Vectorial magnetometer and associated method of acquiring information pertaining to an ambient magnetic field

Abstract

The method can include repeating, in a succession, a sequence of steps of initializing spin populations having different trigonometrical projections of the ambient magnetic field to a reference state, propagating a pulse sequence having a first pulse separated from a second pulse by an interpulse delay which transfers the spin populations to a magnetically sensitive spin state accumulating Ramsey phase during the interpulse delay, and measuring a sum of the percentages of the one or more spin populations which collapse to one of the reference spin state and an other spin state, wherein a configuration of the pulses and a duration of the interpulse delay is varied from one pulse sequence to another in the succession, the Ramsey phase accumulations can be isolated based on variations of the percentages caused by the variations in the configuration, and the vector can be reconstructed based on the variations of the percentages caused by the variations in the duration.

Description

VECTORIAL MAGNETOMETER AND ASSOCIATED METHOD OF ACQUIRING INFORMATION PERTAINING TO AN AMBIENT MAGNETIC FIELDBACKGROUND

[0001] Vectorial magnetometers are systems that measure the orientation and the amplitude of a magnetic field. The orientation is often a tridimensional orientation in space, although in some cases, the orientation may be a bidimensional orientation.

[0002] Some vectorial magnetometers harness the properties of structures, namely crystalline structures having defects which have spin populations (e.g., electrons) having degrees of freedom in more than one characteristic orientation (symmetry) corresponding to different orientations of the defect in the structure. These properties can be harnessed by stimulating the transfer of spin populations between spin states and measuring an effect of the magnetic field on the spin populations as they transfer back to a reference spin state.

[0003] An example is spin state systems formed by nitrogen-vacancy (NV) defects (aka NV centers) in a diamond (carbon - C) lattice. Such structures, namely diamond lattices with NV centers, can be reliably produced in a manner for the defects in different defect orientations to be randomly distributed in the crystalline lattice to the point of forming corresponding statistically representative populations in the different orientations. The spin-states systems in such structures can be sensitive to external influences, such as temperature, pressure, electric and / or magnetic field strength, in the sense that the exact (quantum) amount of energy required to stimulate a given spin population transfer can be affected by the external influence. The external influence can be perceived differently by the populations in the different orientations. In the case of NV defects, for instance, for a given ambient magnetic field, the perceived magnetic field strength can vary based on the given defect orientation, as a function of the varying trigonometrical projection of the magnetic field amplitude on the defects of corresponding orientations. These differences between the effect of an external influence on the defects in the different orientations can, in some cases, be detected and measured to obtain a measurement of the external influence. In the case of NV defects, it was known to do this optically using the optically detected magnetic resonance (ODMR) technique, for instance. These principles can be harnessed to determine the absolute amplitude and orientation of theexternal magnetic field relative to the crystalline structure orientation. Systems designed for performing this latter function are referred to as vectorial magnetometers.

[0004] Some issues may arise, however, in practice. For instance, in some cases, namely when the external magnetic field is relatively low, such as in the order of magnitude of the earth’s magnetic field, the signal detected by a detector can consist of an overlap of signals stemming from two or more spin populations associated to different ones of the four characteristic orientations. In such cases, an additional technique is required to be able to dissociate the overlapping influences of the different spin populations.

[0005] One way to achieve this is by using an external magnetic field, sometimes referred to as bias field. While this approach works, the hardware required for imparting the external magnetic field is inconvenient and often undesirable in practice. Moreover, additional issues may arise such as calibration burden, etc.

[0006] Published international patent application W02022 / 020943 describes a different approach, where the phenomenon of Rabi frequency is harnessed in a manner to allow performing the dissociation of the overlapping influences of the different spin populations without a bias field. More specifically, when the spin populations are manipulated by a pulse of a given range of energy (e.g. range of combination of pulse duration and pulse amplitude), a pulse which would normally transfer a spin population from a base state to an excited state may, instead, partially impede the transfer due to Rabi attenuation. Voluntarily impeding the transfer of some spin populations in a known manner can be harnessed to resolve the individual influences of the different spin populations which overlap in the measured amplitude.

[0007] While such techniques were satisfactory to a certain degree, there always remains room for improvement, be it in terms of ways of addressing a given level of measurement precision in a less costly manner, or in terms of achieving a greater level of measurement of precision, to name two examples.SUMMARY

[0008] It was found that in some embodiments, it could be desired to harness an additional quantum property of the spin populations, namely phase accumulation, when performingmeasurements of orientation and amplitude of an ambient magnetic field. More specifically, spin populations can be manipulated by pulse sequences including a first pulse, an interpulse delay, and a second pulse, in a manner that in accordance with a Ramsey effect, phase accumulates during the interpulse delay. By varying the interpulse delay, from one pulse sequence to the other, information pertaining to the effect of the ambient magnetic field on the spin populations can be extracted. In some cases, the configuration of the pulses can also be varied from one pulse sequence to another. The Ramsey effect, based on the differences in phase accumulation caused by the variations in the interpulse delay, can be used to measure the projected amplitude of the magnetic field on the characteristic orientations of the spin populations, and a Rabi effect stemming from variations in pulse configurations can be used to isolate the overlapping influences of different ones of the spin populations on the Ramsey phase accumulation. The amplitude and orientation of the field can be reconstructed from the projected amplitude on each population.

[0009] In accordance with one aspect, there is provided a method of performing a vectorial measurement of an ambient magnetic field, the method comprising : initializing to a reference spin state spin populations having corresponding characteristic orientations in a structure, the characteristic orientations having different trigonometrical projections of the ambient magnetic field; propagating a pulse sequence onto the spin populations, the pulse sequence including a first pulse separated from a second pulse by an interpulse delay, the pulse sequence transferring one or more of the spin populations from the reference spin state to a magnetically sensitive spin state which accumulates Ramsey phase during the interpulse delay; measuring a sum of percentages of the one or more spin population which collapse to one of the reference spin state and an other spin state; repeating the steps of initializing, propagating and measuring in a succession, including varying a configuration of the first pulse and the second pulse in different ones of the pulse sequences in the succession, the different configurations varying the percentages; and varying a duration of the interpulse delay in different ones of the pulse sequences in the succession, the different durations varying the percentages; isolating the Ramsey phase accumulation of different ones of the spin populations based on the variations of the percentages caused by the variations in the configuration; measuring the trigonometrical projections based on the variations of the percentages caused by thevariations in the duration; and reconstructing a vector of the ambient magnetic field based on the trigonometrical projections.

[0010] In accordance with another aspect, there is provided a vectorial magnetometer comprising : a structure having spin state spin populations in different, characteristic orientations in a structure, the characteristic orientations having different trigonometrical projections of the ambient magnetic field; an emitter operable to propagate a pulse sequence onto the spin populations, the pulse sequence including a first pulse separated from a second pulse by an interpulse delay, the pulse sequence transferring one or more of the spin populations from the reference spin state to a magnetically sensitive spin state which accumulates Ramsey phase during the interpulse delay, and back to the reference spin state; a detector operable to measure a sum of the percentages of the one or more spin population which collapse to the one of reference spin state and an other spin state; a computer having a processor and a memory storing instructions which, when executed by the processor, cause the vectorial magnetometer to initialize the spin populations to the reference spin state, control the emitter to propagate the pulse sequence onto the spin populations, measure the sum of the percentages via the detector, repeat the initializing, controlling, and measuring in a succession, including varying a configuration of the first pulse and the second pulse of different ones of the pulse sequences in the succession, the different configurations varying the percentages and varying a duration of the interpulse delay of different ones of the pulse sequences in the succession, the different durations varying the percentages, isolate the Ramsey phase accumulation of different ones of the spin populations based on the variations of the percentages caused by the variations in the configuration, measure the trigonometrical projections based on the variations of the percentages caused by the variations in the duration; and reconstruct a vector of the ambient magnetic field based on the trigonometrical projections.

[0011] In accordance with another aspect, there is provided a method comprising repeating, in a succession, steps of initializing spin populations having different trigonometrical projections of the ambient magnetic field to a reference state, propagating a pulse sequence having a first pulse separated from a second pulse by an interpulse delay which transfers spin population to a magnetically sensitive spin state accumulating Ramsey phase during theinterpulse delay, measuring a sum of percentages of the one or more spin populations which collapse to one of the reference spin state and an other spin, wherein a configuration of the pulses and a duration of the interpulse delay is varied from one pulse sequence to another in the succession, the Ramsey phase accumulations can be isolated based on variations of the percentages caused by the variations in the configuration, and the vector can be reconstructed based on the variations of the percentages caused by the variations in the duration.

[0012] In some embodiments, a method can measure vector magnetic fields with strengths on the order of the earth’s field using nitrogen-vacancy (NV) centers in diamond without the use of bias magnets. The method involves a system capable of applying green optical illumination and microwave pulses to a diamond containing an ensemble of NVs. The red fluorescence of the ensemble is then measured using a photodiode as the system is subjected to specific sequences of microwave pulses.

[0013] The method can include resolving / dissociating the degenerate signals from the four possible NV orientations by using a specific microwave field orientation that produces a different Rabi frequency for each orientation. With a single microwave tone whose field amplitude is much larger than that of the static field, the NVs spin states can be manipulated without the need for frequency tracking. For instance, upon sweeping the duration of the microwave pulses, the four orientations of NV populations evolve in and out of the reference state at different rates, allowing for their signals to be separated and tagged. Such phenomenon can also be obtained with multiple microwave tones with the added complexity of tracking the required frequency but reducing the microwave power required compared to a single tone operation.

[0014] Two of these microwave pulses can then be separated by a variable delay to perform Ramsey magnetometry. During this period, the NVs accumulate Ramsey phase at a rate that is proportional to the energy difference between the states, the energy difference being proportional to the projection of the magnetic field along their axis. The vector field information can thus be encoded into the fluorescence signal. A challenge may remain in associating which frequency is from which orientation. By designing the microwave delivery and then appropriately sweeping the microwave pulse durations and the inter-pulse delays, the Ramsey phase can be associated with each axis having a known (and isolated) Rabi frequency.

[0015] The use of bias magnets or coils to lift the degeneracy at near zero fields comes with inherent limitations associated with classical sources of drift such as mechanical vibration, thermal expansion or magnetization shifts. Isolating the signal of each NV orientation without the need for a bias field, enables a smaller and less complicated sensing head. At the same time, measurements are more accurate because fewer drift-prone inversion parameters are needed to be recalibrated with the use of external tools.

[0016] Various magnetically sensitive spin states may be used, such as ms=1 , ms=-1 or superpositions of two or more of ms=0, ms=1 and ms=-1. Superpositions of ms=0 and ms=1 and of ms=0 and ms=-1 can be referred to as single quantum basis. The use of the double quantum basis (transferring from ms=0 into a superposition of the ms=1 and ms=-1 states) for measurement can bring additional advantages to the sensor over working in the single quantum basis (transferring into the ms=1 or ms=-1 state). For one, double quantum Ramsey interferometry has twice the effective gyromagnetic ratio as single quantum, meaning the sensitivity can be higher if the sensor is not limited primarily by magnetic noise. Another advantage is that the double quantum basis is robust to thermal drift in the diamond as the shift in frequency is common to both the states forming the subspace.

[0017] Many further features and combinations thereof concerning the present improvements will appear to those skilled in the art following a reading of the instant disclosure.DESCRIPTION OF THE FIGURES

[0018] In the figures,

[0019] Fig. 1 is a block diagram of a vectorial magnetometer in accordance with one example;

[0020] Fig. 2A is a schematic view showing an NV center in a diamond substrate;

[0021] Fig. 2B is a diagram showing energy levels for NV centers;

[0022] Fig. 3A is a schematic view of an example ODMR technique;

[0023] Fig. 3B is a schematic view of Bloch spheres schematizing the rotation from the ms=0 to ms=±1 state by a half rotation around the Bloch sphere;

[0024] Fig. 4 is a graph showing an energy dip centered around a peak transfer energy value;

[0025] Fig. 5 is a diagram showing the splitting of energy levels due to various effects;

[0026] Fig. 6 is a graph showing a plurality of partially superposed energy dips corresponding to the Earth’s magnetic field as measured with ODMR on NV centers;

[0027] Fig. 7 is a graph showing a Rabi curve;

[0028] Figs. 8A and 8B are schematic graphs showing superposed amplitudes;

[0029] Fig. 9 is a schematic view of an example interrogation technique using pulse sequences in accordance with some embodiments;

[0030] Fig. 10 is a schematic view of the effect of a pulse sequence on a spin state transfer;

[0031] Fig. 11 is a graph showing a Ramsey curve;

[0032] Figs. 12A and 12B show different ways of varying pulse energy, namely by varying pulse duration and by varying pulse amplitude, respectively;

[0033] Fig. 13 schematizes the application of a first pulse configuration in accordance with optimal control theory;

[0034] Fig. 14 is a diagram showing an example pulse sequence;

[0035] Fig. 15A is a graph plotting minimal separation of Rabi projections along four crystallographic orientations of diamond;

[0036] Fig. 15B is a graph plotting optimization metric for finding the ideal angle of operation for the microwave field relative to the diamond axes, where flminis normalized by y |BMW| to give the minimal projection;

[0037] Fig. 16 is an example pulse sequence diagram;

[0038] Fig. 17 is a graph showing time domain result of a simulation of a simple case where the donut shape is characteristic of the 2D frequencies;

[0039] Fig. 18 is a set of graphs illustrating Fourier transforms taken along two axes;

[0040] Fig. 19 is a graph showing a line cut along the Y direction will be representative of the Rabi frequency for that orientation;

[0041] Fig. 20 is a graph showing, for one orientation, the magnetic field will shift the evolution frequency by 2y_b B_z (as well as its negative value), and the three possible values of the hyperfine splitting spread that signal into three distinct points separated by 24_||;

[0042] Fig. 21 is a graph showing that for the four orientations and their hyperfine coupling (3 possible values), with the positive and negative frequencies in frequency domain, 24 peaks can be present in the signal;

[0043] Fig. 22 is a set of graphs depicting Ramsey signal for each orientation;

[0044] Fig. 23 is a graph presenting simulated results for a diagonal cut experiment, where t and T are incremented together, in the case where all three hyperfine states are for a single orientation;

[0045] Fig. 24 is a graph presenting FFT of the diagonal cut simulation;

[0046] Fig. 25 is a graph presenting if the sum and differences of the Rabi frequencies and their Ramsey frequencies are well resolved (at least one side band for each orientation), the magnetic field can be extracted;

[0047] Fig. 26 is a graph presenting the inner product along multiple rabi frequencies followed by an inner product along multiple Ramsey frequencies;

[0048] Fig. 27 is a graph presenting the inner product along given Rabi frequencies (labeled in legend) and multiple Ramsey frequencies; and

[0049] Fig. 28 is a diagram representing a computer.DETAILED DESCRIPTION

[0050] Fig. 1 presents an example of a vectorial magnetometer 100 - a system which a) acquires information pertaining to an ambient magnetic field and b) determines an amplitude and orientation of the ambient magnetic field based on the acquired information. The vectorial magnetometer 100 can be said to have an acquisition unit 120 and a controller 120. The acquisition unit 120 has a structure 130 having two or more spin populations having respective characteristic orientations. The acquisition unit 120 can have an emitter 140 operable to propagate a pulse sequence onto the at least two spin populations in a manner to transfer the spin populations from a reference spin state to a magnetically sensitive spin state which accumulates Ramsey phase during the interpulse delay. The acquisition unit 120 can have a detector 150 to measure an amplitude corresponding to a sum of the percentages of the one or more spin populations which collapse to one of the reference spin state and an other spin state.

[0051] When the magnetically sensitive spin state is a superposition, the measurement will collapse the wavefunction to a state. This state would be the reference spin state in the case of interrogating with ODMR, but could be an other state if another interrogation technique is used. Indeed, in some cases, the amplitude measured concerns a single one of the spin populations, but in other cases, the amplitude measured can include contributions from different ones of the spin populations. The controller 110 can have instructions to control the emitter, reference data concerning the structure, the emitter, and their relationship, and instructions to determine an amplitude of the projection of the ambient magnetic field in the different characteristic orientations based on the amplitudes measured by the detector 150 and on the reference data, and to reconstruct the 2D or 3D amplitude and orientation of the ambient magnetic field from the amplitudes of the projections. In practice, the emitter 140 cannot be controlled by a human, and is controlled by the controller which can be embodied as a computer, in which case the same computer can also perform the tasks of determining the amplitudes of the projections and reconstructing the amplitude and orientation of the ambient magnetic field (and in some cases, additional tasks), or another computer can be used for the latter functions.

[0052] In this example, the acquisition unit 120 further has an emitter 160 which is used to initialize the spin populations to a reference state following the previous measurement and prior to application of a next pulse sequence. This emitter 160 is optional. The controller 110 can be sold separately from the acquisition unit 120, and the controller instructions (software) can be sold separately from the acquisition unit 120 and from the controller 110.

[0053] In an embodiment, the structure 130 can be a diamond substrate 12 having NV defects 10 having spin transfers in four different characteristic orientations of the crystalline structure. As shown in Fig. 2A, the defects consist of two of the carbon atoms of the crystalline matrix being substituted by a nitrogen atom and an adjacent vacancy (absence of an atom at a point in the lattice which would normally be expected to hold a carbon atom), respectively. The NV defect 10 can be oriented in any one of four specific orientations associated with the crystalline matrix. Six bound electrons near the NV defect 10 form a triplet spin state. One of the possible motivations of using the NV defect 10 in diamond is that such substrates 12 can be provided in a relatively inexpensive manner with a given, approximately known, concentration of NV defects 10 of the different orientations distributed randomly in the matrix. The substrate 12 will typically have a sufficiently high amount of NV defects 10 to be treated in a statistical manner, with the amount of NV defects 10 of each orientation being approximately equal.

[0054] Fig. 2B shows an energy diagram 22 of this triplet spin state. More specifically, the base state 24 can have any one of three states ms=0, ms=1 and ms=-1 . Via the Zeeman effect, the energy levels between the states ms=1 and ms=-1 is separated by a difference of energy which is related to the projection of the magnetic field along the NV defect axis 11 . The energy values can be identified in any suitable unit. Electronvolts (eV) can be used for instance. However, as values of energy, such as the difference of energy between two states for instance, can correspond to a photon of a given wavelength / frequency, values of energy can alternately and equivalently be identified by a photon frequency or a photon wavelength, for instance.

[0055] The triplet spin state also has an excited state 26. At rest, at room temperature, the NV defects 10 will be in the base state 24, or ground state, and the population will be distributed between the states ms=0, ms=1 , and ms=-1.

[0056] ODMR is one, often convenient, technique which can be used to interrogate the spin states in the diamond substrate 12 having NV defects 10. ODMR can begin by an initialization step, in which the triplets resting in the base state 24 are excited to the excited energy state 26. This can be done using green laser light 28 for instance, or resonant red laser light (not shown). Based on the rule of conservation of angular momentum, the ms=0 state can be excited to the ms=0 excited state, the ms=1 base state can be excited to the ms=1 excited state, the ms=-1 state can be excited to the ms=-1 excited state. The excited ms=0 state 26 will relax (aka: quench) into the base ms=0 state 24, by emitting a photon in the red portion of the optical spectrum and can therefore be said to be “fluorescent”. The excited ms=1 and ms=-1 states may also be quenched back to the ms=0 state, though via a singlet interstate 32 coupling and can be said to be “low fluorescence”. Since all excited states 26 can relax into the ms=0 base state 24, this process can be said to “initialize” the spin states to the ms=0 state. In practice, not “all” of the |+ / -1> excited state population decays back to the |0> ground state, but after a few cycles, the vast majority will be initialized in |0>, probabilistically speaking. In the context of NV defects 10, the process of initialization is quick, and once the states have been converted to the ms=0 base state 24, the relaxation time (Ti) for the ms=0 base state to “re-scramble” into the rest distribution of ms=0, ms=1 , and ms=-1 states is longer, taking the order of a millisecond.

[0057] For the sake of clarity in later reference in this text, the emission of photons used to excite the triplet from the base state 24 to the excited state 26 will be referred to herein as the “transition energy” to refer to the emitted energy which causes the transition from the base state 24 to the excited state 26. In NV defects 10, the transition energy can be provided by photons of different wavelengths or, perhaps, phonons if a sufficient energy level of phonons can be harnessed in a specific application.

[0058] However, by acting quicker than the relaxation time (Ti), the base ms=0 (|0>) state can also be proactively transferred into the ms=1 or ms=-1 (|+ / - 1 >) base states by applying energy of an energy value which corresponds to the energy difference between the ms=0 energy level and the corresponding one of the ms=1 or ms=-1 energy level. The exact amount of energy to transfer ms=0 to ms=1 or ms=-1 can be referred to as the “resonating” energy value. It will depend on the projection of the amplitude of the magnetic field along the corresponding defectaxis, and accordingly, a measurement indicative of the magnetic field can be made by probing the defects to determine the resonating energy value, which can be measured in the form of a “resonant frequency”.

[0059] This emission of an energy value adapted to transfer the spin state of the defect can be referred to herein as the “spin-state-transferring energy”, or simply “transfer energy value” 34 by contradistinction to the “transition” energy, and essentially targets the base ms= |0> to the base ms= |+ / - 1> transitions, schematized on the right hand side of Fig. 2B and in Fig. 3A, rather than exciting the ground triplet 24 to the excited triplet states 26.

[0060] Accordingly, the states can be first initialized from an earlier configuration to the ms=0 state in the base triplet, then manipulated, within the base triplet, from the ms=0 state to another state (e.g., ms=1 , ms=-1 , superposition) and then excited into the same state but in the excited triplet state 26. From there, the amount of fluorescence emitted can depend on the percentage of the spin populations which are in the ms=+-1 state and the percentage of the spin populations which are in the ms=0 state. As will be explained in greater detail below, the percentages of the spin populations in the corresponding states can be affected by the ambient magnetic field, due quantum physical phenomena such as Rabi effects and Ramsey effects.

[0061] In the case of NV defects 10 subject to a moderate magnetic field such as the Earth’s field, the transfer energy value 34 corresponds to photons in the microwave portion of the electromagnetic spectrum and a corresponding microwave field can be applied using a waveguide in the form of a wire, for instance, and of which the frequency can easily be tuned. The orientation of the wire can also be specifically determined relative to the crystalline substrate and can thus be constant and known (e.g. via calibration) relative to the NV defect 10 orientations.

[0062] The spin population transfers can also be sensitive to the ambient magnetic field. In the case of NV defects 10 in diamond, the acquisition unit 120 can be configured to perform optically detected magnetic resonance. Emitter 160 can be used transition the electron levels of the spin population from a base (e.g. reference) state to an excited state, to which a green laser can be adapted, for instance. Transitioning the electron levels can be used in bothinitializing the spin populations to the reference state and in stimulating the red light emission, as evoked above. Emitter 140 can be adapted to perform spin state transfers, to which a microwave emitter can be adapted. The detector 150 can be a photodetector sensitive to light in the red portion of the electromagnetic spectrum generated by electrons transitioning back from the excited state to the base state. Although other structures having different spin populations associated to different characteristic orientations may be used in alternate embodiments, diamond lattice with NV defects may be the most practical for many applications.

[0063] In some alternate embodiments, the detector 150 is adapted to detect an intensity of energy such as radiation either reflected or absorbed, as opposed to photons emitted by the transition of the electrons. In further alternate embodiments, the detector 150 may be adapted to detect an intensity of energy such as a voltage change generated by the electrons oscillating between different spin states (e.g., transitions ms=0 to ms=-1 and ms=0 to ms=+1). The intensity of the energy that is measured by the detector 150 can be an intensity of photons such as energy change affected by the spin state, photons, microwaves and / or voltage, to name some examples.

[0064] The stimulated transfer to ms= |+ / - 1> can be interrogated, for instance, by repeating the step of transitioning the base triplet states 24 to the excited triplet states 26, and measuring the amount of radiation emitted by the excited states 26 transitioning back to the base states 24. Indeed, since the transition energy will transition the base states 24 into their respective excited states 26, and since the ms= |+ / - 1 > excited states are low-fluorescence, the measured intensity of the radiation will be stronger when the transfer from ms= |0> to the ms= |+ / - 1> has failed, than when the transfer has succeeded. This “interrogation” simultaneously has the effect of “initializing” the system back to the ms=0 base state, which is perfect for making another transfer attempt, and this process can be repeated at different frequencies, and the measured amplitude plotted in a chart, producing dips, referred to herein as “peaks” along the graph, at energy values / frequencies at which the transfer has succeeded.

[0065] The entire process for making one measurement, from the initializing transition to the interrogation transition, including the intervening spin-state transfer, can thus be as schematized in Figs. 3A and 3B. If repeated successively at progressively increasing ordecreasing frequencies (e.g. by scanning the frequency spectrum), and in the absence of an external magnetic field, one can form a graph 36 such as presented in Fig. 4 showing a measured signal vs. frequency in the absence of a magnetic field. The detected radiation intensity dips as the energy reaches the nominal field splitting frequency fo, or transfer value. In NV defects interrogated via ODMR, in the absence of an external magnetic field, a single “peak” diminution, or drop, in the fluorescence, such as schematized in Fig. 4, will be detected around 2.87 GHz. For simplicity, the expression peak may be used herein to refer to peak population transfer, independently of the type of structure in which the spin state systems are found and independently of the stimulation / detection methods.

[0066] In practical applications, the entire process, including the spin-state-transfer and the interrogation, is to be performed more quickly than the relaxation time, otherwise the relaxation may cause noise in the form of ms= |+ / - 1> states induced by relaxation rather than spin state transfer, which can ultimately overwhelm the effect of the proactively induced spin-state- transfer. In practice, the entire process for making one measurement can be performed in less than 10 micro-seconds, and perhaps even in the 1 micro-second range which can be preferred for quantum reasons. This can be entirely suitable in the case of NV defects 10 where the relaxation time Ti can be in the order of a few milliseconds at room temperature, bringing it into a realm which is impossible to control by a human. In a measurement protocol implementation, it can be desired to proceed faster than the quantum phase decoherence time, or dephasing time T2*, which is in the order of a few microseconds.

[0067] Applying the energy using a microwave pulse which is not simultaneous to the initialization can be preferred and can make the line on the graph of Fig. 4 sharper by avoiding phenomena of power broadening encountered when applying microwaves during the optical measurement. Accordingly, using a process such as described above, can allow to make a graph 36 such as presented in Fig. 4, and to measure an absolute value of fo essentially by finding frequency of the minima of the curve (aka center of the peak), for instance. This can be automated using a computer with appropriate instructions.

[0068] Temperature fluctuations can affect the absolute value of fo and can essentially shift (offset) the curve to the right or to the left. If it is desired to measure the variations in temperature, for instance, it will be understood that knowing the relationship between theabsolute temperature and the absolute value of fo (which can in the form of a table, graph, or calibration data for instance), one can proceed to measure the absolute value of fo, and then associate the measured value of fo to the corresponding absolute value of temperature T. However, the process of plotting the entire curve to determine an absolute frequency value such as fo is relatively complex and time consuming. In many cases, rather than tracking the absolute frequency value, it can be preferred to simply track changes in the frequency value, which can be done in a simpler manner.

[0069] For example, in a context where the temperature only shifts the dip in the curve to the right or to the left, and does not, for instance change the amplitude of the curve (e.g. such as schematized in the displacement from the continuous line 38 to the dashed-dot line 40 in Fig. 4), the measurement can be taken at a single frequency (schematized by the vertical dashed line 42 in Fig. 4), and if certain assumptions can be made, such as that the two measurements 44 of intensity are taken on the same side of the dip 46 and the shape of the dip is constant and known, one can essentially plot a given intensity measurement to a given position of the dip along the horizontal axis, and essentially determine fo from the established position of the dip along the horizontal axis. Such as technique can allow to determine a relative difference in temperature AT simply based on a relative difference in intensity APL, essentially using 2 measurements as opposed to a fuller scan. It will be understood that the degree of precision achievable by such a relative measurement can be higher when the movement of the measured intensity occurs along a portion of the dip curve where the slope is higher, and so for fine measurements, regions of higher slope can be preferred over regions of lower slope. Moreover, even in a situation where the shape of the dip curve changes or where the amplitude of the dip curve fluctuates upon a change in temperature, if the change in the curve is predictable and repeatable, calibration can allow to factor out such variations and still achieve a relative measurement using only two measurements. The same approach of using detected changes in amplitude along known curve shapes can be used for measurements other than temperature, such as magnetic field amplitude for instance, and we will come back to this optional technique of making relative measurements rather than absolute measurements further below.

[0070] More specifically, in the case of NV defects 10, in the absence of an external magnetic field, the nominal (“zero-field”) splitting is of fNVo~2.87 GHz between the ms= |0> and the ms= |+ / - 1 > states.

[0071] An ambient magnetic field p will split the resonances, as shown in Fig. 2B and in Fig. 5, forming two measurable “dips” for each NV defect 10 orientation instead of a single dip and temperature variations will shift the entire curve to the right or to the left. Under a weak magnetic field, the equation describing the phenomena is expressed by: fires- ffiv T Cf T + Y^proj

[0072] Where Bproiis the projection of the magnetic field axis on the axis of the NV defect 10 and the plus or minus sign depends on the transition (minus for |0> to |-1 >, plus for |0> to |+1 >). In practice, this relationship can also depend on other parameters such as strain and electric field, and be impacted by off-axis magnetic field, although to a lesser effect than what is described above.

[0073] The NV defects 10 can assume four different orientations in the diamond crystal, one of them being shown in Fig. 2A, while the other possible NV defect 10 orientation can be formed by switching any one of the three other carbon atoms (C) 14 adjacent the nitrogen atom with the vacancy (V) 20 in the structure. This can lead to four pairs of resonance lines each split by the projection of the magnetic field on the given orientation (see Fig. 5). Given knowledge of the temperature fluctuations AT, measuring three of these projections can be sufficient to reconstruct the magnetic field vector in three dimensions as the orientations are linearly independent. If the temperature fluctuations are unknown, one can still reconstruct the magnetic field vector together with the temperature, by using four of these projections, essentially by forming an equation system with four equations and four variables.

[0074] At this point, we have two transitions per orientation times four orientations 48 for a total of eight magnetic resonances; however, we have an additional splitting of each one of those resonances into three due to hyperfine splitting. This splitting leads to a total of 24 resonances, as illustrated in the level structure on the right-hand side of Fig. 5. Nonetheless, as this hyperfine splitting is constant, and the + and - splits are symmetrical relative tofNvo~2.87 GHz, we only have four independent variables in the problem: AT, Bx, By, Bzsuch that measuring the frequency of four resonance lines (from at least three different orientations) can be sufficient.

[0075] To perform vectorial measurements with NV defects 10, the method may aim to isolate the effect on the fluorescence measurements from at least three defect orientations. In a usual context where the magnetic fields are on the scale of the field of the Earth (~50 pT), the full magnetic resonance spectrum of the NV defect 10 has 24 overlapping spectral lines (caused by 4 NV orientations with 3 peaks per orientation), which, when scanned using a technique such as presented above, can yield a graph 52 such as shown in Fig. 6 instead of a graph 36 such as shown in Fig. 4.

[0076] In a magnetometry context, there can be a challenge in identifying the different orientations of the NV defects 10 so to reconstruct the magnetic field vector, and the magnetic moment can become contingent upon the identification.

[0077] In one approach, the resonance lines from the four orientations can be split by adding a bias magnetic field from permanent magnets at the sensor position. In that approach, the lines can become clearly split in a predictable fashion to identify the orientations. However, this method can be unsatisfactory for high-sensitivity (in the order of nT) measurements as the bias field can have stringent requirements in terms of spatial uniformity, temperature sensitivity and mechanical vibration sensitivity. Since the bias field needs to be >1 mT to split the lines cleanly, achieving a nanotesla accuracy requires its knowledge to be one part to one million.

[0078] A Rabi effect which can be referred to herein as Rabi flopping can be affected by the geometrical projection of the ambient magnetic field on the characteristic orientation in the substrate and can thus encode information pertaining to the ambient magnetic field. It was found that instead of using a bias field, this Rabi effect can be harnessed to isolate the effect of the different spin populations in the detected signal, as it can attenuate the spin population transfers of the different spin populations in a different, and known manner, depending namely on the different geometrical projections. We saw above that spin state transfer can be induced on one or more previously initialized spin population by applying energy at an energy value(e.g. frequency in the case of massless particles such as photons) corresponding to the difference of energy between the two states (e.g., referring to Figs. 2B). However, if the spin state transferring energy, of the right energy value, is applied in the form of a pulse of a given pulse energy (which may be affected by duration, amplitude, shape, or a combination thereof), the given pulse energy can potentially generate a phenomena referred to as Rabi flopping which, if fully produced, can entirely cancel the otherwise spin state transferring influence of that spin state transferring energy value. This effect can thus change the percentages of spin populations which will be in the ms=+-1 states or ms=0 state and can thus have a measurable effect. Since the Rabi flopping effect attenuates the population transfer influence, we will refer to it as Rabi attenuation in the context of this specification, independently of the extent (or amplitude) of the attenuation.

[0079] More specifically, the extent of the Rabi attenuation can also depend on parameters of the application of the transfer energy. For instance, if the transfer energy is applied with a microwave pulse, the extent of the Rabi attenuation may vary somewhat sinusoidally based on features of the pulse, such as pulse duration or pulse amplitude. Fig. 7 presents an example of how photoluminescence can be affected by pulse duration in ODMR. Some relatively short pulse durations T (within a range of duration that can produce Rabi flopping or otherwise said within a Rabi range) will lead to a fuller effect of the population transfer influence. The smallest, exact duration of the pulse required to reach a fullest population transfer influence is referred to as a TT-pulse duration and will depend on a quantity referred to as the Rabi frequency, represented schematically in Fig. 7. The effect of a pulse of the transition energy value (e.g., transition frequency) and of the TT-pulse duration is represented by the transition shown with a bold arrow in the Bloch sphere diagram of Fig. 3B. Other odd multiples of the TT-pulse duration can also lead to very or relatively complete population transfer influence.

[0080] However, even multiples of the TT-pulse duration, such as a 2TT-pulse or 4TT-pulse duration for instance, can entirely cancel or negate the population transfer influence, or otherwise said produce the fullest Rabi flopping / attenuation effect, and lead to a situation where, even if the transition energy value (e.g., transition frequency) applied corresponds to the spin population transfer energy value (e.g., is of the right frequency, such as fo on Fig. 4), the selected duration T of the pulse maximally attenuates that influence, which impedes spinpopulation transfer, leaving a greater percentage of the spin population in the high- fluorescence ms=0 state. These even multiples of the TT-pulse duration can be said to produce the fullest Rabi attenuation. Durations intermediate to even and odd multiples of the TT-pulse will lead to partial negating influence, and the extent of the partial attenuation can be in accordance with a sinusoidal shape having a Rabi frequency and can be precisely known. Interestingly, the Rabi frequency itself, and in turn the corresponding TT-pulse duration, can be made to depend on the population’s orientation relative to the polarization of the emitter’s electromagnetic field (the transfer energy). Indeed, if applied in a manner to produce different trigonometrical projections of the excitation on each one of the defect orientations, the different orientations can experience different Rabi frequency, leading to different proportions of Rabi attenuation for a given pulse. Accordingly, the Rabi frequency can depend on the projection of a microwave orientation on the defect orientation, and the Rabi frequency can be highest when the microwaves are perpendicular to the defect orientations.

[0081] The graph presented in Fig. 7 shows that for a given one of the characteristic orientations, the extent of the population transfer fluctuates between no transfer and full transfer in accordance with a generally sinusoidal curve where different pulse energies, or pulse configurations, are mapped to different values of population transfer proportions or percentage of Rabi attenuation. This curve will be referred to herein as the Rabi curve for ease of reference. In the case where pulse duration is varied between different instances of pulse sequences of the succession of pulse sequences, different values of pulse duration are mapped to sinusoidally varying values of population transfer proportion. The sinusoidal curve has a frequency which is referred to as the Rabi frequency, and different values of pulse duration can be said to correspond to different values of phase associated to the Rabi curve. This phase will be referred to herein as the Rabi phase for ease of reference. Measuring the Rabi phase associated to different ones of the pulse sequences can allow to extract information about the Rabi curve, such as the value of the Rabi frequency (or conversely, the value of duration, or period, or each Rabi cycle). Via determining the Rabi frequencies, the method can isolate the overlapping contributions of the spin populations associated to different ones of the characteristic orientations in the signal measured using the detector. It will be noted that Fig. 7 represents an ideal case of a Rabi curve provided for explanation purposes.In practice, it will be understood that various factors can affect the shape of the Rabi curve, such as decreasing amplitude as a function of increase in duration, etc.

[0082] Accordingly, one can essentially engineer a system with different Rabi frequencies for the different population orientations by proactively selecting the excitation orientation relative to the population orientations. Then, one can choose to apply a sequence of microwave pulses at (including operationally near) the transfer energy value / frequency, but of different pulse configurations. In some examples, the different pulse configurations can involve different energy values such as different durations and / or different amplitudes. The most convenient way to vary the pulse energy may be to vary the pulse duration T in some embodiments. Accordingly, different measurements can be associated to the application of different pulse durations being selected in a manner to create a discernible contrast between the amount of Rabi attenuation of respective ones of the population orientations. In one embodiment, the Rabi attenuation can be engineered to be entirely absent for one orientation, and as complete as possible for the other orientations, to best isolate the contribution of a single orientation (or otherwise said, maximize “contrast”), for instance.

[0083] Depending on the embodiment, when the Rabi effect does not fully attenuate the state transfer effect of the pulse, the pulse can be used to create a superposition of the ground state and a magnetically sensitive state (e.g. ms=0 and ms=1), or a superposition of the ground state (ms=0) and the “bright” state (the bright state being itself a superposition of ms=1 and ms=-1) for instance.

[0084] To illustrate this concept, let us begin by taking a relatively simple scenario where it is known, a priori, that two, and only two, known population orientations have a population transfer occurring at a given energy value, i.e. they have overlapping peaks. At that excitation energy value, the detected signal amplitude represents the sum of the amplitude of both individual population orientation amplitudes, and it is desired to dissociate the individual amplitudes of the population orientations on the detected signal. Essentially, we could measure peaks such as shown in Fig. 8A or Fig. 8B, for instance, by scanning across energy values.

[0085] The detected peak, and when looking at it more closely, the measured amplitude at any energy value, is the result of certain variables, including: the central wavelength / frequency of each one of the two peaks a and b which are superposed, the shape and amplitude that the peaks a and b have individually, and the respective attenuation of the peaks. It turns out that if the respective attenuation of the peaks is known given the known relative orientation between the spin populations and the transfer energy emission, and that the shape and amplitude of the individual peaks are known from prior calibration or experiment, the only unknown variables are the central wavelength of each peak. Two unknown variables may not be solvable from a single measurement, but if two measurements are taken, at different pulse durations, one can build a system of two equations with the two unknown variables and solve the system of equations to yield the variables.

[0086] Fig. 8A and 8B provide a visual representation where, in Fig. 8A, the pulse duration is known to maximize the spin population transfer of spin population a (i.e., 100% spin population transfer), while generating 50% Rabi attenuation of the spin population transfer of spin population b. In Fig. 8B, the experiment is repeated but at a pulse duration which is known to maximise the spin population transfer of spin population b (ie. 100% spin population transfer), while generating 25% Rabi attenuation of the spin population transfer of spin population b. With everything other than the central frequencies of spin populations a and b, the resulting system of two equations and two unknowns can allow to solve for the two central frequencies.

[0087] The same reasoning can be extended to a scenario where three, four, or potentially more variables are unknown a priori. For instance, in a vectorial magnetometer, the amplitudes of the unknown magnetic field in at least three different orientations are required to reconstruct the 3D vector. The corresponding system of three equations and three unknowns can be built by taking three measurements, each at a different pulse duration known to produce different and known attenuations on the different orientations. Similarly, the central frequencies can be affected by changes in temperature, and if the change in temperature is a priori unknown, it can be preferred to build a system of four equations where the change in temperature is the fourth unknown variable and then solve for the four unknowns.

[0088] In practice, scanning across the frequency spectrum to determine the shape and amplitude of the resulting peak may not be required to reconstruct a 3D vector. Indeed, themeasurements at any frequency will bear the sum of any dips associated with that frequency. However, to be relevant, the measurements may need to be made at a frequency corresponding to a peak, and one may need to make at least one measurement indicative of a dip caused by each one of the peaks of interest. Accordingly, as few as 3 measurements may be used to reconstruct a 3D vector, and as few as 4 measurements if reconstructing a 3D vector while factoring out temperature changes. If it turns out that one of the measurements does not detect any dip, it may be that that measurement needs to be shifted on the energy value scale. In some embodiments, a calibration routine can be performed to establish the different energy values at which the different measurements will be made. In one example, the calibration can be made based on the Earth magnetic field and can provide a first “guess” as to which energy values should be used for the first measurement. As the strength of the external influence increases, the peaks can begin to shift from the initial estimation based on the Earth magnetic field, the system can detect a corresponding increase or decrease of amplitude at the energy values and automatically shift the energy values to compensate and ensure that each measurement remains relevant. In alternate embodiments, rather than attempting to minimize the number of measurements required to reconstruct a 3D vector, one may prefer to scan across the energy values or use another measurement strategy.

[0089] More details about the above identified approach, including variations thereof, is available in the publication W02022 / 020943.

[0090] Another quantum effect, the Ramsey effect of phase accumulation, can be affected by the geometrical projection of the ambient magnetic field on the characteristic orientation in the substrate, and can thus be used to encode information pertaining to the ambient magnetic field.

[0091] When working with NV centers, the Ramsey oscillations refer to the phase accumulation of the states with nonzero angular momentum, which occurs under the effect of a magnetic field. To obtain a measurable phase, the state that is being under observation must not be an eigenvector of the magnetic field operator Szsuch that the phase accumulated is a partial phase, not a global phase, which couldn’t be measured. In some embodiments, which will be referred to herein as “single quantum” for ease of reference, the state prepared is|0>+'+1>such that the |0) doesn’t pick up a phase while |+1) picks up a factor ofe~i YBzt, a phase proportional to Bzt. That relative phase is then measured by inversing the population with a microwave pulse, making the population in |0) dependent on Bzt.

[0092] One way of harnessing Ramsey effects is presented with reference to Figs. 9, 10 and 11. Referring to Fig. 9, rather than using individual pulses to alter the spin states between the ms=0 and ms=±1 states (or superpositions thereof), pulse sequences having a sequence of two pulses, separated by an interpulse delay during which phase accumulation may occur, can be used. As schematized in Fig. 10, the first pulse of the sequence can perform an intermediary transition between the ms=0 and ms=±1 states (or superpositions thereof). An optimized scenario can involve a TT / 2 transition, for instance. Then, during the interpulse delay, the ambient magnetic field can impart phase accumulation to the state, represented as a variable degree of rotation around the z axis of the Bloch sphere. Then, the second pulse of the sequence can complete the transition between the ms=0 and the ms=±1 state and the measurement can be made. The measurement can yield information pertaining to both the Rabi effect and the Ramsey effect (phase accumulation).

[0093] Indeed, Ramsey fringes refer to the phase accumulation of the spin state when in superposition with a magnetically sensitive spin state. In some embodiments, which will be referred herein as “single quantum” for convenience, the superposition can be between ms=0 and ms=1 states (as seen in Fig. 10). After a pi / 2 pulse, an external magnetic field will accumulate phase on the equatorial plane of the block sphere, representing the phase of the spin state superposition. Once the evolution time, corresponding to the interpulse delay, is done, another pi / 2 pulse can rotate the spin state. Depending on the phase accumulation (and hence, on the external magnetic field), the spin state can be found more in 0 or more in 1 , as measured via a detector (e.g., in the case of ODMR, the red photoluminescence of the NV defect upon green illumination in our case). For instance, in one embodiment, if no phase is allowed to accumulate, the second pulse may complete the transition between 0 and 1 , whereas if 180-degree phase is allowed to accumulate, the same second pulse may then return the state to 0.

[0094] Similarly to the way pulse parameters can be associated to a Rabi curve, varying values of interpulse duration can be associated to an oscillating relationship which can bereferred to as the Ramsey curve, an example of which is shown in Fig. 11. More specifically, Fig. 11 shows a typical Ramsey fringe signal, where a change in the frequency 6f of the signal is proportional to a change in the sensed field SB. The decay of this oscillatory signal relates to the dephasing time T2* of the defect, and C is the Ramsey contrast.

[0095] Different values of interpulse duration can correspond to different points, or phases, along the Ramsey curve. Accordingly, varying a duration of the interpulse delay between different instances of propagating pulse sequences can allow to extract, via the associated measurements, information about the respective Ramsey phase, or position of each pulse sequence along the Ramsey curve, which can, in turn, allow to extract information about the Ramsey curve, such as the Ramsey frequency or conversely the duration / period of Ramsey cycles. It will be noted that in some cases, the interpulse delay may not consist of a perfect absence of stimulation. There may be some form of noise or other minor excitation which nonetheless allows phase accumulation and later retrieval of the information. Similarly, even if the first pulse does not perform a perfect TT / 2 transition, if the extent of the transition is known, its incomplete value may be factorable out from the equations in a manner which nonetheless allows information retrieval.

[0096] A variant which will be referred to herein as “double quantum” for convenience, can involve three spin states. A first pulse can be used to create a superposition of ms=0 and the bright state, which itself is a superposition of ms=1 and ms=-1 states, in other words the state|nthis case, both parts of the expression pick up an opposite phase, allowing phase accumulation at twice the rate of the “single quantum” case exposed above. During the interpulse delay, the Ramsey evolution happens between the bright state and the dark state, where the dark state cannot be accessed by a pulse at the transfer energy value Once the evolution time is finished, and after the second pulse, the measurement can (in the case of pi pulses) represent the population of spin state that was in the bright state at the end of the evolution time. Interestingly, this transition can also be insensitive to strain and temperature, since the effects of strain and temperature on the ms=1 and the ms=-1 states can cancel out. This feature can be an advantage in scenarios where strain or temperature is a source of noise.

[0097] In accordance with one approach, to allow the extraction of information, on one hand, one or more parameters of the pulses can be varied from one pulse sequence to another, such as by varying pulse duration (see Fig. 12A) by varying pulse amplitude (see Fig. 12B) or both, and on the other hand, interpulse delay can be varied from one pulse sequence to another (see Fig. 12A or 12B). Both varying pulse duration and varying pulse amplitude can be considered ways of varying pulse energy. It will be noted that rather than being as shown in Figs. 12A and Fig. 12B, the two pulses of each sequence can have complex shapes, such as being composed of a sum of many smaller pulses having different amplitudes, or a gaussian or other shape, for instance. In some cases, which will be explained below, the pulse parameter(s) which is changed from one pulse sequence to the other can be pulse shape but let us begin by explaining the examples presented in Fig. 12A and Fig. 12B.

[0098] In accordance with a first example technique, a succession of pulse sequences is propagated onto the different spin populations. Each pulse sequence is separated from the other by a measurement, such as a measurement of emitted radiation intensity, and reinitialization. Each pulse sequence includes a first pulse, an interpulse delay, and a second pulse. In some embodiments, it can be preferred for the first pulse to be identical to the second pulse. A first succession of pulse sequences can be performed where from one pulse sequence to the other, the pulse duration and / or pulse amplitude is varied, while the interpulse duration is maintained constant. This can be referred to as scanning the Rabi curve. A second succession of pulse sequences can then be performed where from one pulse sequence to the other, the pulse duration and / or pulse amplitude is varied, while the interpulse duration is maintained constant, but at a different value than for the first succession of pulse sequences. Again, during the second succession of pulse sequences, the Rabi curve is scanned. The process can be repeated for additional successions of pulse sequences, where the interpulse duration is varied between each one of the additional successions of pulse sequences. Accordingly, repeating for additional successions of pulse sequences, with different values of interpulse duration, can be referred to as scanning the Ramsey curve.

[0099] In accordance with another approach, rather than scanning the Rabi curve for each one of a number of differing values of interpulse delay, complex pulse shapes may be engineered to specifically result in the sending of one of the spin populations to the equator ofthe Bloch sphere (such as schematized on Fig. 13), of functionally close to the equator of the Bloch sphere, while simultaneously sending the other spin populations back to their initial state (e.g., ms=0), or functionally close to the initial state. Phase can then be allowed to accumulate only in the spin population which has been sent to the equator of the Bloch sphere, before the second pulse and the measurement and initialization. The next pulse sequence can then have a first pulse engineered to carry the second spin population to the equator while returning the other spin populations back to their initial states, and phase can be allowed to accumulate before the second pulse and the measurement and initialization, and so forth.

[0100] Some detailed examples will now be presented in greater detail for illustrative purposes.

[0101] In one example, associated to NV defects in diamond interrogated via ODMR, individual ones of a plurality of pulse sequences used in succession can be as shown in Fig. 14. From left to right, the first step (pump) is the illumination of the diamond with green light to initialize its state to |0). The second step (MW) is application of resonant microwaves to produce a Rabi oscillation between |0) and |+), it is the step that encodes the rabi frequency. The third step (evolution time) is the free evolution step, where the local magnetic field will generate state evolution between |+) and |-), encoding the resonant frequency in the state phase. The fourth step (MW) is similar to the second step, this time with the purpose of bringing back the population of |+) in 10), which can be observed. The fifth step (probe) is the illumination of the diamond in order to measure the amount of red light emitted, which gives a measure of the population in |0).

[0102] To prepare the bright state, for a given coupling strength of fl for one given orientation, we would need to set fit = n, where t is the microwave duration time. Then r represents the inter-pulse duration sweep (evolution time / no) to allow for phase accumulation of the bright state. This is followed by yet another / Wl / I / pulse to project some of the accumulated phase in the measurement basis. Again, in a scenario driving for perfect recovery we would USe fit = 7T.

[0103] Drawing a picture with no decoherence, the state evolution can be described in a few matrix rotations as follow:

[0104] After the first pulse (green pump in the above diagram), the state is initialized. l 'o> = |0>

[0105] A microwave pulse of fixed amplitude (fl) and varying duration (t) is applied, producing an evolution around Sx. For brevity, we assume here that the amplitude of the microwave field is much larger than the amplitude of the static magnetic field, allowing us to neglect the effect of the magnetic field in this step.

[0106] The prepared state is let to evolve for some other amount of time (T) under the influence of the magnetic field of amplitude Bzalong the orientation of the NV (also known as the Principal Axis), producing an evolution around Sz.

[0107] A second microwave pulse is applied. In the simplest implementation, it is identical to the first microwave pulse.

[0108] Then, a laser is applied, and the photoluminescence measurement is performed, yielding a measurement of the populationwhich is percentages of the spin populations, in |0).

[0109] The latter equation can be referred to as equation 1. At this point, careful examination will reveal that the terms in the parenthesis depend on both t and T, meaning that a 2D Fourier transformation, such as a Fast Fourier Transform (FFT), will clearly place them in the firstquadrant, whereas the terms in the square brackets depend only on one of the time parameters (or even none at all), meaning that in a 2D FFT, they will fall on the axes, since they have at least one DC (time independent) component.

[0110] To differentiate each of the four NV orientations i, the diamond can be positioned relative to the microwave field such that the Rabi frequencyof each axis is well separated from one another. The Rabi frequency is equal to the gyromagnetic ratio of the electron y times the projection of the microwave field BMWalong the dipole moment of the spin transition, which is perpendicular to the NV symmetry axisWe compute the Rabi frequency of each axis as

[0111] The microwave field direction can be parametrized by polar and azimuthal angles in the diamond’s

[0100] frame of reference to compute which angles lead to the largest minimal separation between projections, as shown in Fig. 15.

[0112] In addition to the bare Rabi projection along each axis, there exist additional spectral features that evolve with subharmonic frequencies of n e {- 1, 1,- 3 , 2} times fl;, which may be significant in some embodiments. Accordingly, in some embodiments, to maintain spectral tagging with the Rabi frequencies free of crosstalk between different orientations i and subharmonic n, we define the minimal separation Am„ to be optimized as the minimum difference between the projection of each axis against all the subharmonics of the other axes: min = i m*ji;nn I I proj ‘ - n proj J Il

[0113] Accordingly, in practice, additional constraints can be imposed in choosing an appropriate microwave angle. First, since we require that fl » yBzfor the microwaves to properly address the |0) |+) transition, we require that Q; be all be as large as possible,defined by lmin= min fl,. We take the product of Smin= AminD.mmto thus find the optimal angle of operation, as shown in Figure 15B.

[0114] Fig. 16 presents an experimental pulse sequence used to drive the experiment. Two parameters are varied to collect experimental data point: the free evolution time r, in section ©, and the duration of the microwave pulse t, in section®. Since there are two such pulses, there are two sections ®.

[0115] Where a sweep of the pulse duration, t, labelled 2, is performed. This sweep is what will allow to differentiate the orientations based on their different Rabi frequencies. The second swept parameter, T, labelled 1 , is the evolution time, where each of the orientations and their hyperfine will accumulate phase between the bright and dark states with a Ramsey frequency proportional to the magnetic field along their Principal Axis.

[0116] In another embodiment, the differentiation of the orientations can be done by designed pulse sequences. An example of pulses sequence can be designed by using Optimal Control Theory and find a pulse sequence that fulfills a specific operation. This still relies on the fact that a given pulse sequence will not have the same effect for different orientations. For example, using the GRAPE algorithm from N. Khaneja, T. Reiss, C. Kehlet, T. Schulte- Herbruggen, and S. J. Glaser, “Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms,” Journal of Magnetic Resonance, vol. 172, no. 2, pp. 296-305, Feb. 2005, it could be possible to design a pulse sequence such that its effect is a different preparation for each orientation, preparing one of them into the state of interest for the measurement (for example the “bright state”while preparing the other three in a state independent of the free evolution (for example 10>, | — 1> or | + 1): the eigenvectors of Sz).

[0117] Another point of interest of GRAPE is that, as is the case with Average Hamiltonian Theory, the pulse sequences it designs can be made robust against distributions of parameters such as homogeneity of the magnetic field across the sample, the Zero-Field Splitting, the microwave field, etc. Other techniques such as CRAB, Krotov or other variants can achieve similar results, with some gains on the optimization time or ease of implementation.

[0118] Independently of the approach which was taken to encode the information, the signal received in photoluminescence can contain enormous amounts of information. It can be thought of as a 3-dimensional mix of sinusoidal functions with multiple different frequencies. Fig. 17 is an example of what one could expect from a simple single NV center measurement in Earth’s magnetic field.

[0119] In Fig. 17, time domain results of a simulation of a simple case (one NV orientation without hyperfine) are shown, where the donut shape is characteristic of the 2D frequencies. Along the Y-axis we can see a Rabi oscillation while the X-axis doesn’t show any Ramsey oscillation since that would correspond to a pulse of no duration. A horizontal line slightly above shows Ramsey oscillations.

[0120] One tool used to process the signal is through applying some filters. Filters such as Hanning, Hamming, Blackman or variations (as well as custom) of such windows, and DC offset corrections are used, especially before converting the time-domain data to its frequency domain. Because of the decay in both Rabi and Ramsey signals, mirroring of the data about the y axis could also be implemented.

[0121] In another embodiment of the method, represented in Fig. 18, the phase of the second pulse can be changed.

[0122] More specifically, Fig. 18 (a) shows a double quantum experiment, for a single orientation and no hyperfine splitting. Fig. 18 (b) shows the sum of two double quantum experiments, with the first experiment is a typical experiment and the second experiment has had its second pulse shifted by a phase of TT. Fig. 18 (c) presents a Fourier transform of (a) that displays the three components mentioned in Equation 1. Fig. 18 (d) presents a Fourier transform of (b) that demonstrates that the peak at around 2.5 MHz has been removed by interference, leaving the peaks at twice the Ramsey frequency, the double quantum oscillations.

[0123] This enables another set of data to be collected, that is like the main embodiment, but carries a difference in phase in the signal such that the sum or the difference of the data sets with or without the phase shift will highlight different parts of the signal. Similarly, as done NV-Diamond Magnetic Microscopy using a Double Quantum 4-Ramsey Protocol. Hart et al. 2021 . 10.1103 / PhysRevApplied.15.044020, using a second source of microwaves will unlock a more exhaustive control of the system, producing data sets with various phases, which can then be combined in addition or subtraction to remove signals that are not all as sensitive as the Double Rabi Double Ramsey signal.

[0124] Different methods can be applied to recover the information pertaining to the ambient magnetic field amplitude and orientation. One example is the 2D-FFT inversion technique. This technique can take an FFT along the axis of the swept pulse duration (y axis) followed by an FFT along the inter-pulse duration axis (x axis). Visually this method can yield a 3- dimensional plot with Rabi frequencies along the y-axis, and Ramsey frequencies along the x-axis. One can expect a plot such as shown in Fig. 19 if the experiment is performed with phase control. Fig. 19 shows that a line cut along the Y direction can be representative of the Rabi frequency for that orientation in an example scenario with NV defects in diamond interrogated with ODMR. The four line cuts represent the isolated four different NV orientations.

[0125] Fig. 20 is a graph showing, for one orientation, the magnetic field will shift the evolution frequency by 2y_b B_z (as well as its negative value). In addition, the three possible values of the hyperfine splitting spread that signal into three distinct points separated by 2A_||.

[0126] Fig. 21 is a graph showing that for the four orientations and their hyperfine coupling (3 possible values), with the positive and negative frequencies in frequency domain, 24 peaks can be identified in the signal.

[0127] Another example is hyperfine revival. Indeed, because of the nearby Nitrogen, the effective field at the vacancy can take three values, yBz, yBz- Ay, and yBz+ Ay, where Ay is the hyperfine splitting caused by the nitrogen spin, typically of 2.16 MHz. Because of this, every field that we can measure will be the average of these three fields, and even if we can separate the orientations with their Rabi frequency, the signal will be a mixture of the three fields. In our Ramsey signal, that will appear as an average of three sinusoidal functions with slightly detuned frequencies, which will create beatings and increase the complexity. Careful observation of these frequencies will reveal that regardless of the magnetic field Bz, their signalgets in phase at each time interval of — . Thus, by taking data points at these time points, we can ignore the beatings and measure Bzdirectly, as shown in Fig. 22.

[0128] More specifically, Fig. 22 is a set of graphs depicting Ramsey signal for each orientation, assuming that they are already resolved for each orientation, by isolation of their respective Rabi frequency for instance. Despite the apparent beatings due to three values of the hyperfine splitting, sampling points a regular interval of 1 A || highlights the envelope of the oscillation, which relates to the magnetic field along each orientation. The four graphs represent the four NV orientations, along which the microwave excitation generates different Rabi frequencies, which labels them. The orange line is the full simulation. The blue points give the signal collected at that hyperfine revival frequency and the blue line connects them naively. The red line is the initial guess for the fit. The green curve is the curve of best fit, which can be compared to the magnetic field inputted to generate the simulation and gives the error in the subtitles.

[0129] In another embodiment, the method of inversion needs only to look at points that have the same ratio of pulse duration and free evolution time, such that the experiment effectively reduces to a 1 D experiment, with a single meta parameter that increments the values of the pulse duration and the free evolution time together (see Fig. 23). With that method, the sampled signal can be displayed in the frequency domain (see Fig. 24), and the signal will exhibit frequency modulation, such that the rabi frequency can be assigned a meaning of carrier frequency while the Ramsey frequency can be assigned a meaning of signal, on each side of the carrier frequency.

[0130] In Fig. 24, the “carrier frequencies” at around 0.15 and 0.3 are the large rabi frequencies and the side bands correspond to the Ramsey frequencies

[0131] In other words, as long as the sum and difference of each of the four Rabi frequency and its associated Ramsey frequency, as well as their harmonics are well resolved in the frequency domain, a 1 D experiment is sufficient to separate the four orientations (see concept in Fig. 25). Measuring the Ramsey frequency of each orientation then gives a measure of the magnetic field along that orientation, which is sufficient information to find the vector magnetic field.

[0132] Another method to invert a full magnetic field vector from the given data is using inner products along both swept axes. Since the behaviour of the pulse duration (Rabi oscillation) is separable from the behaviour of the inter-pulse duration (Ramsey oscillation), one can perform inner products on both these parameters. The inner product along the pulse duration axis can be done with the following formulaSt=o P(t, T, fl, Bz)cos(a ), is the target rabi frequency, t is the pulse duration, and fl is the Rabi frequency.

[0133] The rabi frequencies are determined through the mechanical assembly of the device, we can then only perform the inner product along those frequencies. After this application of the first inner product, we are left with the equivalent of a Ramsey signal along the resultant axis.

[0134] Similarly, we can then do another inner product with this result; one along the Ramsey axis. With the formula£=0P(T, ( ,Y, Bz)cos(yit), where ytis the target Ramsey frequency, T is the pulse duration and fl is the Rabi frequency.

[0135] Once both inner products are computed on the data, the frequencies that match in both the targeted Rabi and Ramsey frequencies will be apparent. If we were to target multiple Rabi and multiple Ramsey frequencies with the inner product, we would get something like the FFTs. We then effectively suppress all frequencies that don’t have both a Rabi and Ramsey component, leaving peaks at a given rabi frequency as shown in Fig. 26, while performing the inner product along only the selected rabi frequencies followed by an inner product along multiple Ramsey frequencies yields the result shown in Fig. 27.

[0136] Now, considering each orientation is represented by a different line type, we can find the Ramsey frequency of each peak and invert a magnetic field from these values; with each Ramsey frequency being proportional to Bz.

[0137] Referring to Fig. 28, it will be understood that the expression “computer” 400 as used herein is not to be interpreted in a limiting manner. It is rather used in a broad sense to generally refer to the combination of some form of one or more processing units 412 and some form of memory system 414 accessible by the processing unit(s). The memory system can be of the non-transitory type. The use of the expression “computer” in its singular form as used herein includes within its scope the combination of a two or more computers working collaboratively to perform a given function. Moreover, the expression “computer” as used herein includes within its scope the use of partial capabilities of a given processing unit.

[0138] A processing unit can be embodied in the form of a general-purpose micro-processor or microcontroller, a digital signal processing (DSP) processor, an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, and a programmable read-only memory (PROM, to name a few examples.

[0139] The memory system can include a suitable combination of any suitable type of computer-readable memory located either internally, externally, and accessible by the processor in a wired or wireless manner, either directly or over a network such as the Internet. A computer-readable memory can be embodied in the form of random-access memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro-optical memory, magneto-optical memory, erasable programmable read-only memory (EPROM), and electrically erasable programmable read-only memory (EEPROM), Ferroelectric RAM (FRAM)to name a few examples.

[0140] A computer can have one or more input / output (I / O) interface to allow communication with a human user and / or with another computer via an associated input, output, or input / output device such as a keyboard, a mouse, a touchscreen, an antenna, a port, etc. Each I / O interface can enable the computer to communicate and / or exchange data with other components, to access and connect to network resources, to serve applications, and / or perform other computing applications by connecting to a network (or multiple networks) capable of carrying data including the Internet, Ethernet, plain old telephone service (POTS) line, public switch telephone network (PSTN), integrated services digital network (ISDN), digital subscriber line (DSL), coaxial cable, fiber optics, satellite, mobile, wireless (e.g. Wi-Fi,Bluetooth, WiMAX), SS7 signaling network, fixed line, local area network, wide area network, to name a few examples.

[0141] It will be understood that a computer can perform functions or processes via hardware or a combination of both hardware and software. For example, hardware can include logic gates included as part of a silicon chip of a processor. Software (e.g. application, process) can be in the form of data such as computer-readable instructions stored in a non-transitory computer-readable memory accessible by one or more processing units. With respect to a computer or a processing unit, the expression “configured to” relates to the presence of hardware or a combination of hardware and software which is operable to perform the associated functions. Different elements of a computer, such as processor and / or memory, can be local, or in part or in whole remote and / or distributed and / or virtual.

[0142] As can be understood, the examples described above and illustrated are intended to be exemplary only. Alternate embodiments may use other types of structures having spin populations in more than one characteristic orientation and transferable between spin states at a transfer energy value which varies as a function of the trigonometrical projection of an external influence on the characteristic orientation. Moreover, alternate embodiments may use other detection techniques than ODMR.

[0143] Indeed, while the measurement of magnetic fields via spin state transfers in different orientations of NV defects in a diamond matrix met a strong commercial need at the time of filing this specification, it will be understood that the method of dissociating the transfer amplitudes specific to different orientations proposed herein can be useful in various alternate contexts. For instance, a substrate having NV defects in a diamond matrix may be used to measure electric fields rather than magnetic fields, for instance, and the method proposed herein can be useful for dissociating the amplitudes specific to different orientations used in sensing the electric field rather than the magnetic field. Moreover, other crystalline substrates may have different spin population orientations which may be harnessable similarly as to how the NV defects are harnessed to measure magnetic fields or electric fields. For instance, silicon carbide (SiC) has quantum defects which can be interrogated using electrically detected magnetic resonance (EDMR). Nuclear magnetic resonance (NMR) is another technique which could be used to acquire magnetic field information from spin states. In thecase of NMR, rather than collapsing back to the initial (reference) spin state upon measurement, the spins will collapse to another spin state. Vectorial measurement can be performed using different SiC structures oriented in different orientations, and interrogated independently from one another, for instance, by contrast with a single structure having multiple characteristic orientations and interrogated simultaneously by a unique pulse sequence. NV defects may be preferred over silicon carbide for detecting the vector of a magnetic or electric field because the quantum defects of SiC have a single orientation in the matrix.

[0144] Although there were not many candidates for an alternate substrate to NV centers at the time this specification was filed, the study of alternate quantum substrates was a very active field, and it is likely that suitable alternate quantum substrates exist and are simply waiting to be discovered and / or analysed more thoroughly. The method described herein can be used on such alternate quantum substrates if convenient once and when such substrates are discovered. For instance, while not having yet been the subject of much research, Hexagonal Boron Nitride is an emerging candidate which may well have quantum defects which will be harnessable in a manner like the way NV defects have been used in diamond substrates. The definition of the states between which spin populations are transferred can depend on the exact substrate which is used.

[0145] It will also be noted that while initialization of the spin states (setting the states to a starting state) may be done active actively between measurements, there may be some situations in which such initialization is done passively, and this may be the case, for instance, in a situation where the crystalline matrix is close to 0 Kelvin at the time of taking the measurements, in which situation the initialization may be performed solely by way of performing an intentional waiting time sufficient to allow the spin states to return to the reference spin state. While NV defects are typically initialized in the ms=0 state and then transferred to the ms=+-1 states (or a superposition thereof), there can be alternate scenarios. For instance, in the NV defects could be initialized in one or the other of the ms=+-1 states and then transferred to another state.

[0146] Accordingly, the scope is indicated by the appended claims.

Claims

WHAT IS CLAIMED IS:

1. A method of performing a vectorial measurement of an ambient magnetic field, the method comprising: initializing to a reference spin state spin populations having corresponding, different, characteristic orientations in a structure, the characteristic orientations having corresponding trigonometrical projections of the ambient magnetic field; propagating a pulse sequence differently onto different ones of the spin populations, the pulse sequence including a first pulse separated from a second pulse by an interpulse delay, the pulse sequence transferring one or more of the spin populations from the reference spin state to a magnetically sensitive spin state which accumulates Ramsey phase during the interpulse delay; measuring a sum of percentages of the one or more spin populations which collapse to one of the reference spin state and another spin state; repeating the steps of initializing, propagating and measuring in a succession, including varying a configuration of the first pulse and the second pulse in different ones of the pulse sequences in the succession, the different configurations varying the percentages; and varying a duration of the interpulse delay in different ones of the pulse sequences in the succession, the different durations varying the percentages; isolating the Ramsey phase accumulation of different ones of the spin populations based on the variations of the percentages caused by the variations in the configuration; measuring the trigonometrical projections based on the variations of the percentages caused by the variations in the duration; and reconstructing a vector of the ambient magnetic field based on the trigonometrical projections.

2. The method of claim 1 wherein said repeating includes varying the duration of the interpulse delay for different ones of the pulse sequences while maintaining a first configuration of the first pulse and second pulse, and varying the duration of the interpulse delay for different onesof the pulse sequences while maintaining a second configuration of the first pulse and second pulse, the second configuration associated to different values of the percentages than the first configuration.

3. The method of claim 1 or 2 wherein the first pulse and second pulse are identical, the configuration of the first pulse and the second pulse includes at least one of a duration and an amplitude of the first pulse and the second pulse.

4. The method of any one of claims 1 to 3 further comprising varying the configuration of the first pulse and the second pulse for different ones of the pulse sequences while maintaining a first duration of the interpulse delay for different ones of the pulse sequences.

5. The method of claim 2 wherein in the first configuration, the first pulse directs a spin state of a first one of the spin populations to an equator of a Bloch sphere while maintaining a spin state of one or more other ones of the spin populations at the reference state, and in the second configuration, the first pulse directs a spin state of a second one of the spin populations to an equator of the Bloch sphere while maintaining a spin state of the first one of the spin populations, and any other ones of the spin populations, at the reference state.

6. The method of claim 1 wherein the first pulse and second pulse are identical, the configuration of the first pulse and the second pulse includes at least one of a duration and an amplitude of the first pulse and the second pulse, including varying both the configuration and the duration in different ones of the pulse sequences in the succession.

7. The method of any one of claims 1 to 6 wherein the structure is a crystalline carbon structure and the spin populations are electrons of nitrogen-vacancy (NV) defects of the crystalline carbon structure.

8. The method of claim 7 wherein the reference state is |0) and the magnetically sensitive state . „ |0> + | + l>V2 '9. The method of claim 7 wherein the reference state is |0) and the magnetically sensitive stateJSI-I>+I+I>10. The method of any one of claims 7 to 9 wherein said propagating the pulse sequences includes emitting microwave radiation from a microwave emitter.

11. The method of claim 10 wherein the microwave emitter is oriented in a manner to have different trigonometrical projections of the microwave radiation on the different characteristic orientations.

12. The method of claim 11 wherein the microwave emitter is oriented in an angle Smin= ^min^min where £lmin= min fl;, i are the four NV orientations, fl; are the Rabi frequencies of the minimal separation, wheremin= i m*ji;n n I proj1. - n proi JI , proj1. =BMWis the microwave radiation, and etare NV symmetry axes, and n is asubharmonic.

13. The method of any one of claims 7 to 12 wherein initializing includes propagating green laser light onto the spin populations and transitioning the spin populations from a base energy level to an excited energy level.

14. The method of claim 13 wherein said measuring includes propagating the green laser light onto the spin populations and transitioning the spin populations from the base energy level to an excited energy level, and measuring an amplitude of electromagnetic emission in a red portion of the electromagnetic spectrum when the spin populations relax from the excited energy level back to the base energy level.

15. The method of any one of claims 7 to 12 wherein said measuring includes propagating green laser light onto the spin populations and transitioning the spin populations from the base energy level to an excited energy level, and measuring an amplitude of electromagnetic emission in a red portion of the electromagnetic spectrum when the spin populations relax from the excited energy level back to the base energy level.

16. The method of any one of claims 1 to 15, wherein said isolating and said measuring the trigonometrical projections include performing a first Fast Fourier Transform (FFT) along anaxis of swept pulse duration and / or amplitude, followed by a second FFT along an axis of swept interpulse duration.

17. The method of any one of claims 7 to 15, wherein said isolating and said measuring the trigonometrical projections include identifying slightly detuned frequencies in the magnetic field which get in phase at each time interval of —, where A is the hyperfine splitting caused by the nitrogen spin, regardless of the ambient magnetic field.

18. The method of claim 6, wherein the values of pulse duration or / and pulse amplitude and the values of interpulse delay have a same ratio in different ones of the pulse sequences, wherein said isolating and said measuring the trigonometrical projections include assigning Rabi frequency to a carrier frequency of the measured amplitudes, and assigning Ramsey frequency to a signal on each side of the carrier frequency.

19. The method of any one of claims 1 to 15, wherein said isolating and said measuring the trigonometrical projections include performing an inner product between an axis of swept pulse duration and / or amplitude, and an axis of swept interpulse duration, and identifying from the inner product frequencies that have both a Rabi and a Ramsey component.

20. A vectorial magnetometer comprising: a structure having spin populations having corresponding, different, characteristic orientations in a structure, the characteristic orientations having corresponding trigonometrical projections of the ambient magnetic field; an emitter operable to propagate a pulse sequence onto the spin populations, the pulse sequence including a first pulse separated from a second pulse by an interpulse delay, the pulse sequence operable to transfer one or more of the spin populations from the reference spin state to a magnetically sensitive spin state which accumulates Ramsey phase during the interpulse delay; a detector operable to measure a sum of percentages of the one or more spin populations which collapse to one of the reference spin state and an other spin state; a computer having a processor and a memory storing instructions which, when executed by the processor,initialize the spin populations to the reference spin state; controls the emitter to propagate the pulse sequence onto the spin populations; measures the sum of the percentages via the detector; repeats the steps of initializing, controlling, and measuring in a succession, including varying a configuration of the first pulse and the second pulse of different ones of the pulse sequences in the succession, the different configurations varying the percentages; and varying a duration of the interpulse delay of different ones of the pulse sequences in the succession, the different durations varying the percentages; isolate the Ramsey phase accumulation of different ones of the spin populations based on the variations of the percentages caused by the variations in the configuration; measure the trigonometrical projections based on the variations of the percentages caused by the variations in the duration; and reconstruct a vector of the ambient magnetic field based on the trigonometrical projections.

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