Sensor comprising a piezomagnetic or piezoelectric element on a diamond substrate with a colour centre

Abstract

A sensor (1, 2, 3, 4, 5, 6, 7, 8) comprising a first diamond substrate (9) with at least one color center (15), the sensor (1, 2, 3, 4, 5, 6, 7, 8) further comprising a first piezomagnetic (10) or piezoelectric primary element (11), which primary element (10, 11) is arranged to interact with the color center(s) (15) of the first diamond substrate (9).

Claims

1. A sensor comprising a first diamond substrate with at least one colour centre, wherein the sensor further comprises a first piezomagnetic or piezoelectric primary element, which primary element is arranged to interact with the colour centre(s) of the first diamond substrate solely by means of either a stray electric field or stray magnetic field produced by the primary element.

2. The sensor according to claim 1, wherein the sensor comprises several diamond substrates, each substrate comprising at least one colour centre.

3. The sensor according to claim 1, wherein the sensor comprises several primary piezomagnetic or piezoelectric elements arranged to interact with colour centre(s) of the diamond substrate(s).

4. The sensor according to claim 1, wherein the colour centre(s) is/are nitrogen vacancy centre(s).

5. The sensor according to claim 1, wherein the primary piezomagnetic or piezoelectric element(s) is/are arranged to interact with the colour centre(s) of the substrate(s) magnetically or electrically.

6. The sensor according to claim 1, wherein the primary element(s) is/are piezomagnetic element(s) comprising a solid ferrite material.

7. The sensor according to claim 1, wherein at least part of the first primary element extends as a layer across at least part of a surface of the first diamond substrate.

8. The sensor according to claim 1, wherein the sensor further comprises a first secondary element which is arranged to interact with the first piezomagnetic or piezoelectric primary element.

9. The sensor according to claim 8, wherein the sensor comprises several secondary elements, each arranged to interact with the primary element(s).

10. The sensor according to claim 8, wherein the first secondary element forms an island in or on the first primary element.

11. The sensor according to claim 8, wherein the secondary element(s) is/are piezoelectric.

12. The sensor according to claim 8, wherein the secondary element(s) is/are thermally sensitive.

13. A method in which a change in a first piezomagnetic or piezoelectric primary element is detected by means of detecting a corresponding change in at least one colour centre of a first diamond substrate, which colour centre(s) interact with the first primary element solely by means of either a stray electric field or stray magnetic field produced by the first primary element.

14. The method of claim 13, wherein the change in at least one colour centre is a change in an electric spin of the colour centre(s).

15. The method of claim 13, wherein the method involves optical detection of the magnetic resonance of the colour centre(s).

16. The method of claim 14, wherein the electric spin is polarized by means of optical pumping.

17. The method of claim 13, wherein the change in the colour centre(s) detected is the chance in the colour centre(s) fluorescence.

18. The method of claim 14, wherein the spins are measured with a pulse sensing scheme which is achieved by a microwave field.

19. The method of claim 13, wherein the colour centre(s) are exposed to a microwave field.

20. The method of claim 13, wherein the change in a first piezomagnetic or piezoelectric primary element is induced by a force or a change in a force applied to the first piezomagnetic or piezoelectric primary element.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is illustrated in greater details with the aid of schematic drawings:

(2) FIG. 1a schematically shows in cross-sectional view the structure of (a) a force sensor according to the invention using a piezomagnetic primary element;

(3) FIG. 1b schematically shows in cross-sectional view a force sensor according to the invention using a piezoelectric primary element;

(4) FIG. 1c schematically shows in cross-sectional view an electric field sensor according to the invention using a piezoelectric secondary element and a piezomagnetic primary element;

(5) FIG. 1d schematically shows in cross-sectional view a temperature sensor according to the invention using a thermally sensitive secondary element and a piezomagnetic primary element;

(6) FIG. 1e schematically shows in cross-sectional view of hybrid sensors (i.e. the sensors of FIG. 1a to FIG. 1d) array, thereby obtaining a spatially resolved sensor.

(7) FIG. 2a shows in cross-sectional view a spatially resolved force sensor according to the invention comprising a piezomagnetic primary element layer and a diamond layer that contains an array of colour centres;

(8) FIG. 2b shows in cross-sectional view a spatially resolved electric field sensor according to the invention comprising a piezomagnetic primary element layer, a piezoelectric secondary element island and a diamond layer that contains an array of colour centres;

(9) FIG. 2c shows in cross-sectional view a spatially resolved temperature sensor according to the invention comprising a primary element layer adjacent to the diamond substrate, a thermally sensitive secondary element island and a diamond layer that contains an array of colour centers;

(10) FIG. 3 shows on the left an optical microscope image of the microwave resonator structure on glass used in magnetic resonance experiments; On the right, an image of the holder with the strip structure is displayed;

(11) FIG. 4a shows a conceptual representation of an experimental setup for the optical pumping and optical detection of the electron spin of the NV centre;

(12) FIG. 4b shows a confocal map of single NV centres adjusted to a microwave strip line;

(13) FIG. 5 shows a photograph of the magnet stage with a cylindrical magnet attached;

(14) FIG. 6a illustrates the ground spin level structure of a single NV centre, which is a spin triplet (|1>, |0>, and |1>), with a 2.87 GHz crystal field splitting. A Zeeman shift gives rise to the splitting of |1> and |1>. By applying an excitation (green) light with a wavelength of about 530 nm, the NV centre exhibits spin-dependent photo-luminescence near the zero phonon line at the wavelength about 638 nm even at room temperature. This allows for optical pumping and optical detection of the NV centre spin state;

(15) FIG. 6b shows the pulse sequence that is used to measure the response of single NV centres to the external parameters, such as pressure, magnetic field, electric field, and temperature. The NV centre spin is initialized by optical pumping with a green laser; which is further prepared into a coherent superposition of |1> and |1> with microwave field manipulation. After a free evolution time t, the phase information resulting from external signals is mapped back to spin state population with microwave field manipulation, which is then readout by optical detection with a green laser;

(16) FIG. 6c shows the separation between two resonance frequencies in the ODMR spectra as a function of the pressure a;

(17) FIG. 6d shows the signal as a function of the applied uniaxial stress a at the acquisition time ta; and

(18) FIG. 6e shows the shot-noise-limited sensitivity for the measurement of stress and force as a function of interrogation time.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

(19) Diamond Material

(20) Bulk diamond grown using high pressure high temperature (HPHT) method or chemical vapour deposition techniques as well as diamond nanocrystals can be employed for the invention. Doping of diamond with NV centres can be performed by electron irradiation of nitrogen containing diamond and implantation of nitrogen with subsequent annealing. Isotopic enrichment of diamond provides for a prolongation of the coherence time of NV centres but sensing experiments can also be performed in diamond crystals with different isotopic content (including natural abundance). A layer of NV centres at a controllable distance to the interface (with an depth uncertainty of 1-2 nm) in a synthetic diamond is created by nitrogen delta-doping, as described in David D. Awschalom et al. Engineering shallow spins in diamond with nitrogen delta-doping, Appl. Phys. Lett. 2012, vol. 101, pp. 082413. The method is described in detail on page 1 and in the left column of page 2, which are incorporated into the present disclosure by way of reference. Note that the lateral positions of NV centres are not necessary to be in a regular lattice in order to gain the collective enhancement of measurement sensitivity.

(21) Fabrication of Hybrid Diamond-Piezo Sensing Devices

(22) Piezo-active thin films, i.e. piezomagnetic or piezoelectric thin films are deposited on the substrate of diamond with the methods of sputter deposition, such as radio frequency magnetron sputtering. The process is similar to the deposition of piezo-active thin films on other substrates, such Si and LaAlO.sub.3. A suitable method of sputter deposition is disclosed by M. Ohring et al. in Materials Science of Thin Films: Deposition and Structure, Academic Press, 2002. The method is described in detail in this paper's Chapter 5 (pages 205 to 230), which is incorporated into the present disclosure by way of reference.

(23) Piezo-active thin films may also be grown on single-crystal diamond by means of chemical vapour deposition. A suitable method is similar to the method used to grow zinc oxide (ZnO) thin films on diamond surface to fabricate surface acoustic wave device, as disclosed by B. Zhao et al. in Preparation and optimization of ZnO films on single-crystal diamond substrate by metal-organic chemical vapour deposition, Semicond. Sci. Technol. 19, 770, 2004. The method is described in detail in this paper's Experiments section (page 771), which is incorporated into the present disclosure by way of reference. However, in the method used for depositing a piezo-active film to manufacture a sensor according to the present invention, in the step of LP-MOCVD the precursors of diethyl zinc (DEZn) and O.sub.2 for ZnO films are replaced by the ones for the specific piezo-active elements accordingly.

(24) Piezoelectric and thermally active islands are fabricated by cutting thin films using, e.g., focused ion-beam patterning, photolithography, electron-beam lithography or other methods known to the skilled person. A suitable method of focused ion-beam patterning is disclosed by S. Bilhlmann et al. in Size effect in mesoscopic epitaxial ferroelectric structures: Increase of piezoelectric response with decreasing feature size, Appl. Phys. Lett. 80, 3195, 2002. The method is described in detail in this paper's paragraph 3 (on page 3195), which is incorporated into the present disclosure by way of reference. A suitable photolithographic method is disclosed by K. Lee et al. in Two-dimensional planar size effects in epitaxial PbTiO3 thin films, Appl. Phys. Lett. 85, 4711, 2004. The method is described in detail in this paper's Paragraphs 4-5 (on page 4711), which is incorporated into the present disclosure by way of reference. A suitable method of electron-beam lithography is disclosed by Chia-Wen Wu et al. in Electron-beam lithography assisted patterning of surfactant-templated mesoporous thin films, Nanotechnology 15, 1886-1889 2004. The method is described in detail in this paper's Experiments section (pages 1887), which is incorporated into the present disclosure by way of reference.

(25) Overview of the Experimental Setup

(26) FIGS. 1a to 2c conceptually detail embodiments of sensors 1, 2, 3, 4, 5, 6, 7, 8 comprising a diamond substrate layer 9 and a piezomagnetic 10 or piezoelectric primary element layer 11, which in some embodiments is provided with a piezoelectric 12 or thermally sensitive secondary element island 13. The primary element layer is exposed to the magnetic field of a permanent magnet 14 as shown in FIG. 5. The diamond layer 9 contains a colour centre 15, which is an NV centre. A laser serves to polarize and read a colour centre's 15 spin. In order to move the diamond into the focus of the laser, the diamond or microscope objective lens is mounted on a piezo stage (not shown). The magnet 14 is mounted on rotation/translation stages of vector electromagnet (not shown) are used for alignment of the magnetic field with the crystallographic axis of the colour centre. FIG. 3 shows a microwave source used for the ODMR measurements and the coherent manipulation of the colour centre spin. The principle of the ODMR measurement is sketched in FIG. 4a. The colour centre 15 is exposed to (typically green) laser light 16 and the colour centre's 15 fluorescence light 17 is detected by means of photo detectors 18. A fluorescence image of a diamond substrate on top of the 4-strip microstructure is shown in FIG. 4b. On the top and the bottom of the image, one strip is displayed each. Between the strips, the diamond area can be seen. Bright spots correspond to the fluorescence emissions of NV centres.

(27) Force Sensor Using Piezomagnetic Substrate

(28) A sensor 1 according to the invention which can be used for measuring a force or pressure is shown in FIG. 1a. The device consists of a diamond substrate layer 9 with implanted NV centres 15 and a piezomagnetic element layer 10 directly adjacent and in contact to the diamond substrate layer 9. The response of the piezomagnetic layer 10, which has large magnetostriction, to a mechanical force or pressure leads to the change of the magnetization directions of magnetic domains of the piezoelectric material, and in turn to a change in the stray magnetic field that affects the energies of the ground spin levels of NV centres 15. A bias magnetic field is applied to piezomagnetic element layer 10 in order to render it more sensitive to pressure.

(29) The spin-dependent fluorescence of the NV centre spins provides an efficient mechanism to perform optically detected magnetic resonance (ODMR) measurements in the ground state. The effect of pressure or force on the primary element layer, and thereby the value of force or pressure, is determined by the resonance frequencies in ODMR spectra. A suitable method of ODMR measurements of NV centre spin is described in A. Gruber et al. Scanning Confocal Optical Microscopy and Magnetic Resonance on Single Defect Centers, Science 1997, vol. 276, pp. 2012 to 2014. The method is described in detail in this paper's paragraph 3 (on page 2013), which is incorporated into the present disclosure by way of reference.

(30) An alternative method of using NV spin as a magnetometer to measure a magnetic field is a pulsed sensing scheme as describe in J. R. Maze et al. Nanoscale magnetic sensing with an individual electronic spin in diamond, Nature 2008, vol. 455, pp. 644 to 647. The method is described in detail in this paper's FIG. 1 including the figure caption on page 645, the methods summary on page 647 and the publication's Methods supplement (lacking a page number), which are incorporated into the present disclosure by way of reference. The NV spin is first prepared into a coherent superposition state of two ground spin-sublevels by applying a microwave field. The energies of the ground spin-sublevels, which show dependence on the applied stress on the piezomagnetic layer, result in a dynamical phase and are measured via optical fluorescence of NV spin.

(31) Force Sensor Using Piezoelectric Substrate

(32) Another sensor 2 according to the invention which can be used for measuring a pressure or a force is shown in FIG. 1b. This device comprises piezoelectric element layer 11 directly adjacent and in contact to of the diamond substrate layer 9 with implanted NV centres 15. The response of the piezoelectric layer 11, which has a large piezoelectric constant, to a force or pressure leads to the change of the charge distribution within the piezoelectric material and in turn to a change in the stray electric field that affects the energies of the ground spin levels of NV centres as determined by ODMR scheme or pulsed magnetic sensing scheme. The value of force or pressure is thereby obtained from the stray electric field. The method relies on the measurement of stray electric field with a single NV spin sensor as described in F. Dolde et al. Electric-field sensing using single diamond spins, Nature Physics 2011, vol. 7, pp. 459 to 463. The method is described in detail in this paper's FIGS. 1 and in 3 including the figure captions and in the methods section (pages 462), which are incorporate into the present disclosure by way of reference relevant portions of which are incorporated into the present disclosure by way of reference.

(33) Electric Field Sensor

(34) FIG. 1c shows a sensor 3 similar to the one in FIG. 1a but for the measurement of an electric field. For this, the sensor 3 comprises in addition to the piezomagnetic primary element layer 10 and a diamond substrate layer 9 containing NV centres 15 a piezoelectric secondary element island 12 provided in avoid of the primary element layer 10. An internal mechanical strain in the piezoelectric element island 12 is generated from an applied electrical field. The electric-field-induced strain generates a force which is transduced to the piezomagnetic element layer 10 generates a magnetic field, and is detected in the diamond substrate's 9 NV centres 15. The sensor 3 can be used for the sensing of a remote elementary charge (e.g. a single electron).

(35) Temperature Sensor Using a Thermally Sensitive Island

(36) FIG. 1d shows a sensor 4 for measuring the temperature. It comprises a thermally sensitive secondary element island 13, a piezomagnetic primary element layer 10 and a diamond substrate layer 9 containing NV centres 15. A change in temperature leads to the thermal expansion of thermal sensitive element island 13. The thermally induced strain generates a force which is transduced to the piezomagnetic element layer 10 generates a magnetic field, and is detected in the diamond substrate's 9 NV centres 15. This can solve the problem, according to the invention, of providing a sensitive transducer for various physical parameters, such as magnetic field, electric field, pressure (force) and temperature. Possible applications of temperature sensing include, the observation of chemical reactions at the nanoscale, or the observation of temperature inside cells to monitor biological processes at the nanoscale.

(37) Spatially Resolved Force Sensor

(38) FIG. 2a shows a spatially resolved force sensor 6 according to the invention comprising a diamond substrate 9 with a two-dimensional array of NV centres 15, a piezomagnetic primary element layer 10 and a diamond layer containing an array of colour centres 15. With this sensor 6, a force or pressure distribution on the surface of the sensor can be measured.

(39) Spatially Resolved Electric Field Sensor

(40) FIG. 2b shows a spatially resolved electric field sensor 7 according to the invention comprising a diamond substrate layer 9 with a two-dimensional array of NV centres 15, a piezomagnetic primary element layer 10, a piezoelectric secondary element island 12, the diamond layer 9 containing an array of colour centres.

(41) Spatially Resolved Temperature Sensor

(42) FIG. 2c shows in cross-sectional view a spatially resolved temperature sensor 8 according to the invention comprising a diamond substrate layer 9 with a two-dimensional array of NV centres 15, a primary element layer 10 adjacent to the diamond layer 9, and a thermally sensitive secondary element island 13 the diamond layer 9 containing an array of colour centres.

(43) A layer of NV centres in a synthetic diamond is created with nitrogen delta-doping, as described in David D. Awschalom et al. Engineering shallow spins in diamond with nitrogen delta-doping, Appl. Phys. Lett. 2012, vol. 101, pp. 082413. A diamond with a lateral surface area above 1 mm.sup.2, in which the NV spins (with the number on the order of 10.sup.9) in the entire diamond increases the sensitivity for the overall pressure measurement by at least a factor of 10.sup.4.

(44) Sensor Arrays

(45) The sensors 1, 2, 3, 4 of FIGS. 1a to 1d can be combined into arrays, thereby obtaining a spatially resolved sensor array 19. For example, by combining the sensors 1, 2 of FIG. 1a or 1b, a surface pressure collector can be created. When combining the sensor 1, 2, 3, 4 into a sensor array, each individual sensor can have its own substrate 9, primary element layer 10, 11 and possibly secondary element islands 12, 13 (FIG. 1e). To physically combine them into an array, they a mounted on a common substrate 20; suitable substrates are known to the skilled person.

(46) It is an achievable advantage of the spatially resolved sensors 6, 7, 8 and the sensor array 19 discussed above that they are scalable, i.e. that in principle an unlimited number of sensing units (In the case of FIGS. 2a to 2c) or sensors 1, 2, 3, 4 (in the case of FIG. 1) can be combined with each other. This can solve the problem of integration of pressure sensors towards applications such as tactile imaging, electronic skin, and interactive input/control devices. Such surface pressure collector can be used to detect acoustic and vibrational motion, detect the Casimir effect where minute forces have to be measured at smallest distances (below 100 nm), and to study fundamental quantum physics phenomena.

(47) Detection Scheme Based on Optically Detected Magnetic Resonance (ODMR)

(48) In the present embodiments, single NV centres are detected using a confocal microscopy technique. A laser beam diode pumped solid state laser operating at 532 nm is focussed onto a diffraction limited spot using a high numerical aperture microscope objective (Olympus UPLAPO 60). The sample is scanned using a piezo driven stage (nPoint, Inc.). Fluorescence is collected by the same microscope objective and focussed on avalanche photodiodes with single photon sensitivity (SPCM-AQRH, Excelitas). By observation of photon-antibunching, it can be detected that an individual NV centre is in focus. Fluorescence detection of magnetic resonance on single electron spin is based on optical contrast of spin states associated with NV centres. The method of side-collection spin-dependent photoluminescence as developed in D. Le Sage et al. Efficient photon detection from colour centres in a diamond optical waveguide, Phys. Rev. B 85, 121202(R) (2012), is used for improve the optical detection efficiency. The method is described in detail on pages 1 and 2 of the publication, which are incorporated into the present disclosure by way of reference.

(49) Initialization of NV Centre Electron Spin

(50) Electron spins associated with NV centres are polarised by the application of a short (300 ns) laser 4 pulse. Optical pumping is achieved by excitation of the NV centre into an excited electronic state. The decay of this state occurs predominantly into one of the spin sublevels of the ground state.

(51) Microwave Excitation for Coherent Manipulation of NV Centre Electron Spin

(52) In order to excite microwave transitions of single colour centres in diamond, the sample is placed on a home built microwave strip line providing efficient excitation of the diamond. At the top in FIG. 3, an optical microscopic picture of the structure is shown, which is fabricated on a glass cover slip by conventional photolithography and is used in the magnetic resonance experiments. The width and gap of each microstrip is 20 m. At the bottom in FIG. 3, a picture of the holder with the strip line can be seen. The signal is applied via coaxial cables connected to SMA connectors and matched to the two coplanar microstrips.

(53) A commercial microwave source (Anritsu MG 37020A) is used in the experiments. In order to achieve Rabi frequencies of a few MHz, the source is amplified using a commercial high power microwave amplifier (10 W, Gigatronics GT 1000A). Phase control of microwave fields is achieved using commercially available phase shifters (Narda, Inc.). Microwave pulses are formed using commercial microwave switches (General Microwave, F9914). The strength of the microwave drive is controlled by the output level of the microwave source.

(54) Time Resolved Measurements

(55) Optical pulses for optical spin polarisation and time resolved detection of magnetic resonance are produced using acousto-optical modulators (Crystal Technology). Microwave, optical pulses, sample scanning and data acquisition is synchronised by a computer controlled pulse generator (Tektronix, DTG) connected to drivers of acousto-optical modulators, microwave switches and a fast photon counter (FastComtec, P7998).

(56) The optical detection of magnetic resonance is carried out in accordance with the scientific publications Jelezko, F. et al., Single defect centres in diamond: A review. Physica Status Solidi (a) Applications and Materials Science, 2006. 203(13): pages 3207 to 3225, Jelezko, F. et al., Read-out of single spins by optical spectroscopy., Journal of Physics-Condensed Matter, 2004. 16(30): pages R1089 to R1104 and Jelezko, F., et al., Observation of coherent oscillations in a single electron spin, Physical Review Letters, 2004. 92(7), the relevant portions of which are incorporated into the present disclosure by way of reference.

(57) Magnetic Field Control

(58) A magnetic field on the order of up to 1 T is generated by a permanent magnet 14 (magnets4you GmbH) located about 100 m from the diamond face. In order to align the magnetic field with the crystallographic axis (z-axis) of the NV defect, the magnet is moved using rotation and translation stages 21 (Micos GmbH) as shown in FIG. 5.

(59) Sensing of Pressure Response of the Piezo Elements Layers

(60) The ground .sup.3A.sub.2 level of the NV spin exhibits a zero field splitting of D=2.87 GHz between the m.sub.s=0 and m.sub.s=1 spin sub-levels. The ground spin level structure is illustrated in FIG. 6a. The spin Hamiltonian, including the Zeeman interaction with an external magnetic field, and the coupling with an external electric field, is given by
H=(D+d.sub.gs.sup.//E.sub.z)[S.sub.z.sup.2S(S+1)]d.sub.gs.sup.[E.sub.x(S.sub.xS.sub.y+S.sub.yS.sub.x)+E.sub.y(S.sub.x.sup.2S.sub.y.sup.2)]+(B.sub.xS.sub.x+B.sub.yS.sub.y+B.sub.zS.sub.z),(1)
where is the electron gyromagnetic ratio, B.sub.x,y,z and E.sub.x,y,z represent the three components of the magnetic field and the electric field, which arise from both the applied external magnetic/electric field and the stray magnetic/electric field generated by the piezomagnetic film. The effect of the strain on the NV centre, as quantified by E, induces ground state spin sub-level mixing and is usually much smaller (on the order of MHz) than the energy splitting along the NV axis.

(61) The resonance frequencies .sub.1 in the optically detected magnetic resonance (ODMR) measurements spectra correspond to the electronic transitions from the spin sub-level m.sub.s=0 and m.sub.s=1 respectively, which depend on the magnetic field acting on the NV centre. FIG. 6c shows one example of the response of the ODMR resonance spectra of the NV spin under a weak pressure (sub-MPa). The separation A between two resonance frequencies in the ODMR spectra as a function of the stress a is shown. The value of is 15.55 GHz for =0. The dimension of the Terfenol-D film is chosen as (15 nm).sup.3, and the distance from the NV centre to the interface is d=15 nm. The applied external magnetic field is B.sub.0=2350 G along the 001 direction, and the stress is along the 111 direction. The temperature is 300K.

(62) In the pulse-sensing scheme, an example of which is illustrated in FIG. 6b, the nitrogen-centre electronic spin is first prepared into a coherent superposition state |={square root over ()}(|1+|+1) by applying a microwave field H.sub.d=[ cos(.sub.+1t)|+10|+cos(.sub.1t)|10|]+h. c. for a duration t.sub./2=/. The ideal evolution of the NV centre spin is |=(|1+e.sup.it|+1), where is the frequency difference of the resonance in ODMR spectra. For the NV centre spin in isotopically engineered diamond, the magnetic noise from the .sup.13C nuclear spin bath is negligible, and the dominant magnetic noise in the present model arises from the fluctuation in the piezo element layers.

(63) The real dynamics of the NV centre spin under the environmental noise is described by the master equation as follows

(64) $\begin{array}{cc}\frac{d}{dt}=-i\left[H,\right]+{}_z\left(0\right)\left(,s_z\right)+{.Math.}_{k=1}{}_{}\left({}_k\right)\left(,s_{0k}\right)& \left(2\right)\end{array}$
where .sub.(.sub.k) and .sub.z(0) represent the power spectra of the magnetic noise parallel and perpendicular to the NV axis, (,s.sub.z)=s.sub.zs.sub.z with s.sub.z=|+1+1||11|, and (,s.sub.0k)=L(,|k0|)+L(,|0k|) with L(,A)=AA.sup.(A.sup.A+A.sup.A). The spin state of the NV center after a free evolution time t is given by the solution of the master equation in Eq. (2):

(65) $\begin{array}{cc}\left(t\right)=\left(\begin{array}{ccc}{p}_{-1}& 0& q\\ 0& p_0& 0\\ q^{*}& 0& \frac{1}{2}\end{array}\right)& \left(3\right)\end{array}$
where

(66) $p_{-1}=\frac{1}{4}\left[1+e^{-t{}_{}\left({}_{-1}\right)}\right],p_0=\frac{1}{4}\left[1-e^{-t{}_{}\left({}_{-1}\right)}\right],\mathrm{and}$$q=\frac{1}{2}{e}^{-\frac{t}{2}{}_{}\left({}_{-1}\right)}{e}^{-4t{}_z\left(0\right)}{e}^{-it}.$
The fluorescence measurement after the acquisition time t measures the state m.sub.s=0 population is as follows:

(67) $\begin{array}{cc}P\left(,t\right)=\frac{1}{8}\left[3+e^{-t{}_{}\left({}_{-1}\right)}\right]+\frac{1}{2}\cos \left(t\right)e^{-t{}_{}\left({}_{-1}\right)}{e}^{-4t{}_z\left(0\right)}& \left(4\right)\end{array}$

(68) By choosing a larger acquisition time of t, it is possible to improve the sensitivity, while the spin will suffer more from the magnetic noise. The sensitivity for pressure measurement can achieve n.sub.0.35 kPa Hz.sup.1/2 with a layer area 200 nm.sup.2, which corresponding to a force measurement sensitivity n.sub.F of 75 femto-Newton (f N) Hz.sup.1/2. The optimal choice of t is on the order of the coherence time of the NV centre spin. The sensitivity may be further improved by optimizing the dimension of the hybrid system, and using an array of NV centres.

(69) Sensing of Electric Field with Colour Centres in Diamond and Piezo Element

(70) In a method of the invention, a hybrid device that consists of a synthetic diamond layer formed by chemical vapour deposition (CVD) doped with NV centres during growth, a piezomagnetic element layer, and a piezoelectric element island on a substrate, measures electric field. An electric field induces a stain e of the piezoelectric element island, which generates a stress =.Math.Y acting on the attached piezomagnetic layer with Y denotes the Young's modules of the piezoelectric material. For a piezoelectric island which has large piezoelectric constants, such as Pb[Zr.sub.xTi.sub.1-x]O.sub.3 (PZT), the electric-field-induced strain can be as large as .sub.e=0.0002 (MV/m).sup.1, the corresponding Young's modules is Y10.sup.5 MPa. The sensitivity for the measurement of electric field thus reaches
.sub.E=.sub./(.sub.e.Math.Y)(5)

(71) The sensitivity for the measurement of pressure of .sub.0.35 kPa Hz.sup.1/2 implies the sensitivity for the measurement of electric field .sub.E0.2 (V cm.sup.1) Hz.sup.1/2, which represents three orders of magnitudes of improvement over the result reported by F. Dolde et al. in Electric-field sensing using single diamond spins, Nature Physics 2011, vol. 7, pp. 459-463. This sensitivity would allow for the detection of the electric field produced by a single elementary charge at a distance from the NV-spin sensor of 8 m in around is, and thus opens the possibility of remote sensing of a single charge.

(72) FIG. 6e shows the shot-noise-limited sensitivity for the measurement of stress (and force) within the total experiment time of 1 second as a function of interrogation time t.sub.a.

(73) $\begin{array}{cc}{}_{,t_a,}=\frac{\sqrt{\left(3+{}_{}^2\left(t_a\right)\right)\left(5-{}_{}^2\left(t_a\right)\right)}}{8C{}_{}\left(t_a\right){}_{.Math..Math.}\left(t_a\right)t_a\left(\frac{d}{d}\right)}\sqrt{\frac{t_a+t_p}{T}}& \left(6\right)\end{array}$

(74) The value of is 0.3, the NV spin preparation and readout time is t.sub.p=600 ns. The other parameters are the same as in FIG. 6c.

(75) Measurement of Temperature with Colour Centres in Diamond and Piezo Element

(76) In a method of the invention, a hybrid device that consists of a synthetic diamond layer formed by chemical vapour deposition (CVD) doped with NV centres during growth, a piezomagnetic element layer, and a thermal sensitive element island on a substrate, measures temperature. A change of temperature induces the expansion of the thermal sensitive element island with a thermal expansion constant .sub.T, which can be as high as 2.310.sup.5 K.sup.1 (Aluminium), and 1.210.sup.5 K.sup.1 (Steel). The thermal expansion generates a stress acting on the attached piezomagnetic layer .sub.T=.sub.T.Math.Y, where Y denotes the Young's modules of the thermal sensitive material, Y=710.sup.4 MPa (Aluminium), and 210.sup.5 MPa (Steel). The sensitivity for the measurement of temperature thus reaches
.sub.T=.sub./(.sub.T.Math.Y)(7)

(77) The sensitivity for the measurement of pressure of .sub.0.25 kPa Hz.sup.1/2 implies the sensitivity for the measurement of electric field .sub.E0.25 mk Hz.sup.1/2.

(78) The features described in the above description, claims and figures can be relevant to the invention in any combination.

REFERENCE NUMBER LIST

(79) 1, 2, 3, 4, 5, 6, 7, 8 Sensor 9 Diamond substrate layer 10 Piezomagnetic primary element layer 11 Piezoelectric primary element layer 12 Piezoelectric secondary element island 13 Thermally sensitive secondary element island 14 Permanent magnet 15 Colour centre 16 (Typically green) laser light 17 Fluorescence light 18 Photo detectors 19 Sensor array 20 Common substrate 21 Rotation and translation stages