孙惠军, 曹晓宇, 田中群, 陈忠 2020 光谱学与光谱分析 40 665 Xin-Chang Wang C D H H J S X Y C Z Q T Wen-Long Jiang, Chen Z 2020 Spectrosc. Spectral Anal. 40 665
[70]	Jiang M, Bian J, Li Q, Wu Z, Su H, Xu M, Wang Y, Wang X, Peng X 2021 Fundamental Research 1 68 Google Scholar
[71]	Jiang M, Bian J, Liu X, Wang H, Ji Y, Zhang B, Peng X, Du J 2018 Phys. Rev. A 97 062118 Google Scholar
[72]	Jones J A, Karlen S D, Fitzsimons J, Ardavan A, Benjamin S C, Briggs G A D, Morton J J 2009 Science 324 1166 Google Scholar
[73]	Bermudez A, Jelezko F, Plenio M B, Retzker A 2011 Phys. Rev. Lett. 107 150503 Google Scholar
[74]	Zhao N, Hu J L, Ho S W, Wan J T, Liu R 2011 Nat. Nanotechnol. 6 242 Google Scholar
[75]	Schweiger A, Jeschke G 2001 Principles of Pulse Electron Paramagnetic Resonance (Oxford: Oxford University Press on Demand) pp29–32
[76]	Xiao D W, Hu W H, Cai Y, Zhao N 2020 Phys. Rev. Lett. 124 128101 Google Scholar
[77]	Qin S, Yin H, Yang C, et al. 2016 Nat. Mater. 15 217 Google Scholar

Cited By

图 1 基于相互作用系统的量子传感实验示意图　(a)实验装置示意图; (b)多参数传感的基本过程, 包括探针态制备、未知磁场编码以及探针态的读出; (c) ⁸⁷Rb原子磁力计示意图

Figure 1. Experimental schematic of interaction-based quantum sensing: (a) Diagram of the experimental setup; (b) basic procedure of quantum sensing, including probe state preparation, encoding unknown magnetic field, and probe readout; (c) diagram of the ⁸⁷Rb atomic magnetometer.

DownLoad: Full-Size Img PowerPoint

图 2 在不同方向磁场下测量的¹³CH_n分子谱学　(a), (b) ¹³C-甲酸; (c), (d) ¹³C-甲醛; (e), (f) ¹³C-乙腈. 分裂模式与插图中显示的跃迁高度匹配

Figure 2. Spectra of ¹³CH_n molecules measured at various orientations of the magnetic field: (a), (b) ¹³C-Formic aci; (c), (d) ¹³C-formaldehyde; (e), (f) ¹³C-acetonitrile. The splitting patterns match well the transitions shown in the inset.

DownLoad: Full-Size Img PowerPoint

图 3 使用甲酸分子进行磁场测量　(a)测量矢量磁场的实验过程; (b)重构矢量磁场的实例; (c)当谱振幅受高斯噪声$ \sim {\cal{N}}(0, \sigma^2) $影响时, θ和ϕ的测量精度; (d)进行300次重复测量磁场强度的直方图

Figure 3. Magnetic field measurement with formic acid molecules: (a) The procedure of determining a magnetic field vector; (b) as one example of reconstructing the magnetic field vector; (c) measured precision of θ, ϕ when spectral amplitude suffers from Gaussian noise $ \sim {\cal{N}}(0, \sigma ^2) $; (d) histograms of magnetic field strength obtained from 300 repeated measurements.

DownLoad: Full-Size Img PowerPoint

[1]	Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photonics 5 222 Google Scholar
[2]	Degen C L, Reinhard F, Cappellaro P 2017 Rev. Mod. Phys. 89 035002 Google Scholar
[3]	Pezze L, Smerzi A, Oberthaler M K, Schmied R, Treutlein P 2018 Rev. Mod. Phys. 90 035005 Google Scholar
[4]	Braun D, Adesso G, Benatti F, Floreanini R, Marzolino U, Mitchell M W, Pirandola S 2018 Rev. Mod. Phys. 90 035006 Google Scholar
[5]	Aasi J, Abadie J, Abbott B, et al. 2013 Nat. Photonics 7 613 Google Scholar
[6]	Budker D, Romalis M 2007 Nat. Phys. 3 227 Google Scholar
[7]	Safronova M, Budker D, DeMille D, Kimball D F J, Derevianko A, Clark C W 2018 Rev. Mod. Phys. 90 025008 Google Scholar
[8]	彭世杰, 刘颖, 马文超, 石发展, 杜江峰 2018 物理学报 67 167601 Google Scholar Peng S J, Liu Y, Ma W C, Shi F Z, Du J F 2018 Acta Phys. Sin. 67 167601 Google Scholar
[9]	Álvarez G A, Suter D, Kaiser R 2015 Science 349 846 Google Scholar
[10]	Lucchesi L, Chiofalo M L 2019 Phys. Rev. Lett. 123 060406 Google Scholar
[11]	Kong J, Jiménez-Martínez R, Troullinou C, Lucivero V G, Tóth G, Mitchell M W 2020 Nat. Commun. 11 1 Google Scholar
[12]	Peyronel T, Firstenberg O, Liang Q Y, Hofferberth S, Gorshkov A V, Pohl T, Lukin M D, Vuletić V 2012 Nature 488 57 Google Scholar
[13]	Dooley S, Hanks M, Nakayama S, Munro W J, Nemoto K 2018 NPJ Quant. Inf. 4 1 Google Scholar
[14]	Nolan S P, Szigeti S S, Haine S A 2017 Phys. Rev. Lett. 119 193601 Google Scholar
[15]	Zhou H, Choi J, Choi S, et al. 2020 Phys. Rev. X 10 031003
[16]	Frérot I, Roscilde T 2018 Phys. Rev. Lett. 121 020402 Google Scholar
[17]	Roy S, Braunstein S L 2008 Phys. Rev. Lett. 100 220501 Google Scholar
[18]	Napolitano M, Koschorreck M, Dubost B, Behbood N, Sewell R, Mitchell M W 2011 Nature 471 486 Google Scholar
[19]	Boixo S, Flammia S T, Caves C M, Geremia J M 2007 Phys. Rev. Lett. 98 090401 Google Scholar
[20]	Chu Y, Zhang S, Yu B, Cai J 2021 Phys. Rev. Lett. 126 010502 Google Scholar
[21]	Rams M M, Sierant P, Dutta O, Horodecki P, Zakrzewski J 2018 Phys. Rev. X 8 021022
[22]	Rovny J, Blum R L, Barrett S E 2018 Phys. Rev. Lett. 120 180603 Google Scholar
[23]	Kominis I, Kornack T, Allred J, Romalis M V 2003 Nature 422 596 Google Scholar
[24]	Boixo S, Datta A, Davis M J, Flammia S T, Shaji A, Caves C M 2008 Phys. Rev. Lett. 101 040403 Google Scholar
[25]	李辉, 江敏, 朱振南, 徐文杰, 徐翔, 彭新华 2019 物理学报 68 160701 Google Scholar Li H, Jiang M, Zhu Z N, Xu W J, Xu M X, Peng X H 2019 Acta Phys. Sin. 68 160701 Google Scholar
[26]	张语珊, 许廷发 2016 地球物理学进展 31 2346 Google Scholar Zhang Y S, Xu T F 2016 Prog. Geophys 31 2346 Google Scholar
[27]	Wang X, Zhu M, Xiao K, Guo J, Wang L 2019 J. Magn. Reson. 307 106580 Google Scholar
[28]	Szczykulska M, Baumgratz T, Datta A 2016 Adv. Phys.: X 1 621
[29]	Vidrighin M D, Donati G, Genoni M G, et al. 2014 Nat. Commun. 5 1
[30]	Hou Z, Tang J F, Chen H, Yuan H, Xiang G Y, Li C F, Guo G C 2021 Sci. Adv. 7 eabd2986
[31]	Roccia E, Cimini V, Sbroscia M, et al. 2018 Optica 5 1171 Google Scholar
[32]	Hou Z, Zhang Z, Xiang G Y, Li C F, Guo G C, Chen H, Liu L, Yuan H 2020 Phys. Rev. Lett. 125 020501 Google Scholar
[33]	Seltzer S, Romalis M 2004 Appl. Phys. Lett. 85 4804 Google Scholar
[34]	Patton B, Zhivun E, Hovde D, Budker D 2014 Phys. Rev. Lett. 113 013001 Google Scholar
[35]	Thiele T, Lin Y, Brown M O, Regal C A 2018 Phys. Rev. Lett. 121 153202 Google Scholar
[36]	Li R, Quan W, Fan W, Xing L, Wang Z, Zhai Y, Fang J 2017 Chin. Phys. B 26 120702 Google Scholar
[37]	Liu J, Yuan H 2017 Phys. Rev. A 96 042114 Google Scholar
[38]	Legchenko A, Baltassat J M, Beauce A, Bernard J 2002 J. Appl. Geophys. 50 21 Google Scholar
[39]	Gross S, Barmet C, Dietrich B E, Brunner D O, Schmid T, Pruessmann K P 2016 Nat. Commun. 7 1
[40]	Genovese M 2016 J. Optics 18 073002 Google Scholar
[41]	王宁, 金贻荣, 邓辉, 吴玉林, 郑国林, 李绍, 田野, 任育峰, 陈莺飞, 郑东宁 2012 物理学报 61 213302 Google Scholar Wang N, Jin Y R, Deng H, Wu Y L, Zheng G L, Li S, Ye T, Ren Y F, Chen Y F, Zheng D N 2012 Acta Phys. Sin. 61 213302 Google Scholar
[42]	Komar P, Kessler E M, Bishof M, Jiang L, Sørensen A S, Ye J, Lukin M D 2014 Nat. Phys. 10 582 Google Scholar
[43]	Donley E A 2010 IEEE Sensors Waikoloa, HI, USA, November 01–04, 2010 p17–22
[44]	Walker T G, Happer W 1997 Rev. Mod. Phys. 69 629 Google Scholar
[45]	Kornack T, Ghosh R, Romalis M 2005 Phys. Rev. Lett. 95 230801 Google Scholar
[46]	Hurwitz L, Nelson J 1960 J. Geophys. Res. 65 1759 Google Scholar
[47]	Wu T, Blanchard J W, Kimball D F J, Jiang M, Budker D 2018 Phys. Rev. Lett. 121 023202 Google Scholar
[48]	Garcon A, Blanchard J W, Centers G P, et al. 2019 Sci. Adv. 5 eaax4539 Google Scholar
[49]	Jiang M, Su H, Garcon A, Peng X, Budker D 2021 arXiv: 2102.01448
[50]	Farooq M, Chupp T, Grange J, et al. 2020 Phys. Rev. Lett. 124 223001 Google Scholar
[51]	Adams R W, Aguilar J A, Atkinson K D, et al. 2009 Science 323 1708 Google Scholar
[52]	Theis T, Ganssle P, Kervern G, Knappe S, Kitching J, Ledbetter M, Budker D, Pines A 2011 Nat. Phys. 7 571 Google Scholar
[53]	Maly T, Debelouchina G T, Bajaj V S, et al. 2008 J. Chem. Phys. 128 02B611
[54]	Spagnolo N, Aparo L, Vitelli C, Crespi A, Ramponi R, Osellame R, Mataloni P, Sciarrino F 2012 Sci. Rep. 2 1
[55]	Jiang M, Wu T, Blanchard J W, Feng G, Peng X, Budker D 2018 Sci. Adv. 4 eaar6327
[56]	Jiang M, Frutos R P, Wu T, Blanchard J W, Peng X, Budker D 2019 Phys. Rev. Appl. 11 024005 Google Scholar
[57]	Tayler M C, Theis T, Sjolander T F, Blanchard J W, Kentner A, Pustelny S, Pines A, Budker D 2017 Rev. Sci. Instrum. 88 091101 Google Scholar
[58]	Jiang M, Xu W, Li Q, Wu Z, Suter D, Peng X 2020 Adv. Quantum Technol. 3 2000078 Google Scholar
[59]	Ledbetter M, Theis T, Blanchard J, et al. 2011 Phys. Rev. Lett. 107 107601 Google Scholar
[60]	Appelt S, Häsing F, Sieling U, Gordji-Nejad A, Glöggler S, Blümich B 2010 Phys. Rev. A 81 023420 Google Scholar
[61]	Gemmel C, Heil W, Karpuk S, et al. 2010 Eur. Phys. J. D 57 303 Google Scholar
[62]	Sjolander T F, Tayler M C, King J P, Budker D, Pines A 2016 J. Phys. Chem. A 120 4343 Google Scholar
[63]	Alcicek S, Put P, Kubrak A, Alcicek F C, Barskiy D, Gloeggler S, Dybas J, Pustelny S 2023 Commun. Chem. 6 165 Google Scholar
[64]	Picazo-Frutos R, Sheberstov K F, Blanchard J W, et al. 2024 Nat. Commun. 15 4487 Google Scholar
[65]	Zeeman P 1897 Nature 55 347
[66]	Condon E U, Condon E, Shortley G 1935 The Theory of Atomic Spectra (Cambridge: Cambridge University Press) pp378–380
[67]	Hou Z, Jin Y, Chen H, Tang J F, Huang C J, Yuan H, Xiang G Y, Li C F, Guo G C 2021 Phys. Rev. Lett. 126 070503 Google Scholar
[68]	Bao G, Wickenbrock A, Rochester S, Zhang W, Budker D 2018 Phys. Rev. Lett. 120 033202 Google Scholar
[69]	王忻昌, 江文龙, 黄程达, 孙惠军, 曹晓宇, 田中群, 陈忠 2020 光谱学与光谱分析 40 665 Xin-Chang Wang C D H H J S X Y C Z Q T Wen-Long Jiang, Chen Z 2020 Spectrosc. Spectral Anal. 40 665
[70]	Jiang M, Bian J, Li Q, Wu Z, Su H, Xu M, Wang Y, Wang X, Peng X 2021 Fundamental Research 1 68 Google Scholar
[71]	Jiang M, Bian J, Liu X, Wang H, Ji Y, Zhang B, Peng X, Du J 2018 Phys. Rev. A 97 062118 Google Scholar
[72]	Jones J A, Karlen S D, Fitzsimons J, Ardavan A, Benjamin S C, Briggs G A D, Morton J J 2009 Science 324 1166 Google Scholar
[73]	Bermudez A, Jelezko F, Plenio M B, Retzker A 2011 Phys. Rev. Lett. 107 150503 Google Scholar
[74]	Zhao N, Hu J L, Ho S W, Wan J T, Liu R 2011 Nat. Nanotechnol. 6 242 Google Scholar
[75]	Schweiger A, Jeschke G 2001 Principles of Pulse Electron Paramagnetic Resonance (Oxford: Oxford University Press on Demand) pp29–32
[76]	Xiao D W, Hu W H, Cai Y, Zhao N 2020 Phys. Rev. Lett. 124 128101 Google Scholar
[77]	Qin S, Yin H, Yang C, et al. 2016 Nat. Mater. 15 217 Google Scholar

[1]	XU Jiaxin, XU Lechen, LIU Jingyang, DING Huajian, WANG Qin. Research progress of artificial intelligence empowered quantum communication and quantum sensing systems. Acta Physica Sinica, 2025, 74(12): 120301. doi: 10.7498/aps.74.20250322
[2]	LIU Gangqin. Magnetic resonance and quantum sensing with color centers under high pressures. Acta Physica Sinica, 2025, 74(11): 117601. doi: 10.7498/aps.74.20250224
[3]	ZHAO Liqiang, LI Yuchen, YIN Haochuan, ZHANG Shengyu, WU Ze, PENG Xinhua. Quantum control based on solid-state nuclear magnetic resonance and its applications. Acta Physica Sinica, 2025, 74(7): 077402. doi: 10.7498/aps.74.20241709
[4]	Wu Bo, Lin Yi, Wu Feng-Chuan, Chen Xiao-Zhang, An Qiang, Liu Yi, Fu Yun-Qi. Quantum microwave electric field measurement technology based on enhancement electric filed resonator. Acta Physica Sinica, 2023, 72(3): 034204. doi: 10.7498/aps.72.20221582
[5]	Liu Gang-Qin. Diamond spin quantum sensing under extreme conditions. Acta Physica Sinica, 2022, 71(6): 066101. doi: 10.7498/aps.71.20212072
[6]	Tian Yu, Lin Zi-Dong, Wang Xiang-Yu, Che Liang-Yu, Lu Da-Wei. Experimental progress of quantum machine learning based on spin systems. Acta Physica Sinica, 2021, 70(14): 140305. doi: 10.7498/aps.70.20210684
[7]	Jiang Chuan-Dong, Wang Qi, Du Guan-Feng, Yi Xiao-Feng, Tian Bao-Feng. Characteristics of surface nuclear magnetic off-resonance signal and complex envelope inversion. Acta Physica Sinica, 2018, 67(1): 013302. doi: 10.7498/aps.67.20171464
[8]	Liu Gang-Qin, Xing Jian, Pan Xin-Yu. Quantum control of nitrogen-vacancy center in diamond. Acta Physica Sinica, 2018, 67(12): 120302. doi: 10.7498/aps.67.20180755
[9]	Kong Xiang-Yu, Zhu Yuan-Ye, Wen Jing-Wei, Xin Tao, Li Ke-Ren, Long Gui-Lu. New research progress of nuclear magnetic resonance quantum information processing. Acta Physica Sinica, 2018, 67(22): 220301. doi: 10.7498/aps.67.20180754
[10]	Pan Jian, Yu Qi, Peng Xin-Hua. Experimental technique for multi-qubit nuclear magnetic resonance system. Acta Physica Sinica, 2017, 66(15): 150302. doi: 10.7498/aps.66.150302
[11]	Wu Liang, Chen Fang, Huang Chong-Yang, Ding Guo-Hui, Ding Yi-Ming. Multi-exponential inversion of T2 spectrum in NMR based on improved nonlinear fitting. Acta Physica Sinica, 2016, 65(10): 107601. doi: 10.7498/aps.65.107601
[12]	Tian Bao-Feng, Zhou Yuan-Yuan, Wang Yue, Li Zhen-Yu, Yi Xiao-Feng. Noise cancellation method for full-wave magnetic resonance sounding signal based on independent component analysis. Acta Physica Sinica, 2015, 64(22): 229301. doi: 10.7498/aps.64.229301
[13]	Ling Hong-Sheng, Tian Jia-Xin, Zhou Shu-Na, Wei Da-Xiu. Time-optimized quantum QFT gate in an Ising coupling system. Acta Physica Sinica, 2015, 64(17): 170301. doi: 10.7498/aps.64.170301
[14]	Li Zheng, Zhou Rui, Zheng Guo-Qing. Quantum criticalities in carrier-doped iron-based superconductors. Acta Physica Sinica, 2015, 64(21): 217404. doi: 10.7498/aps.64.217404
[15]	Li Jun, Cui Jiang-Yu, Yang Xiao-Dong, Luo Zhi-Huang, Pan Jian, Yu Qi, Li Zhao-Kai, Peng Xin-Hua, Du Jiang-Feng. Quantum control of nuclear magnetic resonance spin systems. Acta Physica Sinica, 2015, 64(16): 167601. doi: 10.7498/aps.64.167601
[16]	Li Xin, Xiao Li-Zhi, Liu Hua-Bing, Zhang Zong-Fu, Guo Bao-Xin, Yu Hui-Jun, Zong Fang-Rong. Optimization of nuclear magnetic resonance refocusing pulses to enhance signal intensity in gradient B0 field. Acta Physica Sinica, 2013, 62(14): 147602. doi: 10.7498/aps.62.147602
[17]	Yao Xi-Wei, Zeng Bi-Rong, Liu Qin, Mu Xiao-Yang, Lin Xing-Cheng, Yang Chun, Pan Jian, Chen Zhong. Subspace quantum process tomography via nuclear magnetic resonance. Acta Physica Sinica, 2010, 59(10): 6837-6841. doi: 10.7498/aps.59.6837
[18]	Li Shao, Ren Yu-Feng, Wang Ning, Tian Ye, Chu Hai-Feng, Li Song-Lin, Chen Ying-Fei, Li Jie, Chen Geng-Hua, Zheng Dong-Ning. Detection of nuclear magnetic resonance in the microtesla range using a high Tc dc-superconducting quantum interference device. Acta Physica Sinica, 2009, 58(8): 5744-5749. doi: 10.7498/aps.58.5744
[19]	Pan Ke-Jia, Chen Hua, Tan Yong-Ji. Multi-exponential inversion of T2 spectrum in NMR based on differential evolution algorithm. Acta Physica Sinica, 2008, 57(9): 5956-5961. doi: 10.7498/aps.57.5956
[20]	Wang He, Li Geng-Ying. Combination of inversion and fitting as an effective method for the analysis of NMR relaxation data. Acta Physica Sinica, 2005, 54(3): 1431-1436. doi: 10.7498/aps.54.1431

Catalog

Vol. 74, Issue 11 - 2025-06-05

Metrics

Abstract views: 1266
PDF Downloads: 192
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板