TECHNICAL FIELD AND BACKGROUND

The present disclosure relates to a method and detector for measuring, e.g. detecting and/or quantifying, microscopic material properties such as magnetic fields, in particular by means of a colour center having a luminescence behavior which is dependent on its electron-spin.

Generally, a colour center may be formed in a material comprising a solid lattice with a photoluminescent point defect possessing an internal degree of freedom linked to its electron-spin (m _s ). Advantageously, the electron-spin is sensitive to its (microscopic) environment, e.g. magnetic fields, yet can be initialized and/or read out through optical means. One example of a colour center is the Nitrogen-Vacancy (NV) center in a diamond lattice. The NV center can be pumped by green light resulting in red photoluminescence depending on its electron-spin. Because the colour center is intrinsically very small it can be used to sense magnetic fields, e.g. with a resolution lower than a nanometer. Furthermore, quantum coherence properties of the colour center can be exploited through different sensing protocols to detect tiny magnetic fields or other quantities. Because the colour center is held in a solid lattice it is relatively easy to handle, opening the way to industrial applications. Colour centers are currently investigated as a versatile quantum sensor, e.g. for magnetic or electric field mapping, temperature sensing or for ESR and NMR detection.

For example, U.S. Patent 8,547,090 B2 describes a magnetometer for detecting and measuring a magnetic field. The magnetometer comprises a source of RF radiation, an optical system configured to collect and transmit there through photons of optical radiation, and a solid state diamond lattice disposed in a magnetic field to be measured. The lattice comprises one or more Nitrogen-Vacancy centers having an electronic spin, being responsive to said optical radiation and RF radiation. The electronic spin is configured to undergo a Zeeman shift in energy level when disposed in a magnetic field, the Zeeman shift being proportional to magnetic field strength. A detector is configured to detect output optical radiation from the electronic spin of the diamond lattice, after it has been exposed to the optical and RF radiation, to measure the Zeeman shift from the output optical radiation so as to determine the magnetic field.

Unfortunately, it is difficult to accurately control the optical source and RF source in relation to the colour centre. Accordingly, a desire remains to simplify the known methods and systems while improving control.

SUMMARY

The present disclosure relates to measurements involving colour centers to determine magnetic fields or other (microscopic) quantities affecting their electron spin and corresponding luminescence behavior. More particularly, the present disclosure relates to the use of an electron beam for interacting with the colour centers during the measurement, e.g. controlling or otherwise affecting spin dynamics of the one or more colour centers during initialization, progression, and/or readout. For example the electron beam is directed at or near the colour center for interacting with its electron-spin and a luminescence of the colour center is measured for determining the corresponding electron-spin which is dependent on the interaction with the electron beam and can be a function of the (microscopic) quantities to be measured.

Some embodiments comprise generating an electron beam and directing the electron beam at the start of a measurement to coincide with the colour center for controlling an initial state of the electron-spin of the colour center. For example, the initial state may comprise a defined eigenstate or coherent superposition of eigenstates of the colour center. According to other or further embodiments, the electron beam is directed during a measurement (between initialization and readout) to a proximal distance away from the colour center and used for spin-manipulation by generating a magnetic field that influences a progression, i.e. time- dependent evolution or development, of the electron-spin of the colour center from its initial state to a progressed state, e.g. in order to configure the electron-spin to be sensitive to the magnetic field (or other quantities). In some embodiments, the magnetic field can also be used to reach a specific superposition of states. According to yet further or other embodiments, the electron beam is directed at the end of a measurement to coincide with the colour center, e.g. back to its first position if the beam is also used for initializing the state. The coinciding electron beam for initialization or readout may excite an electronic transition to populate an electronic state of the colour center. An amount of luminescence caused by radiative decay of this electronic excited state is subsequently measured. In between the initialization and readout part the spin may interact with a quantity to be measured, e.g. another magnetic field. For example the interaction may occur during the manipulation of the spin, after it, or between two or more manipulations.

By introducing an electron beam for interacting with colour centers during measurements, the present methods and systems can be simplified and/or more precise compared to traditional measurements with colour centers relying on a laser for excitation/readout and/or remote antenna for spin manipulation. For example, a light source such as a laser can be omitted or supplemented when the electronic state is excited by the electron beam, e.g. for initialization or readout or both. For example, a magnetic field source such as an antenna can be omitted or supplemented when the spin-manipulation is effected by the magnetic field of the electron beam. As further advantage, an accuracy of the method and system may be improved because the positioning accuracy of an electron beam can be better controlled compared to a laser beam and/or antenna. For example, magnetic fields can be created locally and in a controlled manner using the electron beam at or near the colour center.

Further advantages may be achieved by various embodiments and combinations, as detailed herein. Depending on the embodiment,

measurements using colour centers may benefit from various advantages involving the interaction with an electron beam. For example, the

interaction with the electron beam may include one or more steps such as initializing the colour center, manipulating a progression or spin-dynamics of the colour center, and readout of the colour center. Of course, while each of these steps may provide separate benefit, it will be appreciated that synergetic further advantages can be achieved by using the electron beam for multiple steps.

The teachings of the present disclosure may benefit a wide variety of measurements involving colour centers. For example, one or more steps of using an electron beam as described herein may find novel application to replace traditional equipment in otherwise known techniques such as Relaxometry, Ramsey Fringes, Spin echo sequence, Carr-Purcell-Meiboom- Gill sequence (CPMG), Double Electron-Electron resonance, et cetera.

Details of the measurements may be different and each can be sensitive to different (microscopic) quantities. Still the techniques typically have common steps of controlling the initial state, an optional static or modulated magnetic field of some kind to influence the progression of the state, and read-out. At the end, it is the amount of photoluminescence

(cathodoluminescence) that typically gives information on an internal or external quantity to be measured.

By measuring the luminescence, an electron-spin of the colour center in the progressed state can be calculated. For example, an occupancy or energy of the electron-spin states can be measured. Accordingly, it can be deduced if and how the spin -interaction by a magnetic field we aim to study has affected the electron-spin between the time of initialization and readout. By placing the colour center in or near a region of interest, the colour center can act as a probe to determine a property of said region. For example, the magnetic field of the region may affect the spin states of the colour center. Also properties of the sample region such as pressure, temperature, the presence of magnetic species, et cetera may affect the colour center and can be measured via their influence thereon.

By having the electron beam coincide with the colour center this may cause cathodoluminescence, i.e. wherein electrons impacting on the colour center cause the emission of photons. Generally, the electron beam may cause the colour center to transition between an electronic ground state and an electronic excited state. The electronic excited state may decay radiatively or non-radiatively. When a likelihood of a radiative versus non- radiative decay depends on the electron-spin of the colour center, the amount of (cathodo)luminescence may be used as an indicator for the electron-spin. For example, in the Nitrogen-Vacancy center it is found that a likelihood of radiative decay of the electronic excited state is higher for an electron-spin m _s =0 than an electron-spin m _s =±l. Accordingly, the amount of luminescence is higher for m _s =0 than for m _s =±l, e.g. thirty percent more. This can be measured statistically for a single colour center, e.g. by repeated measurements, and/or by using an ensemble of colour centers.

The initial state of the colour center may be controlled e.g. by the electron beam causing a transition of the colour center to an electronic excited state, which -after decay- predominantly leaves the colour center in one of specific spin states. This is also referred to a spin polarization. For example, in the Nitrogen-Vacancy center it is found that after electronic excitation and decay, it is more likely that the electron-spin m _s =0. The spin polarization can be enhanced by repeatedly exciting the colour center. By knowing the initial spin state and measuring the spin after it has progressed for a period of time, the effect of spin-manipulation by the electron-beam and/or the effect of the surroundings can be determined.

Alternatively to setting a specific (pure) spin state, the initial state can be set to a quantum superposition of at least two electron-spin states. A probability of measuring a specific electron-spin state can be dependent on a relative phase of wave functions in the quantum

superposition. For example, a quantum superposition can be set using a controlled magnetic field, e.g. produced by the electron beam. A progression (time-evolution) of the relative phase can be dependent on a relative energy of the electron-spin states, e.g. in accordance with the time-dependent

Schrodinger equation. The relative energy of the electron-spin states can be dependent on the magnetic field affecting the colour center. Alternatively, or in addition, a probability of measuring a specific electron-spin state can be dependent on a coherence of wave functions in the quantum superposition. For example, a coherence of the quantum superposition is dependent on the magnetic field. In any case, a measurement of the luminescence may reveal information about the occupancy of the spin-states and thereby the effect of the magnetic field.

Moving electrons in the electron beam may generally cause the generation of a magnetic field around the beam, e.g. in accordance with

Ampere's law. The generated magnetic field may also be influenced by using a polarized electron beam. The magnitude of the magnetic field at the NV center position may depend e.g. on the amount of electrons (current density), their velocity, their spin-polarization, and a their proximity to the colour center. For the purpose of spin-manipulation, the beam may be disposed at a proximal distance away from the colour center to affect the center e.g. by its magnetic field, while avoiding electron interaction that may re- initialize the electron-spin. The proximal distance may depend on a diameter of the electron beam, e.g. at least one or two diameters distance (e.g. maximum or root-mean-square diameter). Some embodiment comprise modulating the electron beam. In this way a modulated magnetic field can be generated. For example, the magnetic field is modulated by varying one or more of a position of the electron beam, an electric current density of the electron beam, and/or a kinetic energy of electrons in the electron beam. By modulating the electron beam at a particular modulation frequency, the generated field may affect the colour center and/or sample region around the colour center. For example a position, direction, and/or intensity of the magnetic field is modulated.

Various implementations for generating a modulated electron beam can be envisaged. For example, the magnetic field can be modulated by varying a voltage between an anode and a cathode of an electron gun generating the electron beam. For example, the magnetic field can be modulated by varying a current that heats a filament of an electron gun generating the electron beam. For example, the magnetic field can be modulated by varying an electromagnetic wave in a waveguide attached to an electron gun generating the electron beam. For example, the magnetic field can be modulated by variably deflecting the electron beam. For example, the magnetic field can be modulated by generating the electron beam using a laser-driven electron gun which is modulated at a desired modulation frequency. Also combination of these or other means for modulating the electron beam and/or magnetic field are possible.

Some embodiment comprise modulating the magnetic field at a modulation frequency matching an energy difference between electron-spin states of the colour center. In this way a progression of the electron-spin can be manipulated, e.g. by facilitating a transition between the electron-spin states. By repeating the procedure while the modulation frequency is varied over a range of frequencies and measuring the luminescence as a function of modulation frequency, an energy difference between electron-spin states of the colour center can be determined. For example, the measured luminescence is enhanced or suppressed depending on whether the modulation frequency of the electron beam matches the energy difference between the electron-spin states. Additionally, or alternatively, the electronic spin states may undergo a Zeeman shift in energy level when disposed in a magnetic field. Accordingly, a magnetic field strength at the colour center can be calculated based on the energy difference between electron-spin states. This may be used to be sensitive, in an optimal mater, to a quantity for measurement. Alternatively, or in addition, modulating the magnetic field at a modulation frequency matching an energy difference between electron-spin states can be used to create a spin superposition.

For example, by modulating the magnetic field, e.g. at a frequency in the microwave domain (typically up to 300 GHz, preferably 1-20 GHz), this may typically affect electron-spin states in the colour center.

Alternatively, or in addition, by modulating the magnetic field in a radiofrequency domain (preferably 1 kHz - 1 GHz) this may provide manipulation of other spin in a sample region around the colour center. By modulating the magnetic field with both a microwave frequency and a radio frequency the electron-spin of the colour center and manipulating other spin in a sample region around the colour center can be simultaneously affected and/or controlled. For example, the colour center is used for measuring electron spin resonance of a sample region around the colour center. For example, the colour center is used for measuring nuclear magnetic resonance of a sample region around the colour center. Also other

modulation frequencies may be used, e.g. anywhere between 0.1 Hz and 1000 GHz.

Alternatively to a modulated magnetic field, the electron beam can also be configured for generating a static or slow varying magnetic field at the colour center. For example, the magnetic field caused by the electron beam at the colour center may cause a change to an energy difference between different electron-spin states. When the electron spin is initially placed in a quantum superposition, the changed energy difference may influences the rate of progression of one spin state relative to another spin state. This may be used to configure the electron-spin to be sensitive, in an optimal mater, to a quantity for measurement.

Depending on the application, various settings for the electron beam may be envisaged. For example, when the electron beam is too close to the colour center during spin-manipulation, this may cause undesired excitation of the colour center during this period. When the electron beam is too far, the magnetic field strength at the colour center may diminish.

Accordingly, a desired distance at which the electrons travel by the colour center during spin-manipulation is typically at least one nanometer away in a direction transverse to a propagation of the electron beam, preferably between one and ten nanometers. Of course the distance may be closer for some applications, e.g. electronic excitation.

As a further example, when the amount of electrons in the electron beam is too high, this may deteriorate the colour center or a sample material around the colour center. When the amount of electrons is too low, the magnetic field strength at the colour center may be too low to effectively manipulate the spin. Accordingly, a desired amount of electrons in the electron beam is typically at least thousand electrons per millisecond, preferably between 10 ⁴ and 10 ¹³ electrons per millisecond. Alternatively, or in addition, this may be expressed as an electrical current, e.g. between one pico-ampere to a few milli-ampere

As yet a further example, when a velocity or kinetic energy of the electrons is too low this may be insufficient for causing an excited electronic state in the colour center. A minimum (kinetic) energy for an electron to cause an electronic transition in the colour center may depend on a corresponding band gap of the material. For example an NV colour center in diamond has a band gap of about 5.5. eV (electron -Volt) so a typical electron energy of 6 eV or more may be sufficient to cause electronic excitation. Depending on the type of interaction step desired, the energy of the electrons can also be lower, e.g. down to 0.1 eV as long as it is sufficient to generate a noticeable magnetic field at the colour center affecting the spin- dynamics without necessarily having to cause electronic excitation. The energy may also be higher depending on the application and possible energy losses in any intermediate material. In some cases, when the kinetic energy is too high, this may cause deterioration of the colour center and/or surrounding material, e.g. by undesired ionization. This is not necessarily a problem in applying the present methods. The interaction probability with the colour center and/or sample may also depend on the velocity of the electrons, e.g. in accordance with a Bragg curve.

Based on these and other considerations, a desired kinetic energy per electron (e.g. at generation) is preferably at least 0.1 electron-Volt e.g. up to 50 kilo-electron-Volt, more preferably in a range between 0.2 and 5000 eV, more preferably between 1 and 100 eV, more preferably between 5 and 20 eV. For example, a range of 6 andlO eV has the advantage that it is close to the energy for electronic transition (e.g. if this is 5.5 eV) while maximally avoiding other effects such as damage or ionization. On the other hand, e.g. a range of 500 and 5000 eV may also be used as it correspond to the nominal parameters of SEM microscopes while typically not significantly affecting the matrix.

Alternatively, or in addition, for effective spin-manipulation, it may be desired in some embodiments that the magnetic field generated by the electron beam during spin-manipulation causes a (maximum) magnetic field strength at the colour center of at least 1 milli-Gauss, preferably between 2 milli-Gauss - 2 Gauss, or more. This may also depend on the number of electrons and a distance to the colour center.

Some aspects of the present disclosure may be embodied as a detector, e.g. magnetometer. The detector may comprise or be arranged to receive a sample cell. The sample cell may comprise one or more colour centers with an electron-spin dependent luminescence behavior as described herein. For example, the sample may be investigated by dispersing one or more colour centers in a relatively thin volume, allowing the electron beam to penetrate, or on a sample surface . Alternatively, or in addition, one or more colour centers may be disposed in a wall or window of the sample cell with the sample volume adjacent to the wall. For example, the colour center is formed in the wall or window of the sample cell by the wall or window comprising a solid lattice with a photoluminescent point defect possessing an internal degree of freedom linked to its electron-spin.

Some detectors may further comprise or be coupled to an electron beam source, e.g. electron gun. The electron beam source may be configured to generate an electron beam and direct the electron beam in a vicinity of the colour center. In some embodiments, the electron beam source is configured to generate a modulated electron beam. For example, the detector comprises an electron beam modulator configured to modulate the electron beam for generating a magnetic field at the colour center oscillating at a microwave frequency. The modulator may be separate or integrated into electron beam source. The detector may further comprise or be coupled to an optical sensor configured to measure luminescence caused by radiative decay of an electronic excited state in the colour center. For example, the optical sensor is configure to measure luminescence in a particular wavelength range, e.g. between six hundred to eight hundred nanometers. Also other wavelength ranges are possible, depending on the colour center.

Some aspects of the present disclosure may be embodied as a computer readable medium carrying software instructions that when executed by a computer, causes the computer to perform operational acts in accordance with the present disclosure. For example, the detector may be under software and/or hardware control to perform operational acts in accordance with the present disclosure. For example, the detector comprises a controller encoded with program instruction that when executed cause execution of a method as described herein.

BRIEF DESCRIPTION OF DRAWINGS

These and other features, aspects, and advantages of the apparatus, systems and methods of the present disclosure will become better understood from the following description, appended claims, and accompanying drawing wherein:

FIGs 1A-1C illustrate example steps for initializing,

manipulating, and/or reading out electron-spin in a colour center;

FIG 2A illustrates an example of an energy level diagram for an NV center;

FIG 2B illustrates an example of electron-spin state occupancy during the steps of FIG 1A-1C;

FIG 3 illustrates an embodiment of a detector for measuring magnetic fields using a colour center;

FIG 4A illustrates a sample cell with colour centers dispersed in the sample volume;

FIG 4B illustrates a sample cell with colour centers dispersed in a wall of the sample cell;

FIG 5 illustrates one embodiment of a modulated electron beam;

FIG 6 illustrates another embodiment of a modulated electron beam. DESCRIPTION OF EMBODIMENTS

In some instances, detailed descriptions of well-known devices and methods may be omitted so as not to obscure the description of the present systems and methods. Terminology used for describing particular embodiments is not intended to be limiting of the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. The term "and/or" includes any and all combinations of one or more of the associated listed items. It will be understood that the terms "comprises" and/or

"comprising" specify the presence of stated features but do not preclude the presence or addition of one or more other features. It will be further understood that when a particular step of a method is referred to as subsequent to another step, it can directly follow said other step or one or more intermediate steps may be carried out before carrying out the particular step, unless specified otherwise. Likewise it will be understood that when a connection between structures or components is described, this connection may be established directly or through intermediate structures or components unless specified otherwise.

The invention is described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. In the drawings, the absolute and relative sizes of systems, components, layers, and regions may be exaggerated for clarity. Embodiments may be described with reference to schematic and/or cross-section illustrations of possibly idealized embodiments and intermediate structures of the invention. In the description and drawings, like numbers refer to like elements throughout. Relative terms as well as derivatives thereof should be construed to refer to the orientation as then described or as shown in the drawing under discussion. These relative terms are for convenience of description and do not require that the system be constructed or operated in a particular orientation unless stated otherwise.

FIGs 1A-1C illustrate example steps of a method for measuring magnetic fields by means of a colour center (NV). The colour center has an electron-spin (m _s ) which affects its luminescence (L) behavior. For example, the amount of luminescence (L) is dependent on the state of the electron-spin and/or the probability to reside in that state at the moment of measurement. Typically, the colour center as used herein is formed in a material comprising a solid lattice with a photoluminescent point defect possessing an internal degree of freedom linked to its electron-spin. Preferably, the colour center is a Nitrogen- Vacancy center in a diamond lattice. Alternatively, also other colour centers having similar properties, can be used. Accordingly, where the reference "NV is used in the figures and description, this may refer to a general colour center.

In one embodiment, as illustrated in FIG 1A, the method comprises generating an electron beam (e) and directing the electron beam to coincide with the colour center for controlling an initial state "so" of the electron-spin of the colour center. In one embodiment, before spin- initialization, a position of the colour center is measured, e.g. by electron beam microscopy and/or cathodoluminescence microscopy.

In another or further embodiment, as illustrated in FIG IB, the method comprises directing the electron beam (e) to a proximal distance (D) away from the colour center and using the electron beam for generating a magnetic field (B) that influences a progression (P) of the electron-spin of the colour center from its initial state m _s =so to a progressed state m _s =s _p . In one embodiment, a spin-polarized electron beam is used for generating the magnetic field. This may influence, e.g. enhance, the generated magnetic field and/or can be used for increased control of the spin-manipulation.

In another or further embodiment, as illustrated in FIG 1C, the method comprises directing the electron beam (e) back to coincide with the colour center to populate an electronic excited state in the colour center. The method may further comprise measuring an amount of luminescence (L) caused by radiative decay of the electronic excited state in the colour center. In one embodiment, an electron-spin (ms) of the progressed state (s _p ) is calculated based on the measured luminescence (L). Alternatively, or in addition, an energy difference between electron-spin states of the colour center is calculated based on the amount of measured luminescence L. In some embodiments, the colour center NV is disposed in near a sample region R for measuring a property of the sample region. The sample region may e.g. comprise molecules of interest. Accordingly, a property of the sample region (R) may be calculated based on the electron-spin (m _s ) of the colour center (NV).

FIG 2A schematically illustrates an energy level diagram for a typical colour center, e.g. the Nitrogen-Vacancy colour center.

Energy levels indicated with the letter "G" refer to the colour center in the electronic ground state. Energy levels indicated with the letter Έ" refer to the colour center in the electronic excited state. The numbers "3" in ³ G and ³ E and "1" in G and *E represent the number of allowable spin states "m _s ", i.e. spin multiplicity. This may range from -S to S for a total of 2S+1 possible states. For example, in a triplet state where S = 1, m _s can be -1, 0, or 1. The energy difference between the m _s =0 and m _s =±l states typically corresponds to the microwave region. Accordingly by irradiating the colour center (e.g. with magnetic fields) having a modulation frequency "M" in the microwave region, this can affect the relative population of those levels, thereby affecting the luminescence intensity L. This is one of the mechanisms by which the spin state "m _s " can be manipulated.

Transitions between the (electronic) ground triplet state ³ G and

(electronic) excited triplet state ³ E states, may be effected by absorption of photons, or in the present case by excitation with the electron beam (e).

Decay of the electronic excited state ³ E can produce a photon which is measured as luminescence LI or L2. Alternatively, the excited state may decay also to the excited singlet state E via non-radiative transitions NO or Nl, depending on the spin-state m _s . The excited singlet state E may decay to the ground singlet state ^! G via non-radiative decay path N3. The singlet decay may also producing luminescence L3 at a relatively high wavelength (low energy). The ground singlet state *G may non-radiatively convert back to the ground triplet state ³ G.

Preferably, a likelihood of a radiative versus non-radiative decay depends on the electron-spin m _s of the colour center. For example, in the case of the Nitrogen-Vacancy colour center, a likelihood of radiative decay LI for an electron-spin ms=0 is higher than radiative decay L2 for an electron-spin m _s =±l. Conversely, the likelihood of non-radiative decay NO for electron-spin ms=0 is lower than non-radiative decay Nl an electron- spin m _s =±l. The total amount of luminescence L=L1+L2 depends on the likelihood of the radiative decay, which is higher when the colour center is in the ms=0 state. Also, due to the different decay paths, the colour center is more likely to be in the m _s =0 state after excitation, which is one way to initialize the colour center to a known state.

FIG 2B illustrates an example of an average electron-spin state occupancy during different steps of methods as described herein. In a quantum system the spin state is measured in one of discrete eigenstates. The present diagram may thus illustrate the chance of measuring one or the other state, e.g. determined by repeated measurements and/or measuring an ensemble of colour centers.

The average occupancy of the electro-spin may start at an equilibrium value m _s ="s _e ", e.g. determined according to a Boltzmann distribution depending on the energy of the different states. In one embodiment, the initial state m _s =so is set by the first electron beam "ei" coinciding colour center. This may cause a transition of the colour center to an electronic excited state ³ E, which -after decay- predominantly leaves the colour center in one of specific spin states, e.g. m _s =0. This initialized spin state m _s =so may evolve according to a progression (P) which may be influenced (manipulated) using a second electron beam 'W during a time period "t". This second electron beam ¾" may e.g. be disposed at a small distance away from the first electron beam "ei" coinciding with the colour center. In one embodiment, the electron beam ¾" at the proximal distance (D) is distanced from the electron beam "ei" coinciding with the colour center (NV) by at least a diameter of the electron beam. The proximity of the second electron beam ¾" may be chosen such that it is far enough so as not to cause further electronic transitions in the colour center, yet close enough to produce an effective magnetic field to manipulate the electron-spin state. It is noted that the electron beam may also produce a small electric field which may affect the colour center and/or surrounding sample region.

In one embodiment, two or more distinct spin manipulations are performed by the electron beam 'W generating a magnetic field between spin-initialization ("ei") and readout ("ee"), wherein between the two or more spin manipulations, the electron beam 'W is removed from the influence of the colour centre to leave the electron-spin free to interact with a

microscopic quantity to be measured. In another or further embodiment, the spin manipulation may prepare the spin (for example in a superposition of state) in order to make it sensitive to a quantity for measurement. For example, between ei and es, the spin may be manipulated and allowed interaction time with the quantity for measurement. The spin manipulation may be set accordingly to the quantity to be detected. It may comprise several "pulses" and several "interaction=waiting time". For example, said multi-pulses can be synchronized to a time varying phenomenon to be measured. For example, one way to make the spin more sensitive is by manipulating the spin synchronously to a phenomenon to be measured. Or, to make this phenomenon artificially happen in a periodic manner, synchronized with the spin manipulations, e.g. when using a second frequency for manipulate another spin for example, for ESR or NMR measurement.

After manipulating, the spin-state may have progressed to a state m _s =s _p . The progressed spin state "s _p " may be read out using a third electron beam "ee" which is directed to coincide with the colour center. This may produce luminescence light "L", e.g. in accordance with a

cathodoluminescence process. The amount and/or optical frequency of the luminescence L may be a function of the electron-spin (m _s ) which may be dependent on the progression "P" of the of the electron-spin m _s ="s _p ", which may be dependent on the manipulation by the magnetic field "B" produced by the second electron beam 'W and/or by other regional influences, e.g. electric and/or magnetic fields of surrounding molecules.

As described herein, the different phases of initialization, manipulation, and read out may be performed using electron beams which may originate from the same or different beam sources. The beams may differ in a setting of the beam source and/or beam manipulator. For example, a position of the beam is different between the initialization and manipulation phases while the readout phase may use the same beam setting as the initialization phase. Also other properties of the electron beam may be different between different phases, e.g. the current density may be higher or lower, the energy of the electron in the electron beam can be different during spin-manipulation than during initialization or readout.

In some embodiments, the magnetic field B is modulated at a modulation frequency matching an energy difference between electron-spin states m _s of the colour center NV for manipulating a progression of the electron-spin by facilitating a transition between the electron-spin states. In another or further embodiment, the methods as described herein are performed iteratively while the modulation frequency is varied over a range of frequencies. For example, the luminescence is measured as a function of modulation frequency. Accordingly, in some embodiments, an energy difference between electron-spin states m _s of the colour center NV is calculated based on the luminescence measured as a function of the modulation frequency. For example, the measured luminescence is enhanced or suppressed depending on whether the modulation frequency of the electron beam matches the energy difference between the electron-spin states m _s . For example the spin can be configured to be sensitive to a particular external quantity.

In some embodiments, a magnetic field strength at the colour center (e.g. caused by the surrounding sample region) is calculated based on the energy difference between electron-spin states. In one embodiment, the magnetic field B is modulated at a beam modulation frequency M in a microwave domain 0-100 GHz. In another or further embodiment, the magnetic field B is modulated in a radiofrequency domain to provide manipulation of other spin in a sample region R around the colour center NV. In another or further embodiment, the magnetic field B is modulated at two or more frequencies. For example, the magnetic field is modulated with both a microwave frequency and a radio frequency. For example the magnetic field is used for simultaneously manipulating the electron-spin m _s of the colour center NV and manipulating other spin in a sample region R around the colour center NV.

Various applications may be envisaged. In one embodiment, the colour center NV is used for measuring electron spin resonance ESR of a sample region R around the colour center NV. In another or further embodiment, the colour center NV is used for measuring nuclear magnetic resonance NMR of a sample region R around the colour center NV. In another or further embodiment, the electron beam is configured for generating a static or time dependent magnetic field B at the colour center NV. For example, the magnetic field B caused by the electron beam at the colour center NV causes a change to an energy difference between different electron-spin states m _s =0; m _s =±l. For example, it may be that the electronic spin states are configured to undergo a Zeeman shift in energy level when disposed in a magnetic field, the Zeeman shift being proportional to magnetic field strength. The changed energy difference may influence the rate of progression of one spin state m _s =0 to another spin state m _s =±l.

In one embodiment, the state of the electron-spin ms is manipulated after initialization to obtain a quantum superposition of at least two electron-spin states m _s =0; m _s =±l. For example, a probability of measuring a specific electron-spin state is dependent on a relative phase of wave functions in the quantum superposition. Accordingly, a progression of the relative phase may be dependent on a relative energy of the electron- spin states and/or the relative energy of the electron-spin states is

dependent on the magnetic field B. In one embodiment, a probability of measuring a specific electron-spin state is dependent on a coherence of wave functions in the quantum superposition. For example, a coherence of the quantum superposition is dependent on the magnetic field B.

FIG 3 illustrates a detector 100 for measuring magnetic fields in a sample region (R) using a nearby colour center (NV).

In one embodiment, the detector 100 comprises an optical sensor 14 configured to measure luminescence L caused by radiative decay of an electronic excited state E in the colour center NV. In another or further embodiment the detector 100 comprises optics for directing the

luminescence and/or electronics for reading out he luminescence. For example, the detector or system may comprise an optical microscope objective. For example, the detector may comprise filtering or gating means (not shown), e.g. electronics or optical filters to selectively measure the luminescence. For example, the optical sensor 14 is configured to measure at a specific optical wavelength matching the wavelength of the luminescence light and/or at a specific time-window matching the time after the excitation by the electron beam during readout of the electron-spin. For example, the optical sensor 14 is configure to measure luminescence in a wavelength range between six hundred to eight hundred nanometers. In some embodiments, a confocal microscope may be used to measure luminosity from specific parts of the sample

In some embodiments, as shown, the detector 100 comprises a sample cell 13 comprising a colour center NV with an electron-spin dependent luminescence behavior. Preferably, the detector 100 comprises an electron beam source 11 configured to generate an electron beam "e" and direct the electron beam in a vicinity of the colour center NV. In one embodiment, the detector 100 comprises a controller 15 encoded with program instruction that when executed cause execution of a method as described herein, e.g. including initialization, beam displacement, spin- manipulation, and readout.

In a preferred embodiment, the detector 100 comprises an electron beam modulator 12 configured to modulate the electron beam for generating a magnetic field and/or electric field at or near the colour center oscillating, e.g. at a modulation frequency "M" in the microwave and/or radio wave frequency domain. For example, one embodiment (not shown) involves the use of an external pulse generator, and a capacitive pulse junction box (or equivalent depending on the design of the electron gun). Using these additional elements may enable the superposition of the microwave signal with the grid's (cathode) power supply. Alternatively, instead of modulating the grid's voltage, it is possible to modulate the current that heats the filament of the electron gun. For example, the superposition of an RF voltage and the source's power supply modulates the emission of electrons from the filament, producing a pulsing source of electrons. Yet another embodiment to modulate the electron beam is to attach a waveguide at the electron gun output and to supply an

electromagnetic wave, in the desired frequency, in order to accelerate or stop the electrons in the beam. Beam Blanking is yet another approach to pulsing the electron beam. For example, the technique includes deflecting the beam in order to interrupt the flow of electrons through the output of the electron gun. To produce the deflection, a pulsed signal feeds a set of magnetic coils, or electrostatic lenses, installed near the output of the electron gun. Yet another approach involves the use of a laser-driven photoelectron gun instead of a (traditional) thermionic electron gun. In this type of electron gun, a laser excites the electrons of a material which are released and collected to form the electron beam. The modulation of the laser beam enables the generation of a pulsing electron beam at the same frequency as the laser. One embodiment (not shown) comprises an

integrated SEM microscope with additional modulation stage. Also combinations of these or other embodiments can be envisaged for generating a modulated electron beam. FIG 4A illustrates one embodiment of a sample cell 13 wherein the sample cell is configured to hold a sample S with one or more colour centers NV dispersed in the sample volume.

FIG 4B illustrates another embodiment of a sample cell 13 wherein the sample cell is configured to hold a sample S and wherein one or more colour centers NV are disposed in a wall or window 13w of the sample cell 13. For example, the colour center NV is formed in the wall or window 13w of the sample cell 13 by the wall or window 13w comprising a solid lattice with a photoluminescent point defect possessing an internal degree of freedom linked to its electron-spin.

FIGs 5 and 6 illustrate embodiments wherein the electron beam "e" is configured for generating a modulated (time-dependent) magnetic field B(t). For example, the modulated magnetic field B is generated at the colour center NV and/or at a sample region R near the colour center NV. For example, a direction and/or intensity of the magnetic field B is modulated. In FIG 5, the magnetic field B is modulated by varying a position of the electron beam. A modulation time interval Tm (inverse modulation frequency) may be determined by a periodicity of the modulation. For example, the position of the electron beam can be periodically varied using a beam modulator 12 comprising plates wherein the charge is varied. In some embodiment, the beam modulator is alternatively or additionally used for displacing the electron beam between the initialization and manipulation phases, and between the manipulation and readout phases.

In FIG 6, the magnetic field B is modulated by varying an electron density (i.e. electrical current) of the electron beam "e". For example, the electron density of the electron beam can be varied using a beam modulator 12 comprising a waveguide that accelerates or decelerates electrons. For example, the magnetic field B is modulated by varying an electromagnetic wave in a waveguide attached to an electron gun generating the electron beam "e".

Also other or further measures can be envisaged for modulating the electron beam. For example, the magnetic field B may be alternatively or additionally modulated by variably deflecting the electron beam (not shown). Alternatively, or in addition, the electron density may be varied by varying a current to the electron source 11. For example, the magnetic field B is modulated by varying a current that heats a filament of an electron gun generating the electron beam. Alternatively, or in addition, the magnetic field B is modulated by varying a kinetic energy of electrons in the electron beam at a beam modulation frequency M. Alternatively, or in addition, the magnetic field is modulated by varying a voltage between an anode and a cathode of an electron gun generating the electron beam. Alternatively, or in addition, the magnetic field is modulated by generating the electron beam using a laser-driven electron gun which is modulated at a desired

modulation frequency. Also other means for modulating the electron beam can be envisaged. For the purpose of clarity and a concise description, features are described herein as part of the same or separate embodiments, however, it will be appreciated that the scope of the invention may include

embodiments having combinations of all or some of the features described. For example, while embodiments were shown for initialization, spin- manipulation, and readout of colour centers using electron beams, also alternative ways may be envisaged by those skilled in the art having the benefit of the present disclosure for achieving a similar function and result. E.g. steps of the procedure may be combined or performed separately or in one or more alternative steps or omitted. For example, instead of an electron beam also another (charged) particle beam can be used.

While the embodiments may show the electron beam at or near a single colour center, the beam may also affect multiple colour centers.

Accordingly, the electron beam can be used simultaneously or sequentially for initialization, manipulation, and/or readout of one or more colour centers (ensemble). For example, the beam may coincide with multiple colour centers during initialization and/or readout. For example, the beam may be in a proximity of multiple colour centers during spin-manipulation.

Alternatively, the beam position may change to sequentially affect one colour center at a first instance of time and a second or further colour center at a later instance of time.

The various elements of the embodiments as discussed and shown offer certain advantages, such as a simplified system with easy control. Of course, it is to be appreciated that any one of the above embodiments or processes may be combined or split up with one or more other embodiments or processes to provide even further improvements in finding and matching designs and advantages. For example, the steps of spin-initialization, spin- manipulation, and spin-readout by an electron beam may provide synergetic advantages but can also provide individual advantages when performed separately. For example, initialization and/or readout may be performed using conventional means such as a light source while the electron beam is used only for spin-manipulation. This may still provide the advantage of providing accurate manipulation while allowing to omit another magnetic field source. Alternatively, or in addition magnetic fields may be created by conventional means, e.g. antennas or permanent magnets while only the initialization and/or readout is performed by an electron beam. This may still provide advantages of resolution and/or that a light source can be omitted. Alternatively still, the step of spin-manipulation can be omitted and the electron beam used exclusively for initialization and/or readout, e.g. in a relaxation measurement (or Tl measurement) which can measure e.g. surrounding magnetic noise. This may be carried out e.g. on an integrated SEM without modulation.

Additionally, or alternatively to measuring the amount of luminosity, also a spectral distribution of the luminosity can be measured to reveal further information. In some embodiments, the sample may be brought to cryogenic conditions to cause narrowing of spectral features or to study quantities at low temperature. It is appreciated that this disclosure offers particular advantages to measurement of magnetic fields, and in general can be applied for any application wherein material properties are measured which may influence the electron-spin of the colour center.

While the present systems and methods have been described in particular detail with reference to specific exemplary embodiments thereof, it should also be appreciated that numerous modifications and alternative embodiments may be devised by those having ordinary skill in the art without departing from the scope of the present disclosure. For example, embodiments wherein devices or systems are disclosed to be arranged and/or constructed for performing a specified method or function inherently disclose the method or function as such and/or in combination with other disclosed embodiments of methods or systems. Furthermore, embodiments of methods are considered to inherently disclose their implementation in respective hardware, where possible, in combination with other disclosed embodiments of methods or systems. Furthermore, methods that can be embodied as program instructions, e.g. on a non-transient computer- readable storage medium, are considered inherently disclosed as such embodiment.

Finally, the above-discussion is intended to be merely illustrative of the present systems and/or methods and should not be construed as limiting the appended claims to any particular embodiment or group of embodiments. The specification and drawings are accordingly to be regarded in an illustrative manner and are not intended to limit the scope of the appended claims. In interpreting the appended claims, it should be understood that the word "comprising" does not exclude the presence of other elements or acts than those listed in a given claim; the word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements; any reference signs in the claims do not limit their scope; several "means" may be represented by the same or different item(R) or implemented structure or function; any of the disclosed devices or portions thereof may be combined together or separated into further portions unless specifically stated otherwise. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage. In particular, all working combinations of the claims are considered inherently disclosed.