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Searching for an exotic spin-dependent interaction with a single electron-spin quantum sensor

Searching for an exotic spin-dependent interaction with a single electron-spin quantum sensor ARTICLE DOI: 10.1038/s41467-018-03152-9 OPEN Searching for an exotic spin-dependent interaction with a single electron-spin quantum sensor 1,2,3 1,2,3 1,2 1,2,3 1,3 1,3 1,3 Xing Rong , Mengqi Wang , Jianpei Geng , Xi Qin , Maosen Guo , Man Jiao , Yijin Xie , 1,2,3 1,2,3 1,2,3 4,5 6 1,2,3 Pengfei Wang , Pu Huang , Fazhan Shi , Yi-Fu Cai , Chongwen Zou & Jiangfeng Du Searching for new particles beyond the standard model is crucial for understanding several fundamental conundrums in physics and astrophysics. Several hypothetical particles can mediate exotic spin-dependent interactions between ordinary fermions, which enable laboratory searches via the detection of the interactions. Most laboratory searches utilize a macroscopic source and detector, thus allowing the detection of interactions with submillimeter force range and above. It remains a challenge to detect the interactions at shorter force ranges. Here we propose and demonstrate that a near-surface nitrogen-vacancy center in diamond can be utilized as a quantum sensor to detect the monopole–dipole interaction between an electron spin and nucleons. Our result sets a constraint for the N e electron–nucleon coupling, g g , with the force range 0.1–23 μm. The obtained upper bound s p N e −15 of the coupling at 20 μmis g g < 6.24 × 10 . s p CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 2 3 230026, China. Hefei National Laboratory for Physical Sciences at the Microscale, USTC, Hefei 230026, China. Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, Hefei 230026, China. CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, 5 6 USTC, Hefei 230026, China. School of Astronomy and Space Science, USTC, Hefei 230026, China. National Synchrotron Radiation Laboratory, USTC, Hefei 230026, China. Xing Rong, Mengqi Wang and Jianpei Geng contributed equally to this work. Correspondence and requests for materials should be addressed to P.W. (email: wpf@ustc.edu.cn) or to J.D. (email: djf@ustc.edu.cn) NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 1 | | | 1234567890():,; ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 evelopment of new techniques to search for new particles mediated monopole–dipole interaction can be described as beyond the standard model is important in eliminating 2 N e h g g 1 1 r s p Dour ignorance of the ultraviolet completion of particle λ ð1Þ V ðÞ r ¼ þ e σ  e ; sp r physics . A type of hypothetical ultralight scalars, such as axions 8πm λr r or axion-like particles (ALPs) , has attracted a lot of attention in a wide variety of researches. This has been well motivated for where r is the displacement vector between the electron and decades from the need of cosmology , namely, the dark matter nucleon, r ¼ jj r and e = r/r are the displacement and the unit 4 5 N e candidate , the dark energy candidate , and from the under- displacement vector, g and g are the scalar and pseudoscalar s p standing of the symmetries of charge conjugation and parity in coupling constants of the ALP to the nucleon and to the electron, quantum chromodynamics (QCD) as well as predictions from m is mass of the electron, λ = ħ/(m c) is the force range, m is the a a fundamental theories such as string theory . The exchange of mass of the ALP, σ is the Pauli vector of the electron spin, ħ is such particles results in spin-dependent forces, which were ori- Plank’s constant divided by 2π, and c is the speed of light. Such ginally investigated by Moody and Wilczek . Various laboratory interaction is equivalent to the Hamiltonian of the electron spin ALP searching experiments focus on the detection of macroscopic in an effective magnetic field B (r) arising from the nucleon, sp monopole–dipole forces between polarized electrons/nucleons N e 8–15 hg g 1 1 r and unpolarized nucleons . Previous laboratory searching has s p ð2Þ B ðrÞ¼ þ e e ; sp r set the limit on the monopole–dipole coupling between electron 4πmγ λr r N e 16 and nucleon, g g , with a force range λ >20 μm . The experi- s p mental investigation of this interaction at force range shorter than where γ is the gyromagnetic ratio of the electron spin. 20 μm, however, remains elusive due to the following challenges: An NV-based optically detected magnetic resonance setup (i) the size of the sensor should be small compared to the combined with an atomic force microscope (AFM) (shown in micrometer force range; (ii) the geometry of the sensor should Fig. 1, see Supplementary Fig. 1 and Supplementary Note 1 for allow close proximity between the sensor and the source; (iii) the details) is constructed to search for this electron–nucleon sensitivity of the sensor should be sufficient for searching or for interaction. A near-surface electron spin, which is a defect in providing stringent bound for such interaction; (iv) the unwanted diamond composed of a substitutional nitrogen atom and a noises, such as the magnetic and electric field introduced by neighboring vacancy , is utilized as a quantum sensor to detect environment, should be isolated well. its electron–nucleon interaction with nucleons in a fused silica Here we develop a method to investigate the electron–nucleon half-ball lens. The NV center is <10 nm close to the surface of the monopole–dipole interactions using a near-surface electron-spin diamond, so that it allows close proximity between the electron qubit in diamond. Constraints for the electron–nucleon coupling, and the nucleon. Hereafter, the electron spin of the NV center N e g g , have been set for the interaction range 0.1–23 μm. For a s p and the half-ball lens are denoted as S and M for convenience, force range of 20 μm, our constraint is bounded to be less than respectively. M is placed on a tuning fork actuator of the AFM, −15 6.24 × 10 . The method can be further extended to investigate which enables us to position M near and away from S, as well as other spin-dependent interactions and opens the door for the to drive M to vibrate with a frequency. Figure 1b shows single-spin quantum sensor to explore new physics beyond the geometric parameters in the experiment. The radius of M is the standard model. R = 250(2.5) μm. The vibration amplitude of M is denoted as A. The time-dependent distance between the bottom of M and S can be described as d = d + A[1 + cos(ω t)], where d is the 0 m 0 Results minimal distance between M and S, and ω is the vibration Monopole–dipole interaction and experimental system. We use angular frequency of M driven by the tuning fork. The effective a near-surface single electron spin, which is a nitrogen-vacancy magnetic field felt by S arising from the hypothetic (NV) center in diamond, to investigate the monopole–dipole electron–nucleon interaction can be derived by integrating interaction between an electron spin and nucleons. The axion- Eq. (2) over all the nucleons in M as B ¼ e B , where e is eff rc eff rc ac b M (SiO ) SiO 2A NV m =+1 m = –1 mw Objective m = 0 S (NV) s Fig. 1 Experimental setup and the quantum sensor. a Schematic experimental setup. An NV center in diamond, which is labeled as NV, is used to search for the monopole–dipole interaction with nucleons. The nucleons are provided by a fused silica half-ball lens, which is labeled as SiO . The half-ball lens is placed on a tuning fork actuator of an AFM. A static magnetic field B is applied along the symmetry axis of the NV center. b Schematic experimental parameters. The electron spin and the half-ball lens are denoted as S and M, respectively. The radius of M is R. M is located right above S and driven to vibrate with amplitude A. The distance between S and the bottom of M is d when M vibrates to the position nearest S. c Atomic structure and energy levels of the NV center in diamond. The NV center consists of a substitutional nitrogen atom with an adjacent vacancy cite in the diamond crystal lattice. 3 3 3 3 3 The ground and excited states are denoted as A and E. The NV center can be excited from A to E by a laser pulse, and decays back to A emitting 2 2 2 photoluminescence. The optical transitions are used to initialize and readout the spin state of the NV center. The spin statesji m ¼ 0 andji m ¼1 of A S S 2 are encoded as a quantum sensor. The state of S can be manipulated by microwave pulses 2 NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications | | | Tuning fork mw wire Diamond NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 ARTICLE =  ⁄ eff Laser (/2) () (/2) x x mw mw Read Init. z z z z z mw x y x y x y x y Fig. 2 Electron–nucleon interaction detection scheme. a Time variation of the distance d (upper) and the effective magnetic field B (lower). The distance d eff is between S and the bottom of M. The waiting time, τ = π/ω , is half period of the vibration of M, and B is the effective magnetic field on S generated by m eff the nucleons in M. b Experimental pulse sequence (upper) and state evolution of S (lower). The pulse sequence applied on S is synchronized with the vibration of M. Green laser pulses were used to initialize and read the state of S. The microwave π/2 and π pulses were applied only when M passed through the equilibrium point of the vibration the unit distance vector along the symmetry axis of M and Pulse sequence to detect the monopole–dipole interaction.If mass M is placed near the electron spin S, a static effective DC magnetic field B caused by monopole–dipole interaction will N e eff hg g ρ s p affect S. A straightforward approach to detect such DC magnetic ð3Þ B ¼ f ðλ; R; dÞ; eff 2mγ field is to perform a Ramsey sequence . The Ramsey sequence can be written as π/2 − τ − π/2, where π/2 stands for the microwave pulse with rotating angle π/2 and τ stands for a 30 −3 with ρ = 1.33 × 10 m being the number density of nucleons waiting time. The first π/2 microwave pulse prepares S to a pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 2 2 R þðdþRÞ d dþR superposition stateðÞ ji 0  iji 1 = 2. During the waiting time τ, λ λ λ in M and f(λ, R, d) = λ e  e + e + dþR the electron spin precesses about the z axis and accumulate a pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 i 2 2 2 R þðdþRÞ R þðdþRÞ 2 phase proportional to the strength of the magnetic field B . After d 2 2 d λ R þðdþRÞ eff λd  λ  λ λ λ λ λ e − e + e − e 2 2 2 2 ðdþRÞ ðdþRÞ ðdþRÞ ðdþRÞ the second π/2 pulse, the phase information will be encoded in (see Supplementary Note 2 for details). If M is moved far away the population of the stateji m ¼ 0 , which can be detected with a from S with distance much larger than the force range λ, the laser pulse. However, during the waiting time, noises, such as the monopole–dipole interaction is negligible. By comparing fluctuation of the Overhauser field and the slow drift of the the magnetic field detected by S with and without M, the external static magnetic field, will cause the dephasing. Thus electron–nucleon interaction between S and the nucleons in the sensitivity of such method is limited by the dephasing time of M can be measured. the electron spin, which is about T ¼ 0:67ð4Þ μs measured in Figure 1c shows the atomic structure and energy levels of the our experiment. NV center. The ground state of the NV center is an electron-spin To suppress the dephasing and to enhance the sensitivity of 3 22 triplet state A with three substatesji m ¼ 0 andji m ¼ ±1 .A detecting B , a spin echo sequence can be applied instead of S S 2 eff static magnetic field B of about 300 G is applied along the NV the Ramsey sequence. The spin echo sequence can be written as symmetry axis to remove the degeneracy of theji m ¼ ±1 spin π/2 − τ − π − τ − π/2, where π/2 (π) stands for the microwave states. The spin statesji m ¼ 0 andji m ¼1 are encoded as a pulse with rotating angle π/2 (π) and τ stands for a waiting time. S S quantum sensor . Microwave pulses with frequency matching With this spin echo sequence, the coherence time of the electron the transition betweenji m ¼ 0 andji m ¼1 are delivered by spin is enhanced to about T = 8.3(8) μs in our experiment, which S S 2 a copper microwave wire to manipulate the state of the quantum is of an order longer than T . Since the positive phase sensor. Theji m ¼ 1 state remains idle due to the large detuning. accumulated during the first waiting time τ is exactly canceled A laser pulse can be applied to pump the NV center from A to by the negative phase accumulated during the second τ, the total 3 3 the excited state E. When the NV center decays back to A , phase due to static B is zero. To solve this problem, we drive M 2 eff photoluminescence can be detected. The optical process can be to vibrate periodically to make B an oscillating signal (shown in eff utilized to realize state initialization and readout of this quantum Fig. 2a). If B is modulated in phase with the spin echo sequence, eff sensor. Because of the convenient state initialization and a nonzero accumulated phase due to B can be obtained, while eff 20 21 readout procedures, precise control , long coherence time , the unwanted noise can be canceled. We use a homebuilt pulse and its atomic size, the NV center serves as a magnetic sensor generator and a comparator to make sure that the tuning fork at nanometer scale, which is now extended to search for the oscillation and the pulse sequence are synchronized well (see axion-mediated interactions beyond the standard model. Supplementary Fig. 4 and Supplementary Note 1 for details). NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 3 | | | ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 following microwave π pulse rotates the Bloch vector by an angle W/O M I = I + A cos( +  ) 1 = 0.000 ± 0.013 PL PL,0 PL mw 1 of π around x axis. After the π pulse, the electron spin experiences 0.95 another free evolution for half of the vibration period under B . eff 0.90 At the end of this evolution, the state is evolved into pffiffiffi 5τ=2 iφ 0.85 ðÞ ji 0 þ ie ji 1 = 2 with φ ¼ φ  γB ðtÞcosθdt.A final eff 0 3τ=2 microwave π/2 pulse with phase φ then rotates the Bloch Exp. mw 0.80 vector by an angle of π/2 around the axis e cos φ + e sin φ Fit x mw y mw 0.75 (with e and e being the unit vector along the x and y axis), x y 0369 12 transforming the state into cos φ þ φ =2 ji 0 + mw (rad) mw iφ mw e sin φ þ φ =2 1 . After this spin echo sequence, a laser ji mw pulse is applied and the photoluminescence intensity I is b PL I = I + A cos( +  ) 2 = 0.000 ± 0.012 With M PL PL,0 PL mw 2 detected. The measured I reflects the population P of state PL j0i 0.95 ji m ¼ 0 for the final state, with P ¼ 1=2 þ 1=2cos φ þ φ . S j0i mw 0.90 Therefore, I can be expressed as PL 0.85 I ¼ I þ A cos φ þ φ : ð4Þ PL PL;0 PL mw Exp. 0.80 Fit 0.75 By measuring the photoluminescence intensity I with a set of PL 0369 12 different phases φ of the final microwave π/2 pulse, we can mw (rad) mw extract φ which contains the information of B arising from the eff N e spin–mass interaction. The coupling g g can be derived to be Fig. 3 Experimental results for detecting the electron–nucleon interaction. a s p The measured photoluminescence intensity I without M. b The measured PL 1 2m φ N e g g ¼ : R R photoluminescence intensity I with M. In both panels, the experimental PL s p 3τ=2 5τ=2 cosθ  hρ f ðλ; R; dðtÞÞdt  f ðλ; R; dðtÞÞdt data are represented by black circles with error bars, and the red solid lines τ=2 3τ=2 represent the fitting of the experimental data. Each experimental data is the ð5Þ average with six million experimental trails, which are divided into 1200 samples. Error bars of the experimental data represent s.e.m., which are calculated as the sample standard deviations divided by the square root Experimental results. Figure 3 shows the experimental results. of the sample size. The parameter values A = 0.091(1) and I = 0.8476 PL PL,0 All the experimental data shown in Fig. 3 are obtained with (8) (A = 0.091(1) and I = 0.8563(8)) are obtained by fitting the PL PL,0 six million averages (see Supplementary Figs. 5, 6, and experimental data for the cases without M in panel a (with M in panel b). Supplementary Note 4 for details). To exclude the influence of The phases φ and φ are the accumulated phases of the states of S without 1 2 any possible oscillating magnetic field from other sources, we first and with M. The phase shift due to the electron–nucleon interaction implement the pulse sequence without M as a benchmark between S and M is obtained by φ = φ − φ to be φ = 0.000 ± 0.018 rad 2 1 experiment. The experimental data without M is shown in Fig. 3a. By fitting the data with Eq. (4), we obtain φ = 0.000 ± 0.013 rad Figure 2a shows schematically the distance d and correspond- as a benchmark. Then the spin echo sequence is implemented ing time-varying effective magnetic field B arising from the with vibrating M and the result has been shown in Fig. 3b. The eff hypothetical electron–nucleon interaction. The mass is driven to experimental data with M is fitted with Eq. (4) to extract φ with vibrate with an angular frequency ω = 2π × 187.29 kHz. The φ = 0.000 ± 0.012 rad. The accumulated phase φ of the m 2 vibration amplitude A and shortest distance d are A = 41.1(1) electron spin’s state owing to B generated by M, which is 0 eff nm and d = 0.5(1) μm, respectively. When M vibrates to the obtained by φ = φ − φ , is determined to be φ = 0.000 ± 0.018 0 2 1 position nearest to S, the distance d reaches the minimum value rad. The electron–nucleon interaction has not been observed at d and the corresponding effective magnetic field B achieves a the current experimental condition, but an upper limit can be set 0 eff maximum value. When M vibrates to the position furthest from to constrain the interaction. S, d reaches the maximum value d + 2A and B achieves a Table 1 is the systematic error budget of our experiment. One 0 eff minimum value. systematic error is due to the diamagnetism of M in a 300 G Figure 2b shows the pulse sequence applied on S (a detailed magnetic field. M is modulated in phase with the spin echo description of the pulse sequence is presented in Supplementary sequence, so the in phase AC component rather than the DC Fig. 3 and Supplementary Note 1) and the corresponding state component of magnetic field due to the diamagnetism of M evolution of S on the Bloch sphere. The pulse duration of the π would cause a phase shift in our result. If the NV center locates (π/2) pulse is 118 ns (59 ns) and the waiting time τ is fixed to 2.67 exactly under the center of the mass, the magnetic field caused by μs. To optimize the phase accumulation, the microwave π/2 and π the diamagnetism of M is perpendicular to the NV symmetry pulses in the spin echo sequence are applied only when M axis, and the AC part of this magnetic field is estimated to be −6 vibrates passing through the equilibrium point of the vibration. about 1.5 × 10 G (see Supplementary Fig. 7 and Supplementary The electron spin S is initialized intoji m ¼ 0 by a laser pulse, Note 4 for details). Due to the large energy splitting (2.0286 GHz) corresponding to the unit vector along z axis in the Bloch along the symmetry axis of NV center, the phase shift caused by −10 sphere. The first microwave π/2 pulse transforms the state into this component is estimated to be 1.7 × 10 rad. Because the pffiffiffi NV center may deviate from the exact location under the center ðÞ ji 0  iji 1 = 2. Then S evolves under the effective magnetic field of the mass (see Supplementary Fig. 8 and Supplementary B for half of the vibration period τ, corresponding to the eff Note 4), there could be a residual magnetic field along the spin precessing around the z axis. As a result, the state is pffiffiffi iφ symmetry axis of NV. The amplitude of this in phase AC evolved intoðÞ ji 0  ie ji 1 = 2 at the end of the free evolution, −8 magnetic field is estimated to be about 1.1 × 10 G (see 3τ=2 where φ ¼ γB ðtÞcosθdt is the accumulated phase, and N e eff 0 τ=2 Supplementary Note 4). Therefore, the correction to the g g pffiffiffi s p −20 θ ¼ arccosð1= 3Þ is the angle between B and the NV axis. The for 20 μm due to the diamagnetism of M is 5(5) × 10 . The eff 4 NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications | | | I (a.u.) I (a.u.) PL PL NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 ARTICLE Table 1 Systematic error summary N e Systematic error Size of effect Correction to g g for 20 μm s p −6 −20 Diamagnetism of M −11.28 × 10 (5 ± 5) × 10 −6 −20 Diamagnetism of the tuning fork −11.28 × 10 (3.8 ± 0.3) × 10 −27 Phase jitter of microwave 1.3 ps (0.0 ± 1.7) × 10 −27 T dephasing 670 ± 41 ns (0.0 ± 1.9) × 10 −17 Shortest distance between M and S 0.5 ± 0.1 μm (0.1 ± 3.0) × 10 −17 The amplitude of the modulation of M 41.1 ± 0.1 nm (0.0 ± 1.3) × 10 −18 The radius of M 250 ± 2.5 μm (0.1 ± 3.7) × 10 ° −16 The angle between B and NV axis 54.7 ± 3 (0.4 ± 4.2) × 10 eff 0.1 to 1 m . The upper limit from the experiment by Terrano –1 –4 –7 –10 m (eV) 10 10 10 10 a et al. is for the range from 0.5 mm to 10 cm. In the range from This experiment –12 10 20 to 500 μm, the experiment by Hoedl et al. provides the upper limit. Our result is represented as the solid red line. It is derived –13 –13 according to Eq. (5) with 2δ as an upper bound of φ, where δ = φ φ –14 10 0.018 rad is the s.d. of the accumulated phase φ. Besides δ , the uncertainties of other experimental parameters, such as d and A, –15 12 20 28  (µm) –21 are also taken into account to derive the upper limit (see Supplementary Note 3 for details). For the force range 0.1 μm< λ Hoedl 2011 N e Excluded region <23 μm, our result provided the upper bound for g g .Asis s p shown in the inset of Fig. 4, the obtained upper bound of the Wineland 1991 –29 N e −15 interaction at 20 μm, g g < 6.24 × 10 , is two orders of s p Terrano 2015 magnitude more stringent than the bound set by Hoedl et al. . −5 Youdin 1996 The possible value of mass of the ALPs, from 10 to 1 eV Heckel 2008 (corresponding to a force range 0.2 μm< λ < 2 cm), is still allowed –37 –8 –4 0 4 by otherwise stringent constraints . The unexplored force range (m) 10 10 10 10 left by the previous experiments has now been searched in our N e N e Fig. 4 Upper limits on g g as a function of the force range λ and mass of s p experiment. We note that the most restrictive constraint on g g s p the axion-like particle m . Our result is represented as the red solid line. The may arise from the combination of the long-range force bound 8–12 16,24 black solid lines represent the results from refs. . The red dashed line and the astrophysical limit . These limits rely on the N e shows the available improvement of the constraint on g g in future (see s p underlying gravitational theory, namely, a chameleon mechanism Supplementary Note 3 for details). The inset shows a comparison of our could invalidate the astrophysical limit, and therefore, it is N e result and that from ref. with the force range nearby 20 μm, which necessary to experimentally constrain g g in laboratories, where s p illustrates an improvement of two orders more stringent for our result at 25 the gravitational effects are negligible . 20 μm compared with that from ref. Discussion material of the tuning fork is SiO . The distance between the The constraint can be further improved by several strategies in tuning fork and the NV center is at least 250 μm. The systematic future. We search for spin–mass interaction by detecting the error due to the diamagnetism of tuning fork leads to a correction accumulated phase of a single electron spin’sstate owingto B . eff N e −20 to g g for 20 μm being 3.8(3) × 10 . The phase jitter of the One effective method is to enhance the coherence time of the s p 12 26 microwave, which would cause the instability of the phase of the electron spin, by synthesizing C-enriched diamond or by 27,28 final π/2 pulse, is measured to be 1.3 ps (Supplementary Fig. 10 applying multi-pulse dynamical decoupling sequences .Once and Supplementary Note 4). Since the waiting time of the spin the coherence time is prolonged, the ability of detecting the echo is fixed, this instability of the phase only causes a small accumulated phase can be enhanced. The frequency of our tuning reduction of the signal contrast rather than a phase shift. The fork at present stage is 187.29 kHz, which is suitable for a spin echo impact of phase jitter is also presented in Table 1. The frequency sequence. If the frequency of the tuning fork is enhanced in future, shift of the microwave generator, the drift of the external multi-pulse dynamical decoupling sequences can be applied to magnetic field and the fluctuation of the Overhauser field (see improve the performance. On the other hand, the accumulated Supplementary Fig. 9 and Supplementary Note 4) will contribute phase is proportional to the number density of nucleons in the to the T dephasing. This dephasing can be well suppressed by source. To use materials with high number density of nucleons as spin echo technique and the correction due to dephasing is also the source, such as Bi Ge O (BGO), can also improve the con- 4 3 12 included in Table 1. The errors due to the uncertainties of the straint. To decrease the measurement uncertainty of the accumu- distance between M and S, the amplitude of the modulation of M, lated phase, one can improve the detection efficiency of the the radius of M and the angle between B and NV axis, have also photoluminescence and increase the number of experiment trails. eff been taken into account in the Table 1. The detailed analysis of On the basis of above extensions of techniques, the available the systematic errors are included in Supplementary Note 4. constraint, which is shown as the red dashed line in Fig. 4, could be Figure 4 shows the new constraint set by this work together about three orders of magnitude improved from the current result with recent constraints from experimental searches for (see detailed discussion in Supplementary Note 3). monopole–dipole interactions . The lines from the experiment Our platform uses a near-surface NV center together with by Heckel et al. are the upper limits in the meter range and AFM setup, thus the force range can be focused within micro- above , except a gap from 10 to 1000 km. The upper limit in this meters. The micrometer and submicrometer range, which is not gap is obtained by the experiment by Wineland et al. . The easily accessed in previous experiments, provides a new window experiment by Youdin et al. sets the upper limit in the range from for investigating new physics beyond standard model. The NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 5 | | | N e g g s p N e g g s p ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 electron–nucleon interaction investigated in our work is one of 11. Terrano, W. A., Adelberger, E. G., Lee, J. G. & Heckel, B. R. Short-range, spin- dependent interactions of electrons: a probe for exotic pseudo-goldstone interactions from new particle exchange . In future, several bosons. Phys. Rev. Lett. 115, 201801 (2015). related interactions can also be investigated with extension of our 12. Hoedl, S. A., Fleischer, F., Adelberger, E. G. & Heckel, B. R. Improved method. For example, spin–spin interaction mediated by ALPs, constraints on an axion-mediated force. Phys. Rev. Lett. 106, 041801 (2011). on which a constraint is recently set at micrometer scale , can be 13. Petukhov, A. K., Pignol, G., Jullien, D. & Andersen, K. H. Polarized He as a further explored with submicrometer scale by two coupled NV probe for short-range spin-dependent interactions. Phys. Rev. Lett. 105, 170401 (2010). centers with technologies developed by Grinolds et al. . Another 14. Ni, W.-T., Pan, S.-s, Yeh, H.-C., Hou, L.-S. & Wan, J. Search for an axionlike case is to explore the interaction mediated by a vector boson, spin coupling using a paramagnetic salt with a dc squid. Phys. Rev. Lett. 82, 31,32 which has been investigated at micrometer force range . 2439–2442 (1999). Therefore, NV centers will not only be a promising quantum 15. Bulatowicz, M. et al. Laboratory search for a long-range t-odd, p-odd 33–38 sensor for physics within standard model , but also be an interaction from axionlike particles using dual-species nuclear magnetic 129 131 resonance with polarized Xe and Xe gas. Phys. Rev. Lett. 111, 102001 important platform for searching for new particles predicted by (2013). theories beyond the standard model. 16. Raffelt, G. Limits on a CP-violating scalar axion-nucleon interaction. Phys. Rev. D 86, 015001 (2012). Methods 17. Dobrescu, B. A. & Mocioiu, I. Spin-dependent macroscopic forces from new Experimental setup. The electron spin of a near-surface NV center in diamond is particle exchange. J. High Energy Phys. 2006, 005 (2006). used as a quantum sensor to search for the hypothetical ALP-mediated 18. Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. monopole–dipole interaction with nucleons in a half-ball lens. The NV center was Rep. 528,1–45 (2013). created by implantation of 10 keV N ions into [100] bulk diamond and annealing 19. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. for 2 h at 800 °C in vacuum. The diamond was then oxidatively etched for 4 h at 89, 035002 (2017). 580 °C. The depth of the NV center was estimated to be <10 nm. Nanopillars were 20. Rong, X. et al. Experimental fault-tolerant universal quantum gates with solid- fabricated to improve the detection efficiency of the photoluminescence, with which state spins under ambient conditions. Nat. Commun. 6, 8748 (2015). −1 a photoluminescence rate of 100 kcounts s was achieved in the experiment. The 21. Bar-Gill, N., Pham, L. M., Jarmola, A., Budker, D. & Walsworth, R. L. Solid- NV center is confirmed to be single by measurement of the second-order correlation state electronic spin coherence time approaching one second. Nat. Commun. function (Supplementary Fig. 2 and Supplementary Note 1). An optically detected 4, 1743 (2013). magnetic resonance setup combined with an AFM, which is similar with setup 22. Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950). reported in ref. , was constructed to search for the spin–mass interaction. The 532 23. Beringer, J. et al. Review of particle physics. Phys. Rev. D 86, 010001 (2012). nm green laser pulse passed through an acousto-optic modulator and an objective to 24. Raffelt, D. & Weiss, A. Red giant bound on the axion-electron coupling be focused on the NV center to initialize the electron-spin state. The phonon reexamined. Phys. Rev. D 51, 1495 (1995). sideband fluorescence with wavelength of 650–800 nm went through the same 25. Jain, P. & Mandal, S. Evading the astrophysical limits on light pseudoscalars. objective and was collected by an avalanche photodiode with a counter card to Int. J. Mod. Phys. D 15, 2095 (2006). realize state readout. Microwave pulses, which were generated by IQ modulation 26. Balasubramanian, G. et al. Ultralong spin coherence time in isotopically −1 with a 4.2 GSa s arbitrary waveform generator (Keysight 81180A) and a vector engineered diamond. Nat. Mater. 8, 383–387 (2009). signal generator (Keysight E8267D) were amplified by a power amplifier (Mini- 27. Du, J. et al. Preserving electron spin coherence in solids by optimal dynamical Circuits ZHL-16W-43-S+) and delivered by a copper microwave wire to manip- decoupling. Nature 461, 1265–1268 (2009). ulate the electron-spin state. The tuning fork-based atomic force microscope was 28. de Lange, G., Wang, Z. H., Ristè, D., Dobrovitski, V. V. & Hanson, R. utilized to position the half-ball lens and to drive the half-ball lens to vibrate. The Universal dynamical decoupling of a single solid-state spin from a spin bath. state initialization, manipulation, and readout of the electron spin were synchro- Science 330,60–63 (2010). nized with the vibration of the half-ball lens with an arbitrary sequence generator 29. Kotler, S., Ozeri, R. & Kimball, D. F. J. Constraints on exotic dipole-dipole (Hefei Quantum Precision Device Co. ASG-GT50-C). Details of the experimental couplings between electrons at the micrometer scale. Phys. Rev. Lett. 115, setup are shown in Supplementary Fig. 1 and Supplementary Note 1. 081801 (2015). 30. Grinolds, M. S. et al. Nanoscale magnetic imaging of a single electron spin Data availability. Data supporting the findings of this study are available within under ambient conditions. Nat. Phys. 9, 215–219 (2013). the article and its Supplementary Information file, and from the corresponding 31. Yan, H. & Snow, W. M. New limit on possible long-range parity-odd authors upon reasonable request. interactions of the neutron from neutron-spin rotation in liquid He. Phys. Rev. Lett. 110, 082003 (2013). 32. Yan, H. et al. Searching for new spin- and velocity-dependent interactions by Received: 8 July 2017 Accepted: 23 January 2018 spin relaxation of polarized He gas. Phys. Rev. Lett. 115, 182001 (2015). 33. Taylor, J. M. et al. High-sensitivity diamond magnetometer with nanoscale resolution. Nat. Phys. 4, 810–816 (2008). 34. Maze, J. R. et al. Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature 455, 644–647 (2008). 35. Balasubramanian, G. et al. Nanoscale imaging magnetometry with diamond References spins under ambient conditions. Nature 455, 648–651 (2008). 1. Schwarz, J. H. & Seiberg, N. String theory, supersymmetry, unification, and all 36. Kolkowitz, S. et al. Probing johnson noise and ballistic transport in normal that. Rev. Mod. Phys. 71, S112–S120 (1999). metals with a single-spin qubit. Science 347, 1129–1132 (2015). 2. Graham, P. W., Irastorza, I. G., Lamoreaux, S. K., Lindner, A. & van Bibber, K. 37. Shi, F. et al. Single-protein spin resonance spectroscopy under ambient A. Experimental searches for the axion and axion-like particles. Annu. Rev. conditions. Science 347, 1135–1138 (2015). Nucl. Part. Sci. 65, 485–514 (2015). 38. Lovchinsky, I. et al. Magnetic resonance spectroscopy of an atomically thin 3. Marsh, D. J. Axion cosmology. Phys. Rep. 643,1–79 (2016). material using a single-spin qubit. Science 355, 503–507 (2017). 4. Bertone, G., Hooper, D. & Silk, J. Particle dark matter: evidence, candidates 39. Kolkowitz, S. et al. Coherent sensing of a mechanical resonator with a single- and constraints. Phys. Rep. 405, 279–390 (2005). spin qubit. Science 335, 1603–1606 (2012). 5. Kamionkowski, M., Pradler, J. & Walker, D. G. E. Dark energy from the string axiverse. Phys. Rev. Lett. 113, 251302 (2014). 6. Peccei, R. D. & Quinn, H. R. CP conservation in the presence of instantons. Acknowledgements Phys. Rev. Lett. 38, 1440–1443 (1977). We are grateful to H.Y. Yan for his systematic introduction about the spin-dependent 7. Moody, J. E. & Wilczek, F. New macroscopic forces? Phys. Rev. D 30, 130–138 forces and fruitful discussion about the experiment. We thank C.K. Duan and D.J. (1984). Kimball for helpful discussion. We thank L.P. Guo for his help on nitrogen ion 8. Wineland, D. J., Bollinger, J. J., Heinzen, D. J., Itano, W. M. & Raizen, M. G. implantation. The fabrication of diamond nanopillars for improving the detection effi- Search for anomalous spin-dependent forces using stored-ion spectroscopy. ciency of the photoluminescence was performed at the USTC Center for Micro and Phys. Rev. Lett. 67, 1735–1738 (1991). Nanoscale Research and Fabrication. This work was supported by the National Key Basic 9. Youdin, A. N., Krause, D. Jr., Jagannathan, K., Hunter, L. R. & Lamoreaux, S. Research Program of China (Grants Nos. 2013CB921800, 2016YFA0502400, and K. Limits on spin–mass couplings within the axion window. Phys. Rev. Lett. 2016YFB0501603), the National Natural Science Foundation of China (Grant Nos. 77, 2170–2173 (1996). 11227901, 91636217, 11722327, and 31470835) and the Strategic Priority Research 10. Heckel, B. R. et al. Preferred-frame and CP-violation tests with polarized Program (B) of the CAS (Grant No. XDB01030400). J.D. and X.R. thank financial electrons. Phys. Rev. D 78, 092006 (2008). support by Key Research Program of Frontier Sciences, CAS (Grants No. QYZDY-SSW- 6 NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications | | | NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 ARTICLE SLH004 and QYZDB-SSW-SLH005). F.S. and X.R. thank the Youth Innovation Pro- Reprints and permission information is available online at http://npg.nature.com/ motion Association of Chinese Academy of Sciences for the support. Y.-F.C. is supported reprintsandpermissions/ in part by the Chinese National Youth Thousand Talents Program, by the CAST Young Elite Scientists Sponsorship Program (2016QNRC001), by the National Natural Science Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in Foundation of China (Grant Nos. 11421303, 11653002), and by the Fundamental published maps and institutional affiliations. Research Funds for the Central Universities. X.Q. thank support by Fundamental Research Funds for the Central Universities (Grant No. WK2030040081). Open Access This article is licensed under a Creative Commons Author contributions Attribution 4.0 International License, which permits use, sharing, J.D. proposed the idea. J.D. and X.R. designed the experiment. M.W., J.G., and M.G. adaptation, distribution and reproduction in any medium or format, as long as you give performed the experiment under the supervision of J.D. and X.R., J.G., M.W., M.J., and appropriate credit to the original author(s) and the source, provide a link to the Creative P.H. carried out the calculations and simulations. X.Q., P.W., M.G., Y.X., and F.S. Commons license, and indicate if changes were made. The images or other third party constructed the experimental setup. M.W. and C.Z. prepared the NV center. X.R., J.G., material in this article are included in the article’s Creative Commons license, unless M.W., Y.-F.C., and M.G. wrote the paper. All authors analyzed the data, discussed the indicated otherwise in a credit line to the material. If material is not included in the results and commented on the manuscript. article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from Additional information the copyright holder. To view a copy of this license, visit http://creativecommons.org/ Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467- licenses/by/4.0/. 018-03152-9. © The Author(s) 2018 Competing interests: The authors declare no competing financial interests. NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 7 | | | http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nature Communications Springer Journals

Searching for an exotic spin-dependent interaction with a single electron-spin quantum sensor

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ARTICLE DOI: 10.1038/s41467-018-03152-9 OPEN Searching for an exotic spin-dependent interaction with a single electron-spin quantum sensor 1,2,3 1,2,3 1,2 1,2,3 1,3 1,3 1,3 Xing Rong , Mengqi Wang , Jianpei Geng , Xi Qin , Maosen Guo , Man Jiao , Yijin Xie , 1,2,3 1,2,3 1,2,3 4,5 6 1,2,3 Pengfei Wang , Pu Huang , Fazhan Shi , Yi-Fu Cai , Chongwen Zou & Jiangfeng Du Searching for new particles beyond the standard model is crucial for understanding several fundamental conundrums in physics and astrophysics. Several hypothetical particles can mediate exotic spin-dependent interactions between ordinary fermions, which enable laboratory searches via the detection of the interactions. Most laboratory searches utilize a macroscopic source and detector, thus allowing the detection of interactions with submillimeter force range and above. It remains a challenge to detect the interactions at shorter force ranges. Here we propose and demonstrate that a near-surface nitrogen-vacancy center in diamond can be utilized as a quantum sensor to detect the monopole–dipole interaction between an electron spin and nucleons. Our result sets a constraint for the N e electron–nucleon coupling, g g , with the force range 0.1–23 μm. The obtained upper bound s p N e −15 of the coupling at 20 μmis g g < 6.24 × 10 . s p CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 2 3 230026, China. Hefei National Laboratory for Physical Sciences at the Microscale, USTC, Hefei 230026, China. Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, Hefei 230026, China. CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, 5 6 USTC, Hefei 230026, China. School of Astronomy and Space Science, USTC, Hefei 230026, China. National Synchrotron Radiation Laboratory, USTC, Hefei 230026, China. Xing Rong, Mengqi Wang and Jianpei Geng contributed equally to this work. Correspondence and requests for materials should be addressed to P.W. (email: wpf@ustc.edu.cn) or to J.D. (email: djf@ustc.edu.cn) NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 1 | | | 1234567890():,; ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 evelopment of new techniques to search for new particles mediated monopole–dipole interaction can be described as beyond the standard model is important in eliminating 2 N e h g g 1 1 r s p Dour ignorance of the ultraviolet completion of particle λ ð1Þ V ðÞ r ¼ þ e σ  e ; sp r physics . A type of hypothetical ultralight scalars, such as axions 8πm λr r or axion-like particles (ALPs) , has attracted a lot of attention in a wide variety of researches. This has been well motivated for where r is the displacement vector between the electron and decades from the need of cosmology , namely, the dark matter nucleon, r ¼ jj r and e = r/r are the displacement and the unit 4 5 N e candidate , the dark energy candidate , and from the under- displacement vector, g and g are the scalar and pseudoscalar s p standing of the symmetries of charge conjugation and parity in coupling constants of the ALP to the nucleon and to the electron, quantum chromodynamics (QCD) as well as predictions from m is mass of the electron, λ = ħ/(m c) is the force range, m is the a a fundamental theories such as string theory . The exchange of mass of the ALP, σ is the Pauli vector of the electron spin, ħ is such particles results in spin-dependent forces, which were ori- Plank’s constant divided by 2π, and c is the speed of light. Such ginally investigated by Moody and Wilczek . Various laboratory interaction is equivalent to the Hamiltonian of the electron spin ALP searching experiments focus on the detection of macroscopic in an effective magnetic field B (r) arising from the nucleon, sp monopole–dipole forces between polarized electrons/nucleons N e 8–15 hg g 1 1 r and unpolarized nucleons . Previous laboratory searching has s p ð2Þ B ðrÞ¼ þ e e ; sp r set the limit on the monopole–dipole coupling between electron 4πmγ λr r N e 16 and nucleon, g g , with a force range λ >20 μm . The experi- s p mental investigation of this interaction at force range shorter than where γ is the gyromagnetic ratio of the electron spin. 20 μm, however, remains elusive due to the following challenges: An NV-based optically detected magnetic resonance setup (i) the size of the sensor should be small compared to the combined with an atomic force microscope (AFM) (shown in micrometer force range; (ii) the geometry of the sensor should Fig. 1, see Supplementary Fig. 1 and Supplementary Note 1 for allow close proximity between the sensor and the source; (iii) the details) is constructed to search for this electron–nucleon sensitivity of the sensor should be sufficient for searching or for interaction. A near-surface electron spin, which is a defect in providing stringent bound for such interaction; (iv) the unwanted diamond composed of a substitutional nitrogen atom and a noises, such as the magnetic and electric field introduced by neighboring vacancy , is utilized as a quantum sensor to detect environment, should be isolated well. its electron–nucleon interaction with nucleons in a fused silica Here we develop a method to investigate the electron–nucleon half-ball lens. The NV center is <10 nm close to the surface of the monopole–dipole interactions using a near-surface electron-spin diamond, so that it allows close proximity between the electron qubit in diamond. Constraints for the electron–nucleon coupling, and the nucleon. Hereafter, the electron spin of the NV center N e g g , have been set for the interaction range 0.1–23 μm. For a s p and the half-ball lens are denoted as S and M for convenience, force range of 20 μm, our constraint is bounded to be less than respectively. M is placed on a tuning fork actuator of the AFM, −15 6.24 × 10 . The method can be further extended to investigate which enables us to position M near and away from S, as well as other spin-dependent interactions and opens the door for the to drive M to vibrate with a frequency. Figure 1b shows single-spin quantum sensor to explore new physics beyond the geometric parameters in the experiment. The radius of M is the standard model. R = 250(2.5) μm. The vibration amplitude of M is denoted as A. The time-dependent distance between the bottom of M and S can be described as d = d + A[1 + cos(ω t)], where d is the 0 m 0 Results minimal distance between M and S, and ω is the vibration Monopole–dipole interaction and experimental system. We use angular frequency of M driven by the tuning fork. The effective a near-surface single electron spin, which is a nitrogen-vacancy magnetic field felt by S arising from the hypothetic (NV) center in diamond, to investigate the monopole–dipole electron–nucleon interaction can be derived by integrating interaction between an electron spin and nucleons. The axion- Eq. (2) over all the nucleons in M as B ¼ e B , where e is eff rc eff rc ac b M (SiO ) SiO 2A NV m =+1 m = –1 mw Objective m = 0 S (NV) s Fig. 1 Experimental setup and the quantum sensor. a Schematic experimental setup. An NV center in diamond, which is labeled as NV, is used to search for the monopole–dipole interaction with nucleons. The nucleons are provided by a fused silica half-ball lens, which is labeled as SiO . The half-ball lens is placed on a tuning fork actuator of an AFM. A static magnetic field B is applied along the symmetry axis of the NV center. b Schematic experimental parameters. The electron spin and the half-ball lens are denoted as S and M, respectively. The radius of M is R. M is located right above S and driven to vibrate with amplitude A. The distance between S and the bottom of M is d when M vibrates to the position nearest S. c Atomic structure and energy levels of the NV center in diamond. The NV center consists of a substitutional nitrogen atom with an adjacent vacancy cite in the diamond crystal lattice. 3 3 3 3 3 The ground and excited states are denoted as A and E. The NV center can be excited from A to E by a laser pulse, and decays back to A emitting 2 2 2 photoluminescence. The optical transitions are used to initialize and readout the spin state of the NV center. The spin statesji m ¼ 0 andji m ¼1 of A S S 2 are encoded as a quantum sensor. The state of S can be manipulated by microwave pulses 2 NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications | | | Tuning fork mw wire Diamond NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 ARTICLE =  ⁄ eff Laser (/2) () (/2) x x mw mw Read Init. z z z z z mw x y x y x y x y Fig. 2 Electron–nucleon interaction detection scheme. a Time variation of the distance d (upper) and the effective magnetic field B (lower). The distance d eff is between S and the bottom of M. The waiting time, τ = π/ω , is half period of the vibration of M, and B is the effective magnetic field on S generated by m eff the nucleons in M. b Experimental pulse sequence (upper) and state evolution of S (lower). The pulse sequence applied on S is synchronized with the vibration of M. Green laser pulses were used to initialize and read the state of S. The microwave π/2 and π pulses were applied only when M passed through the equilibrium point of the vibration the unit distance vector along the symmetry axis of M and Pulse sequence to detect the monopole–dipole interaction.If mass M is placed near the electron spin S, a static effective DC magnetic field B caused by monopole–dipole interaction will N e eff hg g ρ s p affect S. A straightforward approach to detect such DC magnetic ð3Þ B ¼ f ðλ; R; dÞ; eff 2mγ field is to perform a Ramsey sequence . The Ramsey sequence can be written as π/2 − τ − π/2, where π/2 stands for the microwave pulse with rotating angle π/2 and τ stands for a 30 −3 with ρ = 1.33 × 10 m being the number density of nucleons waiting time. The first π/2 microwave pulse prepares S to a pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 2 2 R þðdþRÞ d dþR superposition stateðÞ ji 0  iji 1 = 2. During the waiting time τ, λ λ λ in M and f(λ, R, d) = λ e  e + e + dþR the electron spin precesses about the z axis and accumulate a pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 i 2 2 2 R þðdþRÞ R þðdþRÞ 2 phase proportional to the strength of the magnetic field B . After d 2 2 d λ R þðdþRÞ eff λd  λ  λ λ λ λ λ e − e + e − e 2 2 2 2 ðdþRÞ ðdþRÞ ðdþRÞ ðdþRÞ the second π/2 pulse, the phase information will be encoded in (see Supplementary Note 2 for details). If M is moved far away the population of the stateji m ¼ 0 , which can be detected with a from S with distance much larger than the force range λ, the laser pulse. However, during the waiting time, noises, such as the monopole–dipole interaction is negligible. By comparing fluctuation of the Overhauser field and the slow drift of the the magnetic field detected by S with and without M, the external static magnetic field, will cause the dephasing. Thus electron–nucleon interaction between S and the nucleons in the sensitivity of such method is limited by the dephasing time of M can be measured. the electron spin, which is about T ¼ 0:67ð4Þ μs measured in Figure 1c shows the atomic structure and energy levels of the our experiment. NV center. The ground state of the NV center is an electron-spin To suppress the dephasing and to enhance the sensitivity of 3 22 triplet state A with three substatesji m ¼ 0 andji m ¼ ±1 .A detecting B , a spin echo sequence can be applied instead of S S 2 eff static magnetic field B of about 300 G is applied along the NV the Ramsey sequence. The spin echo sequence can be written as symmetry axis to remove the degeneracy of theji m ¼ ±1 spin π/2 − τ − π − τ − π/2, where π/2 (π) stands for the microwave states. The spin statesji m ¼ 0 andji m ¼1 are encoded as a pulse with rotating angle π/2 (π) and τ stands for a waiting time. S S quantum sensor . Microwave pulses with frequency matching With this spin echo sequence, the coherence time of the electron the transition betweenji m ¼ 0 andji m ¼1 are delivered by spin is enhanced to about T = 8.3(8) μs in our experiment, which S S 2 a copper microwave wire to manipulate the state of the quantum is of an order longer than T . Since the positive phase sensor. Theji m ¼ 1 state remains idle due to the large detuning. accumulated during the first waiting time τ is exactly canceled A laser pulse can be applied to pump the NV center from A to by the negative phase accumulated during the second τ, the total 3 3 the excited state E. When the NV center decays back to A , phase due to static B is zero. To solve this problem, we drive M 2 eff photoluminescence can be detected. The optical process can be to vibrate periodically to make B an oscillating signal (shown in eff utilized to realize state initialization and readout of this quantum Fig. 2a). If B is modulated in phase with the spin echo sequence, eff sensor. Because of the convenient state initialization and a nonzero accumulated phase due to B can be obtained, while eff 20 21 readout procedures, precise control , long coherence time , the unwanted noise can be canceled. We use a homebuilt pulse and its atomic size, the NV center serves as a magnetic sensor generator and a comparator to make sure that the tuning fork at nanometer scale, which is now extended to search for the oscillation and the pulse sequence are synchronized well (see axion-mediated interactions beyond the standard model. Supplementary Fig. 4 and Supplementary Note 1 for details). NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 3 | | | ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 following microwave π pulse rotates the Bloch vector by an angle W/O M I = I + A cos( +  ) 1 = 0.000 ± 0.013 PL PL,0 PL mw 1 of π around x axis. After the π pulse, the electron spin experiences 0.95 another free evolution for half of the vibration period under B . eff 0.90 At the end of this evolution, the state is evolved into pffiffiffi 5τ=2 iφ 0.85 ðÞ ji 0 þ ie ji 1 = 2 with φ ¼ φ  γB ðtÞcosθdt.A final eff 0 3τ=2 microwave π/2 pulse with phase φ then rotates the Bloch Exp. mw 0.80 vector by an angle of π/2 around the axis e cos φ + e sin φ Fit x mw y mw 0.75 (with e and e being the unit vector along the x and y axis), x y 0369 12 transforming the state into cos φ þ φ =2 ji 0 + mw (rad) mw iφ mw e sin φ þ φ =2 1 . After this spin echo sequence, a laser ji mw pulse is applied and the photoluminescence intensity I is b PL I = I + A cos( +  ) 2 = 0.000 ± 0.012 With M PL PL,0 PL mw 2 detected. The measured I reflects the population P of state PL j0i 0.95 ji m ¼ 0 for the final state, with P ¼ 1=2 þ 1=2cos φ þ φ . S j0i mw 0.90 Therefore, I can be expressed as PL 0.85 I ¼ I þ A cos φ þ φ : ð4Þ PL PL;0 PL mw Exp. 0.80 Fit 0.75 By measuring the photoluminescence intensity I with a set of PL 0369 12 different phases φ of the final microwave π/2 pulse, we can mw (rad) mw extract φ which contains the information of B arising from the eff N e spin–mass interaction. The coupling g g can be derived to be Fig. 3 Experimental results for detecting the electron–nucleon interaction. a s p The measured photoluminescence intensity I without M. b The measured PL 1 2m φ N e g g ¼ : R R photoluminescence intensity I with M. In both panels, the experimental PL s p 3τ=2 5τ=2 cosθ  hρ f ðλ; R; dðtÞÞdt  f ðλ; R; dðtÞÞdt data are represented by black circles with error bars, and the red solid lines τ=2 3τ=2 represent the fitting of the experimental data. Each experimental data is the ð5Þ average with six million experimental trails, which are divided into 1200 samples. Error bars of the experimental data represent s.e.m., which are calculated as the sample standard deviations divided by the square root Experimental results. Figure 3 shows the experimental results. of the sample size. The parameter values A = 0.091(1) and I = 0.8476 PL PL,0 All the experimental data shown in Fig. 3 are obtained with (8) (A = 0.091(1) and I = 0.8563(8)) are obtained by fitting the PL PL,0 six million averages (see Supplementary Figs. 5, 6, and experimental data for the cases without M in panel a (with M in panel b). Supplementary Note 4 for details). To exclude the influence of The phases φ and φ are the accumulated phases of the states of S without 1 2 any possible oscillating magnetic field from other sources, we first and with M. The phase shift due to the electron–nucleon interaction implement the pulse sequence without M as a benchmark between S and M is obtained by φ = φ − φ to be φ = 0.000 ± 0.018 rad 2 1 experiment. The experimental data without M is shown in Fig. 3a. By fitting the data with Eq. (4), we obtain φ = 0.000 ± 0.013 rad Figure 2a shows schematically the distance d and correspond- as a benchmark. Then the spin echo sequence is implemented ing time-varying effective magnetic field B arising from the with vibrating M and the result has been shown in Fig. 3b. The eff hypothetical electron–nucleon interaction. The mass is driven to experimental data with M is fitted with Eq. (4) to extract φ with vibrate with an angular frequency ω = 2π × 187.29 kHz. The φ = 0.000 ± 0.012 rad. The accumulated phase φ of the m 2 vibration amplitude A and shortest distance d are A = 41.1(1) electron spin’s state owing to B generated by M, which is 0 eff nm and d = 0.5(1) μm, respectively. When M vibrates to the obtained by φ = φ − φ , is determined to be φ = 0.000 ± 0.018 0 2 1 position nearest to S, the distance d reaches the minimum value rad. The electron–nucleon interaction has not been observed at d and the corresponding effective magnetic field B achieves a the current experimental condition, but an upper limit can be set 0 eff maximum value. When M vibrates to the position furthest from to constrain the interaction. S, d reaches the maximum value d + 2A and B achieves a Table 1 is the systematic error budget of our experiment. One 0 eff minimum value. systematic error is due to the diamagnetism of M in a 300 G Figure 2b shows the pulse sequence applied on S (a detailed magnetic field. M is modulated in phase with the spin echo description of the pulse sequence is presented in Supplementary sequence, so the in phase AC component rather than the DC Fig. 3 and Supplementary Note 1) and the corresponding state component of magnetic field due to the diamagnetism of M evolution of S on the Bloch sphere. The pulse duration of the π would cause a phase shift in our result. If the NV center locates (π/2) pulse is 118 ns (59 ns) and the waiting time τ is fixed to 2.67 exactly under the center of the mass, the magnetic field caused by μs. To optimize the phase accumulation, the microwave π/2 and π the diamagnetism of M is perpendicular to the NV symmetry pulses in the spin echo sequence are applied only when M axis, and the AC part of this magnetic field is estimated to be −6 vibrates passing through the equilibrium point of the vibration. about 1.5 × 10 G (see Supplementary Fig. 7 and Supplementary The electron spin S is initialized intoji m ¼ 0 by a laser pulse, Note 4 for details). Due to the large energy splitting (2.0286 GHz) corresponding to the unit vector along z axis in the Bloch along the symmetry axis of NV center, the phase shift caused by −10 sphere. The first microwave π/2 pulse transforms the state into this component is estimated to be 1.7 × 10 rad. Because the pffiffiffi NV center may deviate from the exact location under the center ðÞ ji 0  iji 1 = 2. Then S evolves under the effective magnetic field of the mass (see Supplementary Fig. 8 and Supplementary B for half of the vibration period τ, corresponding to the eff Note 4), there could be a residual magnetic field along the spin precessing around the z axis. As a result, the state is pffiffiffi iφ symmetry axis of NV. The amplitude of this in phase AC evolved intoðÞ ji 0  ie ji 1 = 2 at the end of the free evolution, −8 magnetic field is estimated to be about 1.1 × 10 G (see 3τ=2 where φ ¼ γB ðtÞcosθdt is the accumulated phase, and N e eff 0 τ=2 Supplementary Note 4). Therefore, the correction to the g g pffiffiffi s p −20 θ ¼ arccosð1= 3Þ is the angle between B and the NV axis. The for 20 μm due to the diamagnetism of M is 5(5) × 10 . The eff 4 NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications | | | I (a.u.) I (a.u.) PL PL NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 ARTICLE Table 1 Systematic error summary N e Systematic error Size of effect Correction to g g for 20 μm s p −6 −20 Diamagnetism of M −11.28 × 10 (5 ± 5) × 10 −6 −20 Diamagnetism of the tuning fork −11.28 × 10 (3.8 ± 0.3) × 10 −27 Phase jitter of microwave 1.3 ps (0.0 ± 1.7) × 10 −27 T dephasing 670 ± 41 ns (0.0 ± 1.9) × 10 −17 Shortest distance between M and S 0.5 ± 0.1 μm (0.1 ± 3.0) × 10 −17 The amplitude of the modulation of M 41.1 ± 0.1 nm (0.0 ± 1.3) × 10 −18 The radius of M 250 ± 2.5 μm (0.1 ± 3.7) × 10 ° −16 The angle between B and NV axis 54.7 ± 3 (0.4 ± 4.2) × 10 eff 0.1 to 1 m . The upper limit from the experiment by Terrano –1 –4 –7 –10 m (eV) 10 10 10 10 a et al. is for the range from 0.5 mm to 10 cm. In the range from This experiment –12 10 20 to 500 μm, the experiment by Hoedl et al. provides the upper limit. Our result is represented as the solid red line. It is derived –13 –13 according to Eq. (5) with 2δ as an upper bound of φ, where δ = φ φ –14 10 0.018 rad is the s.d. of the accumulated phase φ. Besides δ , the uncertainties of other experimental parameters, such as d and A, –15 12 20 28  (µm) –21 are also taken into account to derive the upper limit (see Supplementary Note 3 for details). For the force range 0.1 μm< λ Hoedl 2011 N e Excluded region <23 μm, our result provided the upper bound for g g .Asis s p shown in the inset of Fig. 4, the obtained upper bound of the Wineland 1991 –29 N e −15 interaction at 20 μm, g g < 6.24 × 10 , is two orders of s p Terrano 2015 magnitude more stringent than the bound set by Hoedl et al. . −5 Youdin 1996 The possible value of mass of the ALPs, from 10 to 1 eV Heckel 2008 (corresponding to a force range 0.2 μm< λ < 2 cm), is still allowed –37 –8 –4 0 4 by otherwise stringent constraints . The unexplored force range (m) 10 10 10 10 left by the previous experiments has now been searched in our N e N e Fig. 4 Upper limits on g g as a function of the force range λ and mass of s p experiment. We note that the most restrictive constraint on g g s p the axion-like particle m . Our result is represented as the red solid line. The may arise from the combination of the long-range force bound 8–12 16,24 black solid lines represent the results from refs. . The red dashed line and the astrophysical limit . These limits rely on the N e shows the available improvement of the constraint on g g in future (see s p underlying gravitational theory, namely, a chameleon mechanism Supplementary Note 3 for details). The inset shows a comparison of our could invalidate the astrophysical limit, and therefore, it is N e result and that from ref. with the force range nearby 20 μm, which necessary to experimentally constrain g g in laboratories, where s p illustrates an improvement of two orders more stringent for our result at 25 the gravitational effects are negligible . 20 μm compared with that from ref. Discussion material of the tuning fork is SiO . The distance between the The constraint can be further improved by several strategies in tuning fork and the NV center is at least 250 μm. The systematic future. We search for spin–mass interaction by detecting the error due to the diamagnetism of tuning fork leads to a correction accumulated phase of a single electron spin’sstate owingto B . eff N e −20 to g g for 20 μm being 3.8(3) × 10 . The phase jitter of the One effective method is to enhance the coherence time of the s p 12 26 microwave, which would cause the instability of the phase of the electron spin, by synthesizing C-enriched diamond or by 27,28 final π/2 pulse, is measured to be 1.3 ps (Supplementary Fig. 10 applying multi-pulse dynamical decoupling sequences .Once and Supplementary Note 4). Since the waiting time of the spin the coherence time is prolonged, the ability of detecting the echo is fixed, this instability of the phase only causes a small accumulated phase can be enhanced. The frequency of our tuning reduction of the signal contrast rather than a phase shift. The fork at present stage is 187.29 kHz, which is suitable for a spin echo impact of phase jitter is also presented in Table 1. The frequency sequence. If the frequency of the tuning fork is enhanced in future, shift of the microwave generator, the drift of the external multi-pulse dynamical decoupling sequences can be applied to magnetic field and the fluctuation of the Overhauser field (see improve the performance. On the other hand, the accumulated Supplementary Fig. 9 and Supplementary Note 4) will contribute phase is proportional to the number density of nucleons in the to the T dephasing. This dephasing can be well suppressed by source. To use materials with high number density of nucleons as spin echo technique and the correction due to dephasing is also the source, such as Bi Ge O (BGO), can also improve the con- 4 3 12 included in Table 1. The errors due to the uncertainties of the straint. To decrease the measurement uncertainty of the accumu- distance between M and S, the amplitude of the modulation of M, lated phase, one can improve the detection efficiency of the the radius of M and the angle between B and NV axis, have also photoluminescence and increase the number of experiment trails. eff been taken into account in the Table 1. The detailed analysis of On the basis of above extensions of techniques, the available the systematic errors are included in Supplementary Note 4. constraint, which is shown as the red dashed line in Fig. 4, could be Figure 4 shows the new constraint set by this work together about three orders of magnitude improved from the current result with recent constraints from experimental searches for (see detailed discussion in Supplementary Note 3). monopole–dipole interactions . The lines from the experiment Our platform uses a near-surface NV center together with by Heckel et al. are the upper limits in the meter range and AFM setup, thus the force range can be focused within micro- above , except a gap from 10 to 1000 km. The upper limit in this meters. The micrometer and submicrometer range, which is not gap is obtained by the experiment by Wineland et al. . The easily accessed in previous experiments, provides a new window experiment by Youdin et al. sets the upper limit in the range from for investigating new physics beyond standard model. The NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 5 | | | N e g g s p N e g g s p ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 electron–nucleon interaction investigated in our work is one of 11. Terrano, W. A., Adelberger, E. G., Lee, J. G. & Heckel, B. R. Short-range, spin- dependent interactions of electrons: a probe for exotic pseudo-goldstone interactions from new particle exchange . In future, several bosons. Phys. Rev. Lett. 115, 201801 (2015). related interactions can also be investigated with extension of our 12. Hoedl, S. A., Fleischer, F., Adelberger, E. G. & Heckel, B. R. Improved method. For example, spin–spin interaction mediated by ALPs, constraints on an axion-mediated force. Phys. Rev. Lett. 106, 041801 (2011). on which a constraint is recently set at micrometer scale , can be 13. Petukhov, A. K., Pignol, G., Jullien, D. & Andersen, K. H. Polarized He as a further explored with submicrometer scale by two coupled NV probe for short-range spin-dependent interactions. Phys. Rev. Lett. 105, 170401 (2010). centers with technologies developed by Grinolds et al. . Another 14. Ni, W.-T., Pan, S.-s, Yeh, H.-C., Hou, L.-S. & Wan, J. Search for an axionlike case is to explore the interaction mediated by a vector boson, spin coupling using a paramagnetic salt with a dc squid. Phys. Rev. Lett. 82, 31,32 which has been investigated at micrometer force range . 2439–2442 (1999). Therefore, NV centers will not only be a promising quantum 15. Bulatowicz, M. et al. Laboratory search for a long-range t-odd, p-odd 33–38 sensor for physics within standard model , but also be an interaction from axionlike particles using dual-species nuclear magnetic 129 131 resonance with polarized Xe and Xe gas. Phys. Rev. Lett. 111, 102001 important platform for searching for new particles predicted by (2013). theories beyond the standard model. 16. Raffelt, G. Limits on a CP-violating scalar axion-nucleon interaction. Phys. Rev. D 86, 015001 (2012). Methods 17. Dobrescu, B. A. & Mocioiu, I. Spin-dependent macroscopic forces from new Experimental setup. The electron spin of a near-surface NV center in diamond is particle exchange. J. High Energy Phys. 2006, 005 (2006). used as a quantum sensor to search for the hypothetical ALP-mediated 18. Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. monopole–dipole interaction with nucleons in a half-ball lens. The NV center was Rep. 528,1–45 (2013). created by implantation of 10 keV N ions into [100] bulk diamond and annealing 19. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. for 2 h at 800 °C in vacuum. The diamond was then oxidatively etched for 4 h at 89, 035002 (2017). 580 °C. The depth of the NV center was estimated to be <10 nm. Nanopillars were 20. Rong, X. et al. Experimental fault-tolerant universal quantum gates with solid- fabricated to improve the detection efficiency of the photoluminescence, with which state spins under ambient conditions. Nat. Commun. 6, 8748 (2015). −1 a photoluminescence rate of 100 kcounts s was achieved in the experiment. The 21. Bar-Gill, N., Pham, L. M., Jarmola, A., Budker, D. & Walsworth, R. L. Solid- NV center is confirmed to be single by measurement of the second-order correlation state electronic spin coherence time approaching one second. Nat. Commun. function (Supplementary Fig. 2 and Supplementary Note 1). An optically detected 4, 1743 (2013). magnetic resonance setup combined with an AFM, which is similar with setup 22. Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950). reported in ref. , was constructed to search for the spin–mass interaction. The 532 23. Beringer, J. et al. Review of particle physics. Phys. Rev. D 86, 010001 (2012). nm green laser pulse passed through an acousto-optic modulator and an objective to 24. Raffelt, D. & Weiss, A. Red giant bound on the axion-electron coupling be focused on the NV center to initialize the electron-spin state. The phonon reexamined. Phys. Rev. D 51, 1495 (1995). sideband fluorescence with wavelength of 650–800 nm went through the same 25. Jain, P. & Mandal, S. Evading the astrophysical limits on light pseudoscalars. objective and was collected by an avalanche photodiode with a counter card to Int. J. Mod. Phys. D 15, 2095 (2006). realize state readout. Microwave pulses, which were generated by IQ modulation 26. Balasubramanian, G. et al. Ultralong spin coherence time in isotopically −1 with a 4.2 GSa s arbitrary waveform generator (Keysight 81180A) and a vector engineered diamond. Nat. Mater. 8, 383–387 (2009). signal generator (Keysight E8267D) were amplified by a power amplifier (Mini- 27. Du, J. et al. Preserving electron spin coherence in solids by optimal dynamical Circuits ZHL-16W-43-S+) and delivered by a copper microwave wire to manip- decoupling. Nature 461, 1265–1268 (2009). ulate the electron-spin state. The tuning fork-based atomic force microscope was 28. de Lange, G., Wang, Z. H., Ristè, D., Dobrovitski, V. V. & Hanson, R. utilized to position the half-ball lens and to drive the half-ball lens to vibrate. The Universal dynamical decoupling of a single solid-state spin from a spin bath. state initialization, manipulation, and readout of the electron spin were synchro- Science 330,60–63 (2010). nized with the vibration of the half-ball lens with an arbitrary sequence generator 29. Kotler, S., Ozeri, R. & Kimball, D. F. J. Constraints on exotic dipole-dipole (Hefei Quantum Precision Device Co. ASG-GT50-C). Details of the experimental couplings between electrons at the micrometer scale. Phys. Rev. Lett. 115, setup are shown in Supplementary Fig. 1 and Supplementary Note 1. 081801 (2015). 30. Grinolds, M. S. et al. Nanoscale magnetic imaging of a single electron spin Data availability. Data supporting the findings of this study are available within under ambient conditions. Nat. Phys. 9, 215–219 (2013). the article and its Supplementary Information file, and from the corresponding 31. Yan, H. & Snow, W. M. New limit on possible long-range parity-odd authors upon reasonable request. interactions of the neutron from neutron-spin rotation in liquid He. Phys. Rev. Lett. 110, 082003 (2013). 32. Yan, H. et al. Searching for new spin- and velocity-dependent interactions by Received: 8 July 2017 Accepted: 23 January 2018 spin relaxation of polarized He gas. Phys. Rev. Lett. 115, 182001 (2015). 33. Taylor, J. M. et al. High-sensitivity diamond magnetometer with nanoscale resolution. Nat. Phys. 4, 810–816 (2008). 34. Maze, J. R. et al. Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature 455, 644–647 (2008). 35. Balasubramanian, G. et al. Nanoscale imaging magnetometry with diamond References spins under ambient conditions. Nature 455, 648–651 (2008). 1. Schwarz, J. H. & Seiberg, N. String theory, supersymmetry, unification, and all 36. Kolkowitz, S. et al. Probing johnson noise and ballistic transport in normal that. Rev. Mod. Phys. 71, S112–S120 (1999). metals with a single-spin qubit. Science 347, 1129–1132 (2015). 2. Graham, P. W., Irastorza, I. G., Lamoreaux, S. K., Lindner, A. & van Bibber, K. 37. Shi, F. et al. Single-protein spin resonance spectroscopy under ambient A. Experimental searches for the axion and axion-like particles. Annu. Rev. conditions. Science 347, 1135–1138 (2015). Nucl. Part. Sci. 65, 485–514 (2015). 38. Lovchinsky, I. et al. Magnetic resonance spectroscopy of an atomically thin 3. Marsh, D. J. Axion cosmology. Phys. Rep. 643,1–79 (2016). material using a single-spin qubit. Science 355, 503–507 (2017). 4. Bertone, G., Hooper, D. & Silk, J. Particle dark matter: evidence, candidates 39. Kolkowitz, S. et al. Coherent sensing of a mechanical resonator with a single- and constraints. Phys. Rep. 405, 279–390 (2005). spin qubit. Science 335, 1603–1606 (2012). 5. Kamionkowski, M., Pradler, J. & Walker, D. G. E. Dark energy from the string axiverse. Phys. Rev. Lett. 113, 251302 (2014). 6. Peccei, R. D. & Quinn, H. R. CP conservation in the presence of instantons. Acknowledgements Phys. Rev. Lett. 38, 1440–1443 (1977). We are grateful to H.Y. Yan for his systematic introduction about the spin-dependent 7. Moody, J. E. & Wilczek, F. New macroscopic forces? Phys. Rev. D 30, 130–138 forces and fruitful discussion about the experiment. We thank C.K. Duan and D.J. (1984). Kimball for helpful discussion. We thank L.P. Guo for his help on nitrogen ion 8. Wineland, D. J., Bollinger, J. J., Heinzen, D. J., Itano, W. M. & Raizen, M. G. implantation. The fabrication of diamond nanopillars for improving the detection effi- Search for anomalous spin-dependent forces using stored-ion spectroscopy. ciency of the photoluminescence was performed at the USTC Center for Micro and Phys. Rev. Lett. 67, 1735–1738 (1991). Nanoscale Research and Fabrication. This work was supported by the National Key Basic 9. Youdin, A. N., Krause, D. Jr., Jagannathan, K., Hunter, L. R. & Lamoreaux, S. Research Program of China (Grants Nos. 2013CB921800, 2016YFA0502400, and K. Limits on spin–mass couplings within the axion window. Phys. Rev. Lett. 2016YFB0501603), the National Natural Science Foundation of China (Grant Nos. 77, 2170–2173 (1996). 11227901, 91636217, 11722327, and 31470835) and the Strategic Priority Research 10. Heckel, B. R. et al. Preferred-frame and CP-violation tests with polarized Program (B) of the CAS (Grant No. XDB01030400). J.D. and X.R. thank financial electrons. Phys. Rev. D 78, 092006 (2008). support by Key Research Program of Frontier Sciences, CAS (Grants No. QYZDY-SSW- 6 NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications | | | NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03152-9 ARTICLE SLH004 and QYZDB-SSW-SLH005). F.S. and X.R. thank the Youth Innovation Pro- Reprints and permission information is available online at http://npg.nature.com/ motion Association of Chinese Academy of Sciences for the support. Y.-F.C. is supported reprintsandpermissions/ in part by the Chinese National Youth Thousand Talents Program, by the CAST Young Elite Scientists Sponsorship Program (2016QNRC001), by the National Natural Science Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in Foundation of China (Grant Nos. 11421303, 11653002), and by the Fundamental published maps and institutional affiliations. Research Funds for the Central Universities. X.Q. thank support by Fundamental Research Funds for the Central Universities (Grant No. WK2030040081). Open Access This article is licensed under a Creative Commons Author contributions Attribution 4.0 International License, which permits use, sharing, J.D. proposed the idea. J.D. and X.R. designed the experiment. M.W., J.G., and M.G. adaptation, distribution and reproduction in any medium or format, as long as you give performed the experiment under the supervision of J.D. and X.R., J.G., M.W., M.J., and appropriate credit to the original author(s) and the source, provide a link to the Creative P.H. carried out the calculations and simulations. X.Q., P.W., M.G., Y.X., and F.S. Commons license, and indicate if changes were made. The images or other third party constructed the experimental setup. M.W. and C.Z. prepared the NV center. X.R., J.G., material in this article are included in the article’s Creative Commons license, unless M.W., Y.-F.C., and M.G. wrote the paper. All authors analyzed the data, discussed the indicated otherwise in a credit line to the material. If material is not included in the results and commented on the manuscript. article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from Additional information the copyright holder. To view a copy of this license, visit http://creativecommons.org/ Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467- licenses/by/4.0/. 018-03152-9. © The Author(s) 2018 Competing interests: The authors declare no competing financial interests. NATURE COMMUNICATIONS (2018) 9:739 DOI: 10.1038/s41467-018-03152-9 www.nature.com/naturecommunications 7 | | |

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