![NV center properties. (a) Nitrogen-Vacancy center hosted in the diamond lattice. Nitrogen is represented by a blue sphere, carbon vacancy by a white sphere, carbon atoms by black spheres. The ⟨100⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 100\rangle$$\end{document}, ⟨110⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 110\rangle$$\end{document} and ⟨111⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 111\rangle$$\end{document} crystallographic directions are also indicated. (b) NV center energy levels. Green arrows represent the non-resonant optical pumping from the ground state (G.S.) to the excited state (E.S.). Red arrows represent the radiative transitions; the width of the arrow is qualitatively related to the PL emission rate. Black dashed arrows represents the ISC process through the metastable state (M.S). The transition from the E.S. 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| 0\right\rangle$$\end{document} spin sublevel to the M.S. is 10 times less probable than the one from the ±1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| \pm 1\right\rangle$$\end{document} spin sublevels and it is not represented²⁰. D = 2.87 GHz is the ground state zero field splitting. (c) NV center ground state spin sublevels without (left) and with (right) an external static magnetic field applied. The ODMR spectrum is also represented. ν±=|D±γBNV|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _\pm =|D\pm \gamma B_{NV}|$$\end{document} are the resonance frequencies of the 0→±1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| 0\right\rangle \rightarrow \left| \pm 1\right\rangle$$\end{document} transitions. (d) ODMR spectrum of an ensemble of NV centers. Eight peaks, two for each of the four NV center families, are visible.](https://www.researchgate.net/publication/380821673/figure/fig1/AS:11431281246908482@1716520870480/NV-center-properties-a-Nitrogen-Vacancy-center-hosted-in-the-diamond-lattice-Nitrogen_Q320.jpg)
![Experimental set-up. (a) The linearly polarized laser enters the diamond sample through a {110} plane. A half-wave (λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uplambda$$\end{document} /2) plate allows turning its polarization. The PL is collected from the lateral {100} facet by means of an imaging system composed of a microscope objective, a polarizer, a filter, a lens and a camera. The RF field is brought in proximity of NV centers by means of a coplanar waveguide (CPW) on the top of which the diamond sample is glued. The orientation of the NV center families with respect to the diamond {110} top face are represented with the help of wedge-dash diagrams. Solid lines represent in-plane bonds; dashed lines represent bonds pointing out of the plane away from the viewer; wedge-shaped lines represent bonds pointing out of the plane toward the viewer. Line colors identify NV center families. (b) NV centers orientations with respect to the {100} facet from which the PL is collected. ⟨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle$$\end{document}100⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rangle$$\end{document} and ⟨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle$$\end{document}110⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rangle$$\end{document} diamond crystallographic directions are also represented by, respectively, dashed red lines and dotted blue lines. (c) NV center orientations with respect to the {110} facet from which the laser excitation is performed. ⟨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle$$\end{document}100⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rangle$$\end{document} and ⟨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle$$\end{document}110⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rangle$$\end{document} diamond crystallographic directions are indicated using the same legend as (b). ⟨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle$$\end{document}111⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rangle$$\end{document} directions are indicated by dash-dotted lines. (d) Normalized ODMR spectrum of the NV center ensemble under analysis. The fit (red line) is performed using Eq. (19). The identification between the NV center families and the ODMR peaks is detailed in section “Identification between ODMR peaks and NV center families”.](https://www.researchgate.net/publication/380821673/figure/fig2/AS:11431281246908483@1716520870658/Experimental-set-up-a-The-linearly-polarized-laser-enters-the-diamond-sample-through-a_Q320.jpg)
![ODMR contrast and sensitivity dependence on polarizer axis and laser polarization. (a–d) Measurement (a) and simulation (b) of the relative contrast, ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uprho$$\end{document} (c) and χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upchi$$\end{document} (d) parameters of the four NV center families for different angles of the polarizer. Error bars result from the error propagation of the fit errors (estimated considering a 95% confidence interval) of the contrast of each of the eight ODMR peaks. According to Fig. 2, A and D are the families whose 0→-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| 0\right\rangle \rightarrow \left| -1\right\rangle$$\end{document} transition resonates respectively at the lower and higher frequency. For the experimental results, the zero of the polarizer axis is arbitrarily chosen. For the simulation, it corresponds to the x axis of the laboratory reference frame (Fig. 2b). Shadow areas are added a posteriori to match the measurement with the simulation. (e–h) Measurement (e) and simulation (f) of the relative contrast, ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uprho$$\end{document} (g) and χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upchi$$\end{document} (h) parameters of the four NV center families for different laser polarizations. In the simulation the zero of the laser polarization corresponds to the z-axis of the laboratory frame (Fig. 2c). In Data the zero of the fast axis of the half-wave plate is set, with an accuracy of some degree, along the y axis of the laboratory frame (Fig. 2a). Shadow areas are added a posteriori to match the measurement with the simulation. Error bars are defined as in (a) and (c). The large error bar for values of R and χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upchi$$\end{document} close to zero is due to difficulties in doing the fit when the contrast is lower than the signal-to-noise ratio of the measurement. The plot is cut for values smaller than zero since they have no physical meaning.](https://www.researchgate.net/publication/380821673/figure/fig3/AS:11431281246918274@1716520870893/ODMR-contrast-and-sensitivity-dependence-on-polarizer-axis-and-laser-polarization-a-d_Q320.jpg)
![Measurement (a) and simulation (b) of the relative contrast of the four NV center families for different angles of the polarizer when the PL is collected from the top {110} diamond facet and the laser field is polarized along a ⟨100⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 100\rangle$$\end{document} direction, as for Fig. 3a, b. The color code is the same as in Fig. 2. For the experimental results, the zero of the polarizer axis is arbitrarily chosen. For the simulation, it corresponds to the x axis of the laboratory reference frame (Fig. 2b). Shadow areas are added a posteriori to match the measurement with the simulation.](https://www.researchgate.net/publication/380821673/figure/fig4/AS:11431281246918275@1716520871123/Measurement-a-and-simulation-b-of-the-relative-contrast-of-the-four-NV-center_Q320.jpg)
![(a) Detected PL for different orientations of the polarizer axis. (b) Simulation of S0 (eq. (6)) for different orientations of the PL polarization. (c) Detected PL for different orientations of the λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uplambda$$\end{document}/2 axis. (d) Simulation of S0 (Eq. (6)) for different orientations of the laser polarization.](https://www.researchgate.net/publication/380821673/figure/fig5/AS:11431281246918276@1716520871303/a-Detected-PL-for-different-orientations-of-the-polarizer-axis-b-Simulation-of-S0_Q320.jpg)
May 2024
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The negatively charged nitrogen-vacancy center (NV) presents remarkable spin-dependent optical properties that make it an interesting tool for magnetic field sensing. In this paper we exploit the polarization properties of the NV center absorption and emission processes to improve the magnetic sensitivity of an ensemble of NV centers. By simply equipping the experimental set-up of a half-wave plate in the excitation path and a polarizer in the detection path we demonstrate an improvement larger than a factor of two on the NV center magnetic sensitivity.
![(a) NV center in the diamond lattice. The blue sphere represents the nitrogen atom, the white sphere the associated carbon vacancy and the black spheres are the carbon atoms. (b) NV center energy levels. (c) NV center transition rates [10, 11]. k ij corresponds to the transition rate from level i to level j, according to the level numbering defined in (b).](https://www.researchgate.net/publication/377544733/figure/fig1/AS:11431281223114933@1707544270292/a-NV-center-in-the-diamond-lattice-The-blue-sphere-represents-the-nitrogen-atom-the_Q320.jpg)
![Fig. 2 Q-DiSA set-up and calibration procedure. a Q-DiSA set-up. The inset shows a zoom of the {110} facet from which the PL (red color) is collected when the diamond is shined by the laser source (green color). The magnetic field B generated by the spherical magnet is aligned along one of the two NV center families laying on the {110} plane. b CW-ODMR of the 0 j i ! À1 j i transition for a magnet-diamond distance of ~2 mm. The resonance frequencies of the imaged NV centers are in the range [8.5 GHz; 10 GHz]. c Normalized PL acquired by the camera in the presence of a monochromatic MW signal at 9.5 GHz (top) and 9 GHz (bottom). d Comparison between the spectrum obtained considering only one row of pixels (y = 45, blue curve), and a sum over 40 rows (y from 20 to 60, red curve) showing a strong SNR improvement resulting from the summing procedure. e SNR of the PL integrated over a different number of non-resonant pixels. The signal is defined as the temporal mean of the PL; the noise is its standard deviation. The SNR increases linearly when the PL is integrated over a small number of pixels; the non linear behavior of the SNR for integration areas bigger than 40 pixels is mainly due to the inhomogeneity of the laser beam.](https://www.researchgate.net/publication/362295823/figure/fig1/AS:1182637523775488@1658974166214/Q-DiSA-set-up-and-calibration-procedure-a-Q-DiSA-set-up-The-inset-shows-a-zoom-of-the_Q320.jpg)
![Figure 2: Q-DiSA set-up and calibration procedure. (a) Q-DiSA set-up. The inset shows a zoom of the 110 facet from which the PL is collected. The magnetic field B generated by the spherical magnet is aligned along one of the two NV center families laying on the 110 plane. (b) CW-ODMR of the |0 → |−1 transition for a magnet-diamond distance of approximately 2 mm. The resonance frequencies of the imaged NV centers are in the range [8.5 GHz; 10 GHz]. (c) Normalized PL acquired by the camera in the presence of a monochromatic MW signal at 9.5 GHz (top) and 9 GHz (bottom). (d) Comparison between the spectrum obtained considering only one row of pixels, (y=45, blue curve) and a sum over 50 rows (y from 10 to 60, orange curve) showing a strong SNR improvement resulting from the summing procedure. (e) SNR of the PL integrated over a different number of non-resonant pixels. The signal is defined as the temporal mean of the PL; the noise is its standard deviation. The SNR increases linearly when the PL is integrated over a small number of pixels; the non linear behaviour of the SNR for integration areas bigger than 40 pixels is mainly due to the inhomogeneity of the laser beam.](https://www.researchgate.net/publication/361300454/figure/fig1/AS:1167091990310913@1655267822850/Q-DiSA-set-up-and-calibration-procedure-a-Q-DiSA-set-up-The-inset-shows-a-zoom-of-the_Q320.jpg)
