diff --git "a/8tE3T4oBgHgl3EQfSAk3/content/tmp_files/load_file.txt" "b/8tE3T4oBgHgl3EQfSAk3/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/8tE3T4oBgHgl3EQfSAk3/content/tmp_files/load_file.txt" @@ -0,0 +1,860 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf,len=859 +page_content='Quantum sensing of electric field distributions of liquid electrolytes with NV-centers in nanodiamonds M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Hollendonner,1, 2 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Sharma,2 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Dasari,3 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Finkler,4 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Kusminskiy,2, 5 and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Nagy1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' ∗ 1Friedrich-Alexander-University Erlangen-Nuremberg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 91058 Erlangen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Germany 2Max Planck Institute for the Science of Light,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 91058 Erlangen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Germany 33rd Institute of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' IQST,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' and Research Center SCoPE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' University of Stuttgart,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 70569 Stuttgart,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Germany 4Department of Chemical and Biological Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Weizmann Institute of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Rehovot 7610001,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Israel 5Institute for Theoretical Solid State Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' RWTH Aachen University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 52074 Aachen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Germany (Dated: January 12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 2023) To use batteries as large-scale energy storage systems it is necessary to measure and understand their degradation in-situ and in-operando.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As a battery’s degradation is often the result of molecular processes inside the electrolyte, a sensing platform which allows to measure the ions with a high spatial resolution is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Primary candidates for such a platform are NV-centers in diamonds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' We propose to use a single NV-center to deduce the electric field distribution generated by the ions inside the electrolyte through microwave pulse sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' We show that the electric field can be reconstructed with great accuracy by using a protocol which includes different variations of the Free Induction Decay to obtain the mean electric field components and a modified Hahn-echo pulse sequence to measure the electric field’s standard deviation σE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' From a semi-analytical ansatz we find that for a lithium ion battery there is a direct relationship between σE and the ionic concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Our results show that it is therefore possible to use NV-centers as sensors to measure both the electric field distribution and the local ionic concentration inside electrolytes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' INTRODUCTION Rechargeable batteries play an important role for our society and are a key ingredient for the transition to- wards renewable energy sources [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As the production of batteries is accompanied with a considerable use of re- sources, recyclable [4] batteries with a long lifetime are needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The latter is limited by degradation mechanisms, such as the formation of solid-electrolyte interfaces [5] or lithium-plating [6] which can reduce the battery’s capac- ity with increasing cell age [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As these processes happen on a molecular level within nanometer scales [5], a sensor which is capable of monitoring the ionic concentration in-situ and in-operando with high spatial and temporal resolutions is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Even though MRI allows to recon- struct transport properties [8, 9] of a battery, tools which allow to perform measurements inside the electrolyte are still absent [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' It has been demonstrated that nitrogen-vacancy (NV) centers in diamond (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1(b)) are high-resolution quantum sensors, which can detect oscillating or fluctu- ating [10–13] magnetic fields with nano- [14, 15] and even subpico-Tesla [16] sensitivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Besides this, NV-centers have great ability for the detection of electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' They can not only detect DC [17, 18] or AC [19] electric fields with remarkable precision, but are additionally capable of detecting single fundamental charges [20] even within the diamond lattice [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' This electric field sensitivity was used by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' [22] to show that, based on theoretical con- ∗ roland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='nagy@fau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='de siderations, bulk NV-centers can work as electrochemical sensors if they are in contact with an electrolyte solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Here we show that nanodiamonds equipped with sin- gle NV-centers can act as in-situ electric field sensors inside liquid electrolytes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' By exploiting how transverse and axial electric fields act on the NV-center’s ground state spin states, we find variations of the free- induction decay (FID) pulse sequence, which allow to measure the mean electric field components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Further, we show that it is possible to use variants of the Hahn- echo pulse sequence to additionally obtain the electric field’s standard deviation σE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' From a semi-analytical ansatz we demonstrate exemplarily for a lithium ion bat- tery (LIB) that there is a direct relationship between the electric field’s standard deviation and the local ionic con- centration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' A nanodiamond with a single NV-center can therefore work as a sensor which allows to simultaneously reconstruct the electric field distribution and to measure the ionic concentration with nm spatial resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' ELECTRIC FIELD DISTRIBUTION IN LIQUID ELECTROLYTES Before introducing measurements of the electric field distribution by the NV-center, we would like to develop an analytic expression of the electric field induced inside the nanodiamond by the positive and negative ions of the electrolyte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The potential Φ at position r inside the nanodiamond due to a single charge q at position b, is described by arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='04427v1 [quant-ph] 11 Jan 2023 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (a) Experimental setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' A nanodiamond which is dissolved in the liquid electrolyte of the battery is surrounded by positive (orange) and negative (blue) ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Two perpendicular aligned gold wires allow to generate polarized microwave drives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (b) To work as a quantum sensor, the nanodiamond contains a vacancy (V) next to a nitrogen atom (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (c) Standard deviation of Ez, calculated from 500 repeated sets of randomly placed ions of concentration c around the nanodiamond (rND = 100 nm) and inside a sphere of radius R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The relative permittivities are ϵND = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='8 [22] and ϵe = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='5 [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Solid lines are fits following Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (3) with A as a fit parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (d) Fit parameters A obtained from (c), compared to the theory value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Poisson’s equation ∇2Φ (r) = −ρ (r) ϵ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (1) Here ϵ = ϵ0ϵi with i = e, ND, are the permittivities of, re- spectively, the electrolyte and the nanodiamond in terms of the vacuum permittivity ϵ0 and ρ is the charge density induced by q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The solution inside the nanodiamond, ΦND (see Methods for the detailed derivation), allows to ob- tain the electric field at the center of the nanodiamond, which is END = q 4πϵ0 3 2ϵe + ϵND b b3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (2) By considering the positions of ions of a molar concentra- tion c to be normally distributed within a sphere of radius R around a nanodiamond (radius rND), the standard de- viation of the electric field distribution at the center of the nanodiamond is σEz = A � c � 1 rND − 1 R � A = |q| ϵ0 (2ϵe + ϵND) � 3NA 4π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (3) To validate Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (3), we simulated the standard deviation of 500 sets of uniformly and randomly placed ions for dif- ferent molar ionic concentrations (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As it is the most widely used electrolyte of LIBs [24], we chose LiPF− 6 with ϵe = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='5 [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The total electric field was calculated as the linear sum of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (2) for all randomly placed ions around a 200 nm spherical nanodiamond [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As it can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1(d), the expected A value is in fair agreement with the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (3) it can be calculated that for R = 500 nm, the fluctuations will increase only by 3%, compared to σE (R = 400 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As σE therefore saturates for R ≳ 500 nm, this implies that electric field fluctuations only affect the nanodia- mond within sub-micrometer range and the system is limited by the confocal volume of the experimental setup, which typically is ∼ 1 µm3 [26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' SENSING OF STATIC ELECTRIC FIELDS INSIDE ELECTROLYTES An electric field E can in cylindrical coordinates be expressed by its axial component Ez, its transverse pro- jection E⊥ = � E2x + E2y and an angle φE, which defines the projections onto the x and y axis as Ex = E⊥ cos φE and Ey = E⊥ sin φE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The total Hamiltonian which de- scribes the NV-center in presence of electric and axial magnetic fields will in the following be denoted as ˆH0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' By taking into account that the NV-center can be driven by two perpendicular microwave wires (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1(a)) with amplitude Ω, frequency ωd and a phase φ between each other, the total ground state Hamiltonian in a frame ro- tating with ωd is ˆH = ˆH0 + ˆHd (see Methods), where ˆH0 = (∆ + ξz) ˆS2 z + βz ˆSz − ξ⊥ 2 � ˆS2 +eiφE + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � ˆHd = Ω √ 2 � ϵ−σ0,−1 + ϵ+σ† 0,+1 + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (4) Here ∆ = D − ωd is the detuning between the zero- field splitting, D = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='87 GHz [28], and the microwave drive frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Si, i = x, y, z, are the spin-1 op- erators, which can be used to define ladder operators S± = Sx ± iSy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' σ0,±1 = |0⟩ ⟨±1| are operators which describe transitions between |0⟩ and, respectively, |±1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Frequency contributions generated by electric and axial magnetic fields are considered through ξz = d∥Ez and ξ⊥ = d⊥E⊥ (d∥ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='35 Hz cm/V, d⊥ = 17 Hz cm/V [29]) and βz = γeBz (γe = 28 GHz/T [30]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The phase factors ϵ± = � 1 − ie∓iφ� /2 which enter into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (4), allow to describe the transitions which are caused by circularly (φ = ±π/2) or linearly (φ = 0) polarized microwave drives [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The time-evolution operators of ˆHd, ˆR (t) = e−i ˆ Hdt (see Methods), show that one can induce Rabi oscillations between |0⟩ and |1⟩ for right cir- cularly polarized drives and |0⟩ ↔ |−1⟩ for left circular polarizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Linearly polarized drives allow to drive transitions between |0⟩ and both |±1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' MW Pos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='Electrode3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (a) FID-variations to extract ξ⊥, φE and ξz through subsequent pulse sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Here Tπ (Tπ/2) is the duration of the microwave pulse such that a π-pulse (π/2-pulse) is performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Subscripts ± denote circularly polarized drives which cause oscillations between |0⟩ and either |1⟩ or |−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Subscript 0 denotes linear polarization of the drive and the free evolution is described through ˆF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (b) FIDξ⊥ for different magnetic fields up to βz = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='7 MHz, corresponding to Bz = 1 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' For βz = 0 the signal has the highest contrast with the lowest frequency of oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (c) Fourier transform of FIDξ⊥,ξz with Ω = 10 MHz and Ex,y,z = 10 V/µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Only for T ∗ 2 > 10 µs the peaks at ξ⊥ ± ξz = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='04 MHz and 2ξ⊥ can be resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' In absence of microwave drives, the |±1⟩ states are symmetrically mixed by ξ⊥ and axial electric fields ef- fectively shift |0⟩ from |±1⟩, which can be seen from ˆF (τ) = e−i ˆ H0τ (see Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As axial and transverse electric fields thus act differently on the |ms = 0, ±1⟩ states of the NV-center, one can derive variations of the Free Induction Decay (FID), which allow to extract these electric field components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Measurement of electric field components The FID consists of two microwave pulses separated by a free evolution period τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Electric field contributions ξ⊥, φE and ξz can be sensed through FID-variations, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The NV-center can be initialized into its |0⟩ state via excitation with green laser light, fol- lowed by intersystem-crossing [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' This state can then be driven to −i |1⟩ through a right-polarized π-pulse, de- noted as ˆR (Tπ)+, and will be influenced by both axial magnetic as well as transverse electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The latter induce mixing with |−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' By using a microwave π-pulse with the same polarization as the initial one, the trans- ferred population from |1⟩ to |−1⟩ can be obtained from the FID-signal FIDξ⊥ (τ) = | ⟨0| ˆR (Tπ)+ ˆF (τ) ˆR (Tπ)+ |0⟩ |2 = cos2 � τ � β2z + ξ2 ⊥ � + β2 z β2z + ξ2 ⊥ sin2 � τ � β2z + ξ2 ⊥ � , (5) which is a measure of the population which has been transferred from |1⟩ to |−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 2(b) one can see this FID-signal as a function of the free evolution time τ for βz values up to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='8 MHz, which corresponds to Bz = 1 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Besides having a decreased contrast for βz ̸= 0, the frequency � β2z + ξ2 ⊥ of the FID-oscillations depends on both axial magnetic and transverse electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' It is therefore strongly recommended to perform the measure- ments in a magnetically shielded environment, for exam- ple by a µ-metal as in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' In the following it will be assumed that all measurement are performed without any magnetic field being present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The transverse electric field components are uniquely defined through φE, as ξx = ξ⊥ cos φE and ξy = ξ⊥ sin φE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' A superposition state −eiπ/4 (|1⟩ + |−1⟩) / √ 2 generated through a linearly polarized π-pulse (consid- ered via ˆR (Tπ)0, see Methods) will additionally to ξ⊥ also be affected by φE as this phase differs in its sign for |1⟩ and |−1⟩ (see Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' If either |1⟩ or |−1⟩ is projected to |0⟩ through the final microwave pulse, one obtains an FID-signal, which both depends on ξ⊥ and φE, FIDφE,ξ⊥ (τ) = 1 2 (1 − sin (2τξ⊥) sin φE) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (6) One can obtain φE as the relative fraction between the value of the FID-signal at τ = 0 and its first maxima at 2τξ⊥ = π/2, FIDφE,ξ⊥ � τ = π 2 1 2ξ⊥ � FIDφE,ξ⊥ (τ = 0) = 1 − sin φE .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (7) By using FIDξ⊥ and FIDξ⊥,φE, it is therefore possible to not only determine the electric field’s transverse compo- nent, but also to obtain the projection onto the x and y axes, which are determined through φE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Axial electric field contributions ξz cause a Stark shift between |0⟩ and |±1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' A superposition state (|0⟩ − i |−1⟩) / √ 2 generated by a circularly polarized π/2-pulse (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 2(a)) will therefore be affected both by ξz and ξ⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' If the final microwave π/2-pulse has the same polarization as the initial one, an FID-signal is ob- tained which depends both on ξ⊥ and ξz, FIDξz,ξ⊥ (τ) = 1 4 � 1 − 2 cos (τξ⊥) cos (τξz) + cos2 (τξ⊥) � , (8) if the NV-center was driven with ωd = D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The Fourier 4 transform of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (8) (see Methods), � FID (ω > 0) = π 4 �1 2δ (2ξ⊥ − ω) − δ (ξ⊥ + ξz − ω) − δ (ξ⊥ − ξz − ω) � , (9) shows, that ξz can be measured if it is possible to spec- trally resolve ξ⊥ ± ξz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' To study this, we numerically [34, 35] simulated FIDξz,ξ⊥ and included dephasing at rates 1/T ∗ 2 through a Lindblad operator � 1/T ∗ 2 Sz for T ∗ 2 in the range up to 15 µs (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 2(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' One can re- solve ξ⊥±ξz for nanodiamonds with T ∗ 2 > 10 µs, which is higher than the value of typical nanodiamonds [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' For a nanodiamond with T ∗ 2 ≈ 15 µs it would be possible to distinguish between ξ⊥ and ξz and therefore to determine the projection of the electric field onto the symmetry axis of the NV-center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' INFLUENCE OF FLUCTUATING ELECTRIC FIELDS It can be assumed that the ions surrounding the nan- odiamond will not stay static for the timescales in which measurements are performed but will be subject to, for instance, drift and diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' These fluctuations will affect the electric field inside the nanodiamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Due to the limited T ∗ 2 of nanodiamonds, the FID pulse se- quences as introduced before will be mainly suitable for the measurement of the average electric fields (see Meth- ods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The coherence time of a nanodiamond can be significantly prolonged if instead of an FID, a Hahn- Echo pulse sequence is used [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As it is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 3(a), we propose a modified version of the Hahn- Echo, where after the first free evolution interval, a π- pulse with right-circular polarization is performed, be- fore the spin is allowed to precess freely during a sec- ond free evolution interval τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Before being read out, a right-circularly polarized π-pulse is applied, which leads to a signal Hahn (τ) = (1 − cos (2τξ⊥))2 /4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Simulations of this Hahn-Echo variation show that the averages (see Methods for an example) can be fit by ⟨Hahn (τ)⟩ = 1 4 � 1 − cos (2τξ⊥) e−τ/T2�2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (10) Here T2 is the sum of the intrinsic spin coherence time T2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' = 100 µs [25] and a contribution due to the fluc- tuating electric fields, 1 T2 = 1 T2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' + 1 T2,E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (11) In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 3(b), one can see T2 as a function of the electric field’s standard deviation σE, where solid lines are T2,E = αEm/σ2 E in terms of a fit parameters α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The total spin coherence time is therefore strongly affected by σE and the mean electric field value Em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' If the mean transverse electric field has been sensed by the FID sequence as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (5), it is therefore possible to derive the electric field’s standard deviation, which together with ξ⊥, φE and ξz defines the electric field distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As there is a direct relationship between σE and the local ionic concentration (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1(c)), the proposed Hahn- echo pulse sequence additionally allows to use the NV- center inside the nanodiamond as a local concentration sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (a) Hahn-echo pulse sequence used to simulate Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (b) Total T2 for numerically [34, 35] simulated Hahn-Echoes with T2,int = 100 µs, with the electric field com- ponents sampled from a normal distribution with mean Em and standard deviation σE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' For the simulations a drive of Ω = 10 MHz was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Solid lines are fits of αEm/σ2 E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Every trajectory was obtained from 1000 individual simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Er- ror bars of one standard deviation are smaller than the data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' CONCLUSION AND OUTLOOK In conclusion we have shown here a full reconstruc- tion of the mean electric field generated in a liquid elec- trolyte, through the spin control of a quantum sensor immersed in the electrolyte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' We have found exact ex- pressions correlating the electric field components with the free-induction decay of the sensor spin, and the de- pendence of the variance on the spin-echo measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Together we were able to deduce the electric field distri- bution and also measure the local ionic concentration, a key parameter in characterizing the performance of the liquid electrolyte for battery applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' We envisage that with improved modeling of the electric field distribu- tion in liquid electrolytes and using better quantum con- trol methods, for example using correlation spectroscopy [37], we could enhance the sensitivity of the sensor to the local electric-field environment, allowing for an in-situ monitoring of the battery using the liquid electrolyte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' ACKNOWLEDGMENTS R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' would like to acknowledge financial support by the Federal Ministry of Education and Research (BMBF) 5 project QMNDQCNet and DFG (Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 507241320 and 46256793).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' would like to acknowledge the funding support from BMBF (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 16KIS1590K).' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Dolde, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Burk, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Reinhard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Wrachtrup, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Meriles, “High-resolution corre- lation spectroscopy of 13C spins near a nitrogen-vacancy centre in diamond,” Nature Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1651, June 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1 Quantum sensing of electric field distributions of liquid electrolytes with NV-centers in nanodiamonds - Supplementary Information I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' ELECTRIC FIELD AT CENTER OF NANODIAMOND In the following we would like to deduce the electric field of a single point charge q at a distance b from the origin of the nanodiamond with radius rND by following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' [S1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Poisson’s equation describes the electrostatic potential Φ, ∇2Φ (r) = −ρ (r) ϵ , (S1) where ϵ = ϵ0ϵi, i = e, ND is the permittivity of, respectively, the electrolyte and the nanodiamond in terms of the vacuum permittivity ϵ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' By exploiting azimuthal symmetry of the problem, the above expression reduces to Laplace’s equation for r ̸= b, which in spherical coordinates with |r| = r and θ the angle spanned by r and b is ∇2Φ (r, θ) = 1 r2 ∂ ∂r � r2 ∂Φ ∂r � + 1 r2 sin θ ∂ ∂θ � sin θ∂Φ ∂θ � = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S2) The general solution of this partial differential equation can be expressed in terms of the associated Legendre poly- nomials Pl of order l and in terms of two constants Al and Cl as [S1, S2] Φ (r, θ) = ∞ � l=0 � Alrl + Cl 1 rl+1 � Pl (cos θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S3) As the potential inside the nanodiamond must be finite at r = 0, Cl needs to vanish and one therefore has ΦND (r, θ) = ∞ � l=0 AlrlPl (cos θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S4) By using that 1/|r − b| = �∞ l=0 � rl � Pl (cos θ) [S1, S2] with r≷ being the greater (smaller) of |r| and |b|, one can derive the potential in the electrolyte without discontinuity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' without nanodiamond, to be ˜Φe (r, θ) = q 4πϵ0ϵe ∞ � l=0 rl < rl+1 > Pl (cos θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S5) The general solution would then be given as a superposition of this expression with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S3), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Φe = ˜Φe + Φ, which reads Φe (r, θ) = ∞ � l=0 � Cl 1 rl+1 + q 4πϵ0ϵe rl < rl+1 > � Pl (cos θ) , (S6) where it was used that in this case Al = 0 to ensure a vanishing potential at infinite distances to the origin, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Φe → 0 for r → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The constants Al and Cl, which enter into, respectively, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S4) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S6), can be determined by requiring continuity at the interface between electrolyte and nanodiamond, � ϵeEe − ϵNDEND� nND = 0 (S7) � Ee − END� × nND , (S8) where nND = r/r is the unit vector normal to the surface of the nanodiamond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' These boundary conditions are satisfied, if Al = q 4πϵ0ϵe 1 bl+1 ϵe (2l + 1) ϵNDl + ϵe (l + 1) (S9) Cl = q 4πϵ0ϵe lr2l+1 ND bl+1 ϵe − ϵND ϵNDl + ϵe (l + 1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S10) 2 The electrostatic potential inside the nanodiamond therefore is ΦND (r, θ) = q 4πϵ0ϵe ∞ � l=0 1 bl+1 ϵe (2l + 1) ϵNDl + ϵe (l + 1)rlPl (cos θ) (S11) and the electric field at the center, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' for r = 0, can be calculated as E (r = 0, θ) = q 4πϵ0 3 2ϵe + ϵND b b3 , (S12) if it is used that in cartesian coordinates one has ez = cos θer − sin θeθ with ez the azimuthally symmetric unit vector and er and eθ the radial and altitudinal unit vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Electric field variance The probability of an ion to be located at b witin a sphere of radius R around the nanodiamond is p (b) = � 3 4π 1 R3−r3 ND , rND ≤ b ≤ R 0, otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S13) It can be easily verified that this distribution is normalized, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � R3 d3b p (b) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Direct calculation reveals ⟨Ez⟩ = 0 and therefore σ2 Ez,ion = ⟨E2 z⟩ = 9q2 (4πϵ0)2 1 (2ϵe + ϵND)2 1 R3 − r3 ND � 1 rND − 1 R � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S14) Under the assumption that the electric fields generated by the single ions are uncorrelated, the total fluctuations are given by multiplying the above expression with the number of ions inside the sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The standard deviation σ2 Ez = cNAV σ2 Ez,ion of the electric field components with NA Avogadro’s number, c the molar ionic concentration and V the volume in which the ions reside therefore is σEz = |q| ϵ0 (2ϵe + ϵND) � 3NA 4π � c � 1 rNV − 1 R � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S15) From this it can be seen that the expected electric field fluctuations increase with the molar concentration, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' σEz ∝ √c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' HAMILTONIAN IN ROTATING FRAME As derived by Doherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' [S3], the Hamiltonian of the NV-center in presence of axial magnetic fields Bz and electric field components Ei with i = x, y, z and ℏ = 1 is ˆHNV = � D + d∥Ez � ˆS2 z + γeBz ˆSz + d⊥ � Ex � ˆS2 y − ˆS2 x � + Ey � ˆSx ˆSy + ˆSy ˆSx �� , (S16) with γe = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='8 MHz/G the NV’s gyromagnetic ratio [S4] and d∥ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='35 Hz · cm/V and d⊥ = 17 Hz · cm/V the axial and transverse dipole moments [S5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' By rewriting this Hamiltonian in terms of its frequency contributions βz = γeBz, ξz = d∥Ez and ξ⊥ = d⊥ � E2x + E2y and by introducing the electric field polarization φE, which defines the transverse electric field projections via ξx = ξ⊥ cos φE and ξy = ξ⊥ sin φE, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S16) can be rewritten as ˆHNV = (D + ξz) ˆS2 z + βz ˆSz − ξ⊥ 2 � eiφE ˆS2 + + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � , (S17) where ˆS± = ˆSx ± i ˆSy are spin-1 ladder-operators and h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' means the hermitian conjugate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 3 The NV-center can be driven by perpendicular (compared to the NV’s symmetry axis) microwave magnetic fields of amplitude Ω = γeBd and frequency ωd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' To exert polarized drives onto the NV-center, two wires which are perpendicular to each other (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1(a) main text) are operated with a phase φ between each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' This drive can be described by an Hamiltonian [S6] ˆHd (t) = Ω � ˆSx cos (ωdt) + ˆSy cos (ωdt + φ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S18) Defining phase-factors ϵ± (φ) = � 1 − ie∓iφ� /2, similarly to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' [S6], allows to compactly account for different polarizations as ϵ+ = 1 only if φ = −π/2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' right-circular polarization) and ϵ− = 1 for left-circular polarized microwave fields (φ = +π/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' By transforming ˆHNV + ˆHd (t) into a frame oscillating with ωd through the unitary U = eiωdS2 z, one can derive the Hamiltonian under the rotating-wave approximation, which is ˆH = ˆH0 + ˆHd ˆH0 = (∆ + ξz) ˆS2 z + βz ˆSz − ξ⊥ 2 � eiφE ˆS2 + + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � ˆHd = Ω √ 2 (ϵ− |0⟩ ⟨−1| + ϵ+ |1⟩ ⟨0| + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S19) A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Derivation of time-evolution operators To allow for the efficient calculation of pulse-sequences, time evolution operators of the free evolution ˆF (τ) and the drive ˆR (T) will be derived in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Free Evolution A possible set of eigenstates of ˆH0 is {|0⟩ , |+⟩ , |−⟩} with |+⟩ = cos θ 2eiφE/2 |1⟩ + sin θ 2e−iφE/2 |−1⟩ |−⟩ = sin θ 2eiφE/2 |1⟩ − cos θ 2e−iφE/2 |−1⟩ , (S20) where tan θ = −ξ⊥/βz, with corresponding eigenenergies ω0 = 0 and ω± = ∆ + ξz ± � β2z + ξ2 ⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The time evolution operator of ˆH0 is ˆF (τ) = � i={0,±} e−iωiτ |i⟩ ⟨i|, where the sum is performed over all eigenstates of ˆH0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' In the basis of {|0⟩ , |±1⟩} this is ˆF (τ) = |0⟩ ⟨0| + e−iτ(∆+ξz)� iξ⊥ x sin (τx) � eiφE |1⟩ ⟨−1| + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � + � cos (τx) − iβz x sin (τx) � |1⟩ ⟨1| + � cos (τx) + iβz x sin (τx) � |−1⟩ ⟨−1| � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S21) Here the frequency of oscillation has been defined as x = � β2z + ξ2 ⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Microwave Drive To derive operators which describe the action of the microwave pulses, it will be assumed that these pulses exceed all other frequency scales in magnitude, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Ω ≫ ∆, βz, ξz, ξ⊥, such that ˆH ≈ Ω √ 2 ˆ� Hd with ˆ� Hd = 4 (ϵ− |0⟩ ⟨−1| + ϵ+ |1⟩ ⟨0| + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' By noting that ˆ� H 3 d = ˆ� Hd, the time evolution ˆR (t) = e−it ˆ Hd = ∞ � k=0 � −itΩ √ 2 �n n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � ˆ� Hd �n , (S22) can be calculated as ˆR (t) = |1⟩ ⟨1| � 1 − |ϵ+|2� + |−1⟩ ⟨−1| � 1 − |ϵ−|2� − ϵ+ϵ− |1⟩ ⟨−1| − ϵ∗ +ϵ∗ − |−1⟩ ⟨1| + cos � tΩ √ 2 � � |0⟩ ⟨0| + |ϵ+|2 |1⟩ ⟨1| + |ϵ−|2 |−1⟩ ⟨−1| + ϵ+ϵ− |1⟩ ⟨−1| + ϵ∗ +ϵ∗ − |−1⟩ ⟨1| � − i sin � tΩ √ 2 � (ϵ− |0⟩ ⟨−1| + ϵ+ |1⟩ ⟨0| + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S23) Depending on the polarization, one can induce Rabi oscillations between |0⟩ and either |−1⟩ for φ = π/2 (denoted as ˆR+) or |+1⟩ (φ = −π/2, ˆR−), ˆR (t)± = |∓1⟩ ⟨∓1| + cos � Ωt √ 2 � � |0⟩ ⟨0| + |±1⟩ ⟨±1| � − i sin � Ωt √ 2 � � |0⟩ ⟨±1| + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S24) The system can be driven to both |±1⟩, if a linearly polarized drive is used, R (t)0 = 1 2 (|1⟩ ⟨1| + |−1⟩ ⟨−1| + i |1⟩ ⟨−1| − i |−1⟩ ⟨1|) + cos � tΩ √ 2 � � |0⟩ ⟨0| + 1 2 (|1⟩ ⟨1| + |−1⟩ ⟨−1| − i |1⟩ ⟨−1| + i |−1⟩ ⟨1|) � − 1 + i 2 sin � tΩ √ 2 � (|0⟩ ⟨−1| + |1⟩ ⟨0| + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S25) The last expression can similarly be compactly written by noting that (1 ± i) /2 = e±iπ/4/ √ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' These operators can then be used to describe the action of (polarized) π- and π/2-pulses onto the |ms = 0, ±1⟩-states of the NV-center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' FOURIER TRANSFORMATION OF FID-SIGNAL Some arbitrary signals f and ˜f in time- and frequency-domain are connected to each other as ˜f (ω) = FT [f (τ)] = � +∞ −∞ dτ f (τ) e−iωτ FT−1 � ˜f (ω) � = 1 2π � +∞ −∞ dω ˜f (ω) eiωτ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S26) To simplify the calculation of the Fourier transformed FID-signal, one can rewrite FIDξ⊥,φE (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (6) main text) as FIDξz,ξ⊥ (τ) = 1 4 �3 2 + 1 2 cos (2τξ⊥) − cos (τ [ξ⊥ + ξz]) − cos (τ [ξ⊥ − ξz]) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S27) From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S26), one sees that FT [cos (τx)] = π [δ (x − ω) + δ (x + ω)] and therefore � FID (ω) = π 4 �3 2δ (ω) + 1 2 [δ (2ξ⊥ − ω) + δ (2ξ⊥ + ω)] − [δ (ξ⊥ + ξz − ω) + δ (ξ⊥ + ξz + ω)] − [δ (ξ⊥ − ξz − ω) + δ (ξ⊥ − ξz + ω)] � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S28) 5 IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' SIMULATED PULSE SEQUENCES FOR NORMALLY DISTRIBUTED ELECTRIC FIELDS FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Simulated expected FID-values of FIDξ⊥ (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (5) main text), calculated from 500 individual FID-simulations with drive amplitude of Ω = 10 MHz, intrinsic T ∗ 2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' and electric field components sampled from a normal distribution with mean Em and standard deviation σE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Dephasing is considered through a Lindblad-Operator � 1/T ∗ 2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' For both mean electric field values of (a) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='0 V/µm and (b) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='0 V/µm, it is not possible to resolve ξ⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' To understand how fluctuating electric fields alter the FID-signal, we numerically [S7, S8] simulated FIDξ⊥ (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (5) main text) for normally distributed electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Hereby, at every timestep at which the time-evolution is calcuated, the electric field components are passed from a beforehand sampled normal distribution with mean Em and standard deviation σE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' It can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' S1 that the average FIDξ⊥ signal decays rapidly to its steady-state value of 1/2, which is due to the short T ∗ 2 time of 1 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' For this reason it is proposed to use the Hahn-Echo pulse sequence for measurements of strongly fluctuating electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 0 50 100 150 200 τ in µs 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='8 ⟨Hahn (τ)⟩ Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Fit FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Example of the average Hahn-echo signal, which was obtained numerically from 1000 individual simulations of the pulse sequence shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 3(a) (main text) with a mean electric field value of Em = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='0 V/µm, standard deviation σE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='75 V/µm, drive amplitude Ω = 10 MHz and intrisic T2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' = 100 µs together with the fit following Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (10) (main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' The total T2 value obtained from this fit is T2 = (39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content='86) µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' As described in the main text, the numerically obtained Hahn-echo trajectories (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' S2 for an example) are well fitted by ⟨Hahn (τ)⟩ = 1 4 � 1 − cos (2τξ⊥) e−τ/T2�2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Here both the intrinsic T2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' = 100 µs and T2,E due to fluctuating elecric fields contribute to the total T2 via 1 T2 = 1 T2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' + 1 T2,E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S29) The latter can be fitted in terms of Em and σE via T2,E = αEm σ2 E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S30) The values of the fit parameter α can be found in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 6 1 2 Em in V/µm 30 35 40 α FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' Fit parameter α, obtained by numerically fitting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S29) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' (S30) with T2,int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' = 100 µs to the data from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' 3 (main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE3T4oBgHgl3EQfSAk3/content/2301.04427v1.pdf'} +page_content=' [S1] R.' metadata={'source': 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