Method and apparatus for localizing charge traps in a crystal lattice

Abstract

Method for localizing charge traps in a crystal lattice comprising the following steps: - Arrange, on a crystal lattice (13), a local probe (11) with an inversion-symmetric lattice defect, wherein energy levels of the lattice defect are non-linearly strongly displaceable by means of charge traps (12) in the crystal lattice (13); - Determining strongly shifted photoluminescence emission spectra (62) using a readout unit (10), wherein each of the photoluminescence emission spectra (62) is determined in a respective scanning operation by means of photoluminescence excitation in the crystal lattice (13); - Determining an integrated spectrum (61) by integrating the photoluminescence emission spectra (62); - Determining jump probabilities (92) from successive photoluminescence emission spectra (62) and determining a charge trap configuration from the jump probabilities (92), wherein the charge trap configuration comprises a set of charge trap states of charge traps (12) adjacent to the local probe (11); - Determining simulated spectra (60) using Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, whereby spatial arrangements of the neighboring charge traps (12) are varied and - Determining an optimal spatial arrangement of the adjacent charge traps (12) by comparing the integrated spectrum (61) with the simulated spectra (60).

Description

[0001] The invention relates to a method and a device for localizing charge traps in a crystal lattice. background

[0002] Until now, the local detection of charges with a local probe on a nanoscopic scale was primarily possible by measuring the charges in a magnetic field and for charges with free spin in their localized state. Furthermore, applications were limited to the nanometer scale and could not resolve atomic scales on an angstrom scale. A well-known example is the nitrogen vacancy defect center in diamond (see US 10,620,251 B2). Using known methods, these charges could not be localized with either angstrom resolution or time resolution using nitrogen vacancy centers.

[0003] Alternatively, electric fields can also be measured spectroscopically, for example using Rydberg atoms (see US 11,585,841 B1). However, such measurements rely on the linear Stark effect to induce a spectral shift in the atom-like system. This linear response is prone to sensor saturation, reducing its resolution and applicability.

[0004] In the article by Cem Güney Torun et al. (Quantum Control and Coherence of Orbital Levels of a Tin-Vacancy Color Center in a Diamond Nanopillar, 2023, Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO / Europe-EQEC)) a tin-vacancy color center in diamond (SnV) is revealed, which is a candidate for a spin-photon interface in a quantum network.

[0005] The detection and quantification of desired and undesired charge carriers can be of great importance on both the macroscopic and nanoscopic scales. Electric charges can be measured with electrometers, which have diverse applications in everyday life and for fundamental scientific investigations. However, electrometers are not yet capable of detecting individual charges with sub-nanometer resolution over time.

[0006] However, the precise localization and temporal analysis of charge traps or individual charges at atomic lattice levels is becoming increasingly important. With the miniaturization of silicon transistors to just a few nanometers, they are becoming ever more susceptible to unknown and uncontrollable charge-induced noise. In ion quantum computers, for example, localized electronic states are suspected of causing decoherence through motional heating. Superconducting qubits, in turn, suffer from defect-induced charge noise, which impairs the performance of the most advanced quantum computers. Finally, in atom-like spin qubits in wide-bandgap semiconductors, unpredictable charge noise leads to optical and spin decoherence, significantly limiting the development of quantum networks.Investigating and addressing the underlying mechanisms of such adverse processes in each of these platforms is essential to further improve the performance and application range of nanoscale electronic and photonic devices. Summary

[0007] The object of the invention is to provide a method and a device with which charge traps in a crystal lattice can be located with high accuracy.

[0008] The problem is solved by means of a method and a device for localizing charge traps in a crystal lattice according to the main claim and the dependent claim, respectively. Embodiments are the subject of dependent claims.

[0009] From one perspective, a method for localizing charge traps in a crystal lattice comprises the following steps: - Arranging a local probe with an inversion-symmetric lattice defect on a crystal lattice, wherein energy levels of the lattice defect are non-linearly strongly displaceable by means of charge traps in the crystal lattice; - Determining strongly shifted photoluminescence emission spectra using a readout unit, wherein each of the photoluminescence emission spectra is determined in a respective scan operation by means of photoluminescence excitation in the crystal lattice; - Determining an integrated spectrum by integrating the photoluminescence emission spectra; - Determining jump probabilities from successive photoluminescence emission spectra and determining a charge trap configuration from the jump probabilities, wherein the charge trap configuration comprises a set of charge trap states of charge traps adjacent to the local probe; - Determining simulated spectra using Monte Carlo simulation based on the determined charge trap configuration and the resulting Stark shift, whereby spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0010] According to another aspect, a device for locating charge traps in a crystal lattice has the following characteristics: - a local probe with an inversion-symmetric lattice defect, which is arranged on a crystal lattice, wherein energy levels of the lattice defect are non-linearly strongly displaceable by means of charge traps in the crystal lattice; - a readout unit for photoluminescence spectroscopy and - a data processing facility.

[0011] The data processing facility is set up to perform at least one of the following steps: - Determining strongly shifted photoluminescence emission spectra using the readout unit, wherein each of the photoluminescence emission spectra is determined in a respective scan operation by means of photoluminescence excitation in the crystal lattice; - Determining an integrated spectrum by integrating the photoluminescence emission spectra; - Determining jump probabilities from successive photoluminescence emission spectra and determining a charge trap configuration from the jump probabilities, wherein the charge trap configuration comprises a set of charge trap states of charge traps adjacent to the local probe; - Determining simulated spectra using Monte Carlo simulation based on the determined charge trap configuration and preferably the resulting Stark shift, whereby spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0012] Using the proposed method or device, the spatial positions of single or multiple elementary charges can be determined with time resolution and a spatial resolution of up to several (~3) angstroms by means of Stark shifts in a local electric field. In particular, a device with a nonlinear response can be implemented.

[0013] The local probe can be an atomic solid-state defect with a typical optical energy level structure and a nonlinear electric field response due to its inversion symmetry, for example in the D 3d -point group. In contrast to non-inversion-symmetric configurations of color centers, such as a nitrogen defect center in diamond or a silicon defect center in silicon carbide, the linear polarizability of point defects with an inversion center (e.g., the D) 3dThe point group can be largely neglected, and higher-order terms can lead to a strongly nonlinear response. This property can make local probes with an inversion center particularly sensitive to closely spaced charges and insensitive to background noise from an electric field, while simultaneously maintaining sufficient measurement ranges in low-noise environments. Consequently, the spectral readout can offer exceptionally high spatial resolution, reaching down to several angstroms, even at charge densities of up to several tens of ppm, based on the spectral shift and linewidth broadening of the charge-induced optical transitions.

[0014] By using a nonlinear response of the local probe's electric fields to spatially detect the environment of charge traps with angstrom resolution and to temporally observe the dynamics of individual traps with nanosecond resolution, the spatial resolution can be increased to several angstroms while the sensor / device continues to operate in environments with relatively high electric field background noise. Furthermore, the sensor can be used to determine the local charge trap density of solid materials and solid surfaces. In combination with an electro-optical modulator for fast spectral readout of the sensor, it could achieve a temporal resolution down to the nanosecond range.The detection and quantification of desired and undesired charge carriers can be of particular interest in semiconductors, quantum computers, quantum electrometers, sensors for material quality control, materials science probes, or biological sensors.

[0015] In particular, by means of charge traps in the crystal lattice (lattice) which contain charged vacancies, the energy levels of the lattice defect can be strongly shifted and / or strongly shifted non-linearly. The charge trap states of the charge traps adjacent to the local probe can each represent charges of the charge traps adjacent to the local probe or distributions of (discrete) charges of the charge traps adjacent to the local probe.

[0016] The grating defect (of the local probe) can cause a D 3d -exhibit symmetry. In other words, the local probe can exhibit a D 3d-symmetric lattice defect (a lattice defect with D 3d -point group symmetry).

[0017] The energy levels of the lattice defect can be (essentially) non-linearly DC-strongly shifted / shiftable. In particular, the energy levels of the lattice defect can be (essentially) quadratically (DC-strongly shifted / shiftable).

[0018] The local probe can have a tin vacancy (SnV), a silicon vacancy (SiV), a germanium vacancy (GeV), or a group IV vacancy. The tin vacancy can occupy two lattice sites of the crystal lattice, with a tin atom being located substantially in the middle of the two lattice sites. A similar arrangement can be provided for the silicon vacancy or the germanium vacancy.

[0019] The tin vacancy, silicon vacancy, or germanium vacancy can be (electrically) negatively charged.

[0020] The charge traps in the crystal lattice can include electrically charged single vacancies (monovacancy) and / or double vacancies (two adjacent single vacancies - divacancy), or vacancy complexes that have N vacancies.

[0021] The crystal lattice can be a diamond lattice or a silicon lattice. The crystal lattice can be part of a solid.

[0022] Positioning the local probe on the crystal lattice can involve implanting the local probe within the crystal lattice. The local probe can (after positioning) be stationary within the crystal lattice (especially of the bulk crystal).

[0023] The positioning of the local probe on the crystal lattice can involve placing the local probe close to and / or adjacent to and / or at a distance from the crystal lattice. In particular, the local probe can be embedded in a scanning probe microscope tip (for example, for position-dependent measurements in magnetometry), a nanocrystal (for example, for integration with other materials), or a biological sample.

[0024] The sensor capability of the local probe can be demonstrated by analyzing time-varying optical transition frequencies, which can be associated with the charging of all charge traps / crystal defects in the surrounding crystal lattice under laser irradiation.

[0025] A (charge-induced) local electric field can be determined from the spectral shift. Using this determined local electric field (and the polarizability), the spatial arrangement of charge traps and, in particular, the distances between charge traps and probes can be determined.

[0026] Each photoluminescence emission spectra can be determined in a separate scan using photoluminescence excitation (PLE) in the crystal lattice under laser irradiation (from a laser, specifically a narrowband laser), particularly continuous orange laser light. The charge traps can be additionally excited in each scan using a blue or green laser pulse.

[0027] The orange laser light can have a wavelength of 619 nm. The blue laser pulse can have a wavelength of 445 nm or 450 nm. The green laser pulse can have a wavelength of 520 nm. Each of the photoluminescence emission spectra can be determined with a scan duration (acquisition time) of five seconds.

[0028] The readout unit can comprise or be at least one microscope, one spectrometer, and one CCD camera. The device, in particular the readout unit, can have one or more lasers, especially for irradiating laser pulses and / or laser light, in particular green and / or blue laser pulses and / or orange laser light.

[0029] During scanning, the laser frequency can be controlled by applying an external voltage signal to the laser. The laser frequency can be monitored via a pick-off path directed at a wavemeter. The photoluminescence emission spectra can be acquired as voltage and fluorescence signals. The voltages can be converted into frequencies by comparing them to timestamps.

[0030] Individual scans (scan operations) can be mapped to a frequency axis by selecting a single line scan / scan operation. The scan operation spectra can be frequency-binned (discretized / divided into bins). If multiple data points fall into the same bin (frequency interval), the data points can be averaged. If no data points fall into a bin, the value for that bin can be determined as the average of the previous and the next bin.

[0031] Integrating the scan process spectra can be achieved by (bin-wise) summation of the photoluminescence emission spectra. Specifically, the integrated spectrum can be determined by adding corresponding bins (bins of the same frequency range) of the photoluminescence emission spectra. The integrated spectrum can then be normalized.

[0032] The procedure may also include the following steps: - Determining a plurality of peak frequencies (central frequencies) of peaks from the integrated spectrum as well as frequency ranges (configuration ranges) of the integrated spectrum assigned to the peaks; - Determining scan peak frequencies for each of the photoluminescence emission spectra and assigning the scan peak frequencies to one of the assigned frequency ranges of the integrated spectrum (and / or to a charge trap state) and - Determining the jump probabilities from the respective assigned frequency ranges (for the successive photoluminescence emission spectra).

[0033] The boundaries of the frequency ranges of the integrated spectrum assigned to the peaks, which are adjacent, can coincide with half the spectral distance between two adjacent peaks of the integrated spectrum.

[0034] For example, a particular scan peak of a particular scan can be assigned to a particular frequency range if the scan peak frequency of the particular scan peak is within the particular frequency range.

[0035] The jump probabilities can each indicate a probability of changing the charge trap state, in particular a probability p(i → j) of changing from charge trap state i to charge trap state j.

[0036] The jump probabilities can be determined by calculating how frequently (proportionally of all scans) a jump from one charge trap state i to another charge trap state j has occurred. Whether a jump from one charge trap state i to another charge trap state j has occurred can be determined by comparing a specific scan peak from a given scan to the subsequent scan peak of the following scan. If the specific scan peak does not match the subsequent scan peak, a jump can be determined to have occurred.

[0037] The specific jumps from one charge-trap state i to another charge-trap state j can each be normalized with respect to a total number of all jumps to obtain (jump) probabilities. The jump probabilities can also be determined by multiplying them by uncertainty factors.

[0038] The method can further comprise: determining a brightness duration of a charge-trap state (or several brightness durations of charge-trap states) from the respective associated frequency ranges of the photoluminescence emission spectra as the time interval of successive scan-process spectra for which a scan-process peak is retained (no other scan-process peak is determined for any of the scan-process spectra). The brightness durations can be aggregated into a histogram according to the frequency with which they were observed, preferably to determine average lifetimes and / or switching rates. A probability density can be determined from the histogram. The probability density can be fitted (adjusted) using a Poisson distribution. A lifetime τ(i) for the charge-trap state i and / or a conditional spectral hop rate Γ can also be determined. ct(i → j) can be determined from an average value of the fitted Poisson distribution.

[0039] Determining the charge trap configuration may involve at least one of the following steps: - Determining a number of peaks in the integrated spectrum and a number of jump probabilities that are greater than a predetermined threshold; - Determining charge trap states of the charge trap configuration, in particular a number of (detectable) charge traps of the charge trap configuration, from the number of peaks and the number of jump probabilities.

[0040] The charge trap configuration can specify the number of adjacent charge traps. Furthermore, the charge trap configuration can specify at least one charge (within) the adjacent charge traps.

[0041] For a number M of peaks of the integrated spectrum, a smallest possible number for the number N of detectable charge traps can be determined using M <= 2 N-1 to be determined and a maximum possible number for the number N of detectable charge traps be the number M.

[0042] The specified charge trap configuration can be a most probable charge trap configuration and / or a charge trap configuration with fewest assumptions (a set of charge trap configurations compatible with the integrated spectrum).

[0043] Determining the charge trap configuration may, in particular, include at least one of the following steps: - Determining the number of peaks in the integrated spectrum as M; - Determining the number of jump probabilities that are greater than the predetermined threshold, for example greater than 3% / M; - Setting the number N of detectable charge traps equal to M; - Iterative decrementing of N, determining the possible charge trap states and comparing the possible charge trap states with the number of jump probabilities greater than the predetermined threshold until they match.

[0044] For M peaks, a simplest charge-trap configuration can have N = M - 1 charge traps with N charge-trap states. If only single ionization events are likely, 2 * (M - 1) values ​​are expected that differ from zero (are greater than the threshold) and are all correlated with the least redshifted peak.

[0045] For N = M - 2 charge traps, M - 2 peaks can result from the ionization of M - 2 individual traps, where one peak corresponds to no ionization and one remaining peak results from a charge trap state with two ionized charge traps. The case = M - 2 can be distinguished from the case N = M - 1 by identifying (for example, four) jump probabilities that are greater than zero (or greater than the threshold) and are not correlated with the least redshifted peak. These non-zero elements can uniquely correlate each peak with a charge trap state.

[0046] For N = M - 3 charge traps, M - 3 peaks can result, which are correlated with the individual ionized charge trap states. One peak can correspond to a non-ionized trap state, and the remaining two peaks can be assigned to two charge trap configurations, comprising either two distinguishable, simultaneously ionized charge trap states or two charge trap states with two and three simultaneously ionized charge trap states.

[0047] To further differentiate these two possible charge-trap configurations, higher-order correlations can be used to determine whether subsequent ionization processes have occurred. In particular, a highest-order correlation can be determined.

[0048] To determine the charge-trap configuration, the transition probabilities can be arranged in a correlation matrix (probability matrix). The correlation matrix can show the probabilities of transitioning from one charge-trap state to another. The correlation matrix can contain M · (M - 1) entries, discarding original diagonal elements (no state change). The rows and columns of the correlation matrix can be ordered according to peaks (charge-trap states) from lowest redshift (no ionization) to highest redshift.

[0049] The jump probabilities that are not greater than the predetermined threshold can be set to zero in the correlation matrix.

[0050] The jump probabilities can be determined, starting with a non-ionized case (least redshifted peak) and reaching a specific peak step by step: p(0->i->...T-3 steps...- >k) (higher order correlation matrix).

[0051] The peaks of the integrated spectrum (especially the number of peaks and / or peak frequencies) and / or scan peaks (especially a number of scan peaks and / or scan peak frequencies) can be determined using a peak-finding algorithm.

[0052] The scan duration can be adjusted so that at most two peaks are detected between scans and / or two peaks per scan. This ensures that no more than two ionization processes can occur simultaneously during this time interval. Consequently, the complexity of detectable charge trap configurations can be reduced.

[0053] Starting from the determined charge-trap configuration, the positions (the optimal spatial arrangement) of the neighboring charge traps can be determined in various ways. Firstly, charge-trap positions can be initialized at random locations with spacings corresponding to the spectral Stark shifts of the associated peaks. These spacings are determined by a series of Stark shift equations that are relevant for DC Stark shifts. Secondly, the remaining free parameters (relative angles and spacings) can be minimized by a χ². 2 -Tests are fine-tuned. Based on this χ 2 Tests can determine the most likely charge trap configuration and the most likely charge trap positions.

[0054] When determining simulated spectra using Monte Carlo simulation based on the specified charge trap configuration and the resulting Stark shift, the spatial arrangements of neighboring charge traps and the charges of neighboring charge traps can be varied. Furthermore, when determining simulated spectra using Monte Carlo simulation based on the specified charge trap configuration and the resulting Stark shift, the spatial arrangements of distant charge traps and / or the charges of distant charge traps can also be varied.

[0055] Determining the simulated spectra can include at least one of the following steps: - Determining approximate values ​​for first position values ​​of the spatial arrangements from relative Stark shifts from the integrated spectrum and - Fine-tuning the first location values ​​using Monte Carlo simulation(s), whereby the first location values ​​as well as the second location values ​​of the spatial arrangements are varied. In particular, the optimal spatial arrangement can have finely tuned first location values ​​as well as optimal second location values.

[0056] Alternatively, (both first and second) position values ​​can be determined using Monte Carlo simulation, whereby the (first and second) position values ​​of the spatial arrangements are varied so that preferably a χ 2 -Distribution from the integrated spectrum and the simulated spectra can be minimized.

[0057] Furthermore, when fine-tuning the initial position values ​​using Monte Carlo simulation, a charge trap density ρ can be determined. trap The remote charge traps can be varied. Alternatively, the charge trap density ρ can be used. trapand / or a spatial distribution of distant charges may be predefined. For example, the spatial distribution of the distant charges can be estimated using a physical model (such as the distribution of implantation defects). Without a physical model, a predefined charge distribution (e.g., cylindrically symmetric) can be specified.

[0058] The first and / or the second location values ​​can have spherical coordinates that specify spatial arrangements of the neighboring charge traps (relative to the local probe).

[0059] The first position values ​​can, for example, include at least one of the following quantities: a first distance r1 of a first charge trap to the local probe, a first azimuth angle or polar angle θ1 of the first charge trap with respect to the local probe, a second distance r2 of a second charge trap to the local probe, a second azimuth angle or polar angle θ2 of the second charge trap with respect to the local probe, a third distance r3 of a third charge trap to the local probe, and a third azimuth angle or polar angle θ3 of the third charge trap with respect to the local probe.

[0060] The first position values ​​can in particular include at least one of the following quantities: the first distance r1 of the first charge trap to the local probe, the third distance r3 of the third charge trap to the local probe and the third azimuth angle or polar angle θ3 of the third charge trap with respect to the local probe.

[0061] The first position values ​​(especially the first distance r1, the third distance r3 and the third azimuth angle or polar angle θ3) can be derived (for example in the case of two charge traps and / or four peaks) from the relative Stark shifts Δ ○○ , Δ ○⊙ , Δ ⊙○ , Δ ⊙⊙ can be determined using the following (Stark-displacement) equations: Δ○○=−Δα2E(−1,r→2)2 Δ○⊙=−Δα2[E(−1,r→2)+E(−1,r→1)]2 Δ⊙○=−Δα2[E(−1,r→2)+E(−1,r→3)]2 Δ⊙⊙=−Δα2[E(−1,r→2)+E(−1,r→1)+E(−1,r→3)]2 Δα represents the second-order polarizability and E(−1,r→i)2 The square of the magnitude of the electric field of the electric trap i with elementary charge -1 represents (E(qi,r)=qi4πε0εrrr3, q i∈ e · {-1,0, +1}, elementary charge e). A neutral charge trap is denoted by ○ and a negatively charged charge trap by ⊙. Consequently, a charge-trap state with, for example, a neutral first charge trap and a negatively charged second (or third) charge trap is denoted by ○ ⊙.

[0062] The relative Stark shifts Δ ○○ , Δ ○⊙ , Δ ⊙○ , Δ ⊙⊙ can be determined from the integrated spectrum, in particular from the peak frequencies of the peaks of the integrated spectrum, whereby the peaks are fitted using Voigt profiles.

[0063] The first, second, and third charge traps can be arranged in a common plane. In particular, the first and second charge traps can be arranged in a common plane. The azimuth angles and / or polar angles can be defined with respect to this common plane. The second charge trap can be arranged along the direction of implantation of the local probe with respect to the local probe. The first charge trap can be arranged perpendicular to the direction of implantation with respect to the local probe.

[0064] For example, the spatial arrangements of the first, second, and third charge traps can be parameterized as follows: r→1=r1[cos(θ1),0,sin(θ1)], r→2=[0,0,r2], r→3=[cos(θ3),0,sin(θ3)].

[0065] When determining the simulated spectra, the charges of neighboring charge traps as well as distant charge traps can be varied. For example, distant charge traps can be located at least 2.5 nm (25 Å) away from the local probe. Conversely, neighboring charge traps can be located less than 2.5 nm (25 Å) away from the local probe.

[0066] The second position values ​​can, for example, include at least one of the following quantities: the first azimuth angle or polar angle θ1 of the first charge trap with respect to the local probe and the second distance r2 of the second charge trap to the local probe.

[0067] Comparing the integrated spectrum with the simulated spectra can minimize a χ². 2 -distribution and / or a χ² 2 -Tests include those from the integrated spectrum and the simulated spectra.

[0068] Minimization can be achieved using a global optimization algorithm, in particular simplicial homology global optimization (shgo).

[0069] The χ 2 The distribution can be represented by the following function: ∑iχ(θ,i)=∑n=0,iN(on(θ,i)−En,i)2En,i with values ​​0 n (θ,i) of the simulated spectra and values ​​E n,i of the integrated spectrum for bin n (especially with 0 n (θ, i) as the number of expected counts for Peak i and Bin n and the corresponding value E n,i of the integrated spectrum, where a vector θ specifies at least one of the first position values). For example, the vector θ can specify the first and third distances, specifically θ = [a,b] with fine-tuning factors a,b, where r1'=ar1 and r3'=br3.

[0070] In other words, comparing the integrated spectrum with the simulated spectra can minimize ∑iχ(θ,i)=∑n=0,iN(on(θ,i)−En,i)2En,i with values ​​0 n (θ,i) of the simulated spectra and values ​​E n,i The integrated spectrum comprises bin (interval) n, peak i, and vector θ of initial position values. For example, 170 bins of equal width can be provided over a frequency range of 4 GHz.

[0071] The simulated spectra and / or the integrated spectrum can be divided into sub-spectra (parts of the spectra). The values ​​{0 n (θ,i)} n or {E n,i} n can be considered parts of the entire simulated spectra or the entire integrated spectrum {0 n (θ,i)} n,i or {E n,i} n,i , can be interpreted. The parts of the spectra can also be partially combined. For example, the spectra can be divided according to i ∈ {○○,○⊙, ⊙○+⊙⊙}.

[0072] The integrated spectrum (and / or its parts / sub-spectra) can be adjusted before comparison with the simulated spectra by means of (single or double) Voigt profile fitting.

[0073] The values ​​0 n (θ,i) of the simulated spectra can be determined using the formula S(ω) = 1 / NΣ n L γ (ω - Δ stark,n ) are determined (with normalization constant N (so that max S(ω) = 1), simulation step index n, Stark shift Δ stark,n for simulation step n and Lorentz curve L γ with half-width γ (e.g., γ = 35 MHz for local probe SnV) -1 )). For the simulated spectra, determining the Stark shift Δ can be done stark,n Terms of linear and higher order are included. In particular, the Stark shift Δ stark,n for each simulation step n using the formula Δstrong=−ΔμEs−12ΔαEs2−13!ΔβEs3−14!ΔγEs4 can be determined (with dipole moment Δµ = 6.1 × 10 -4GHz / (MV / m) 2 and differences between higher-order polarizabilities Δα = -5.1 × 10 -5 GHz / (MV / m) 2 , Δβ = -5.5 × 10 -8 GH z / (MV / m) 2 and Δγ = -2.2 × 10 -10 GHz / (MV / m) 2 ), where E s depends on the simulation step n.

[0074] The determination of the simulated spectra can further reveal the following: The second position values ​​(e.g., the first azimuth angle or polar angle θ1 and the second distance r2) and / or the charge trap density ρ trap can be varied (within optimization intervals), for example ρ trap ∈ [35, 100] ppm or θ1 ∈ [0; 0,6] rad. This variation can be performed, for example, over 500 iterations.

[0075] Within each of the iterations, that is, for fixed second position values ​​(e.g., the first azimuth angle or polar angle θ1 and the second distance r2) and / or fixed charge trap density ρ trap of the remote charge traps, the remote charge points can each be compared with respect to the local probe according to the charge trap density ρ trap randomly distributed spatially (when the local probe is implanted within a conical volume (z > 0 nm, the local probe is located at the origin) with an opening angle of 45°, where r q (< 2.5 nm to the local probe, no distant charge points are distributed). The spatial distribution can be uniform. Furthermore, the adjacent charge traps can be charged according to charge probabilities. In the case of two adjacent charge traps with time-varying charges, the charge probabilities can, for example, be p ⊙⊙= 0.041 , p ⊙○ = 0.017, p ○⊙ = 0.63 and p ○○ = 0.31. The charges for the adjacent charge traps can have values ​​q. i · e with q i ∈ {-1,0, +1} and assume elementary charge e, where charge neutrality including the negative charge of the local probe is ensured (-e + e Σ i q i = 0). Accordingly, the field strength at the location of the local probe can be E = Σ i E(q i , r i ).

[0076] The spatial distribution of the distant charge traps and the charging of the neighboring charge traps can be performed for fixed second position values ​​and / or fixed charge trap density ρ. trap For example, it can be repeated 1000 times. The charge probabilities of the neighboring traps can be determined from the (possibly normalized) peak heights of the peaks in the integrated spectrum.

[0077] At least one of the adjacent charge traps (for example, the second charge trap) can be permanently charged. A permanently charged charge trap can lead to peak broadening.

[0078] For fixed second position values ​​and / or fixed charge trap density ρ trap For distributed remote charging points and charged adjacent charging traps, the initial location values ​​(or parts thereof, in particular r1 and r3) can be fine-tuned (within the framework of a Monte Carlo simulation). For this purpose, the χ can be adjusted in each case. 2 -Distribution with ∑iχ(θ,i)=∑n=0,iN(on(θ,i)−En)2En with θ = [a, b] and fine-tuning factors a, b minimized, where r1'=ar1 and r3'=br3. Minimization is performed using simplicial homology global optimization (shgo).

[0079] The finely tuned first position values ​​(or parts thereof, in particular r1 and r3 respectively) r1' and r3') can (together with the corresponding χ) 2 -values) for the (varied) second position values ​​and / or the (varied) charge trap density ρ trap compiled (especially in tabular form).

[0080] The optimal spatial arrangement of (adjacent) charge traps can determine the finely tuned first position values ​​and the second position values ​​with the smallest χ. 2 -value or alternatively from a respective weighted mean of several smallest (for example the 50 smallest) χ 2 The optimal spatial arrangement can also include further optimized (first) position values, which were determined from the remaining first or second position values ​​using the Stark displacement equations. In particular, the (optimized, first) position value θ3 can be determined from the (optimized) second position value θ1 using the Stark displacement equations.

[0081] Confidence intervals for the (first and / or second) location values ​​and / or further values ​​of the optimal spatial arrangement can be determined using χ². 2 -values ​​(for example, a weighted average of the 50 smallest χ) 2 -values ​​including an offset value). In particular, 68% confidence intervals for ρ can be calculated. trap and / or θ1 by means of min{χ 2} + 3.5 will be determined.

[0082] The data processing device may include a processor and / or memory. At least one, preferably each of the steps determining the majority of strongly shifted photoluminescence emission spectra, determining the integrated spectrum, determining the jump probabilities, determining the simulated spectra, and determining the optimal spatial arrangement, as well as intermediate or further steps, may be performed using a data processing device.

[0083] According to the disclosure, a further method may be provided, preferably for localizing charge traps in a crystal lattice, which comprises at least one of the following steps: - Arranging, preferably on a crystal lattice, a local probe with an inversion-symmetric lattice defect, wherein, further preferably, energy levels of the lattice defect are (essentially) non-linearly strongly displaceable (strongly displaced) by means of charge traps in the crystal lattice; - Determining, preferably using a readout unit, strongly shifted photoluminescence emission spectra (line scan spectra), wherein preferably each of the photoluminescence emission spectra is determined in a respective scan operation (line scan) by means of photoluminescence excitation in the crystal lattice; - Determining an integrated spectrum, preferably by integrating the photoluminescence emission spectra; - Determining jump probabilities, preferably from successive photoluminescence emission spectra, and / or determining a charge trap configuration from the jump probabilities, wherein the charge trap configuration preferably comprises a set of charge trap states of charge traps adjacent to the local probe; - Determining simulated spectra using Monte Carlo simulation(s) (based on the determined charge trap configuration) and preferably resulting Stark shift(s), wherein spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0084] According to the disclosure, a device may also be provided, preferably for localizing charge traps in a crystal lattice which has at least one of the following: - a local probe with an inversion-symmetric lattice defect, which is preferably arranged on a crystal lattice, wherein energy levels of the lattice defect are further preferably strongly displaceable non-linearly by means of charge traps in the crystal lattice; - a readout unit for photoluminescence spectroscopy and - a data processing facility.

[0085] The data processing facility is specifically designed to perform at least one of the following steps: - Determining, preferably using the readout unit, strongly shifted photoluminescence emission spectra, wherein each of the photoluminescence emission spectra is further preferably determined in a respective scanning process by means of photoluminescence excitation in the crystal lattice; - Determining an integrated spectrum, preferably by integrating the photoluminescence emission spectra; - Determining jump probabilities, preferably from successive photoluminescence emission spectra, and / or determining a charge trap configuration from the jump probabilities, wherein the charge trap configuration preferably comprises a set of charge trap states of charge traps adjacent to the local probe; - Determining simulated spectra using Monte Carlo simulation(s), preferably based on the determined charge trap configuration, and further preferably the resulting Stark shift(s), wherein in particular spatial arrangements of the neighboring charge traps are varied and - Determining an optimal spatial arrangement of the neighboring charge traps by comparing the integrated spectrum with the simulated spectra.

[0086] In conjunction with the device for localizing charge traps in a crystal lattice, the embodiments described above in connection with the method can be provided accordingly. Description of exemplary implementations

[0087] Further examples of implementation are explained in more detail below with reference to figures in a drawing. These show: Fig. 1 a schematic representation of a device for locating charge traps, Fig. 2 a schematic representation of the device for localizing charge traps in a crystal lattice by means of Stark displacement, Fig. 3. Plot a relative sensitivity |ΔE| / E to changes in an electric field as a function of an electric field E s and a charge trap density ρ trap , Fig. 4. A plot of the sensor's resolution in determining the distance of an elementary charge based on the differentiation of two different charge traps as a function of the charge trap density ρ. trap and the intervals Fig. 5 a schematic representation of a crystal lattice with a tin vacancy and lattice defects, Fig. 6. A plot of the integrated spectrum and the simulated spectrum with assignment of the peaks to the charge trap states and a plot of the photoluminescence emission spectra as a function of the Stark shift. Fig. 7 a schematic representation of the relative positions of the charge traps and their probability distribution with respect to an SnV probe and a table indicating the charge trap states and the position of the identified charge traps, Fig. 8 a schematic representation of the SnV probe, the ionized and neutral lattice defects in the band gap, Fig. 9 example histograms showing how long the charge remains in a charge-trap state before transitioning to another, and a table with jump probabilities and jump rates for the corresponding spectral jumps. Fig. 10 plots of the inhomogeneous broadening of the SnV zero-phonon line due to bulk and surface charges, Fig. 11 a schematic representation of the formation of double charge traps in the crystal lattice during an annealing process, Fig. 12 plots of the simulated densities of the double charge traps as a function of the single charge traps for three different species of color centers, Fig. 13 a plot of the inhomogeneous broadening as a function of the local bias field, Fig. 14 a plot of the normalized uncertainty for the homogeneous linewidth for three different values ​​of the relative sensitivity of the electric field, Fig. 15 a plot of the uncertainty extracted from a fitting as a function of the SNR and the Gaussian component of the Voigt profile, both normalized to the homogeneous line width, Fig. 16 a plot for the experimental estimation of the bias field at the sensor, Fig. 17 plots of control experiments, Fig. 18 plots of extracted parameters from autocorrelation measurements for one emitter E1, Fig. 19 plots on the influence of laser misalignment on photoluminescence emission spectra, Fig. 20 plots of photoluminescence excitation of the C-junction under different charge stabilization schemes at emitter E1, Fig. 21 plots of photoluminescence excitation of the C-junction under different colored stabilization schemes of emitter E2, Fig. 22 plots for comparing different stabilization pulse powers and Fig. 23 a plot to compare the different stabilization performance at emitter E20.

[0088] The detection of individual charges plays a crucial role in fundamental materials science and in the further development of classical and quantum high-performance technologies that operate with low noise. However, it has not yet been possible to determine charges at the lattice scale with time resolution. The development of an electrometer is presented that utilizes the spectroscopy of an optically active spin defect embedded in a solid-state material with a nonlinear Stark reaction. By applying this approach to diamond (diamond lattice), a widely used platform for applications in quantum technology, it is possible to detect charge traps (12 traps, multivacancies, double vacancies, vacancies, V). nto locate (e.g., gaps), quantify their influence on transport dynamics and noise generation, analyze relevant material properties, and develop strategies for material optimization.

[0089] Free charge carriers such as electrons are essential components of the modern world. They enable devices like smartphones and computers. Uncontrolled or unwanted charges, on the other hand, can cause damage and reduce the performance of such devices. Prominent examples include gate oxide breakdown in flash memory and charge noise at the nanoscale. The detection and quantification of desired and unwanted charge carriers using electrometers is of great technological importance at the nanoscale.

[0090] Despite significant progress, electrometers have so far been unable to measure elementary charges with sub-nanometer resolution in a time-resolved manner. However, the precise localization and temporal analysis of charges on atomic lattice scales are becoming increasingly important. For example, the investigation of 2D ferroelectric systems would greatly benefit from the use of a highly sensitive electrometer, which could provide crucial insights into the unresolved fundamental aspects of their physical properties. Furthermore, silicon transistors, measuring just a few nanometers, are becoming increasingly susceptible to charge-induced noise.

[0091] Quantum technology applications, in particular, face challenges: In ion-based quantum computers, localized electronic states are suspected of causing decoherence due to motional heating; superconducting qubits suffer from defect-induced charge noise; and in atom-like spin qubits in wide-bandgap semiconductors, charge noise leads to optical and spin decoherence, significantly limiting the development of quantum networks and sensors. Understanding the underlying mechanisms of such platform-specific adverse processes is essential for improving the performance and application range of electronic and photonic nanodevices, including addressing open questions regarding decoherence processes, electron dynamics, and materials related to lattice defect formation.

[0092] A device (electrometer, quantum electrometer) is presented that can detect electric fields generated by single and multiple elementary charges with a relative sensitivity of 10 -7 and enables the localization of their relative position on the Angstrom scale, while simultaneously providing time-resolved access to the dynamics of individual charges down to nanoseconds.

[0093] The electrometer consists of an optically active, local probe 11 (probe, atom sensor probe, spectral sensor, sensor probe) that is sensitive to electric fields and a readout unit 10 (see Fig. 1) The local probe 11 can be a negatively charged tin vacancy color center 21 (tin vacancy color center, SnV, SnV color center, SnV center) in a diamond (cf. Fig. 2), a solid-state defect with fluorescent transitions and a nonlinear response to the electric field, typical for defects in the D 3d -point group. The optical transition energies depend on the DC Stark effect Δ Stark = -µ ind (E s )E s directly from the local electric field, where µ ind the induced dipole moment of the atomic defect and E s the sum of all static electric fields generated by surrounding charges that shift the optical energies ( Fig. 2).

[0094] The readout unit 10 is a microscope used for photoluminescence excitation spectroscopy at the local probe 11 and therefore does not require magnetic resonance methods. The measurement of the energy shift indicates the magnitude of the electric field at the sensor probe 11E. s about the DC Stark postponement Δstrong=−ΔμEs−12ΔαEs2−13!ΔβEs3−14!ΔγEs4, with Δµ as the change in dipole moment and Δα, Δβ, and Δγ as differences between higher-order polarizabilities. In contrast to non-inversion-symmetric configurations of color centers, such as the nitrogen vacancy center in diamond and the silicon vacancy center in silicon carbide, the negligible linear and strongly nonlinear response due to inversion symmetry makes the sensor applicable to typical semiconductor dopants and defect densities. If Δα dominates and the observed Δ Stark If the charge originates from a localized elementary charge e at a distance r from sensor 20, then the following applies: Δstark(r)∼Δα / r4.

[0095] As the distance of the charges from sensor 20 decreases, increasingly larger spectral shifts occur. This property makes sensors 20 with an inversion center remarkably sensitive to charges in their immediate vicinity and insensitive to the background noise of electric fields.

[0096] The relative sensitivity of the electric field ~ 10 -7 (cf.) Fig. 3) enables the readout of a spectral sensor with exceptionally high spatial resolution, even at charge trap densities (charge density, trap density, density) of up to one hundred ppm (cf. Fig. 4) down to a few µm.

[0097] In Fig. Figure 2 shows a schematic representation of the device for localizing charge traps 12 in a crystal lattice (atomic lattice) using Stark shift. The local probe 20 is an optically active atomic defect with nonlinearly Stark-sensitive energy levels. The readout unit 10 is a microscope with photoluminescence excitation spectroscopy. A nearby charge (adjacent charges, adjacent charge trap 12, near-field trap) shifts the optical transition from C0 to C. s around Δ s (r) depending on their distance r. Additionally, an ensemble of distant fluctuating charges (distant charge traps, far-range traps, remote traps) broadens the signal from C. s up to C s,b depending on the charge density ρ trap In Fig. 3. The relative sensitivity |ΔE| / E to changes in the electric field is calculated as a function of the electric field E. s and the trap density ρ trapshown. To the left of the dashed line, Stark displacements are not large enough to be resolved by the Rayleigh criterion. Larger field strengths correlate with a larger inhomogeneous broadening. In Eq. 1, Δµ = 6.1 × 10 -4 GHz / (MV / m) 2 , Δα = -5.1 × 10 -5 GHz / (MV / m) 2 , Δβ = -5.5 × 10 -8 GHz / (MV / m) 3 and Δγ = -2.2 × 10 -10 GHz / (MV / m) 4 assumed.

[0098] In Fig. Figure 4 shows the resolution of sensor 20 in determining the distance of an elementary charge based on the differentiation of two different charge traps 12 as a function of the charge trap density and the distances. The resolution was determined for a trap 12 with a variable distance r and a bias field corresponding to a trap spacing of 0.8 nm. The dashed white lines indicate the inscribed resolution thresholds.

[0099] In the present embodiment, the local SnV probe 20 is stationary within a bulk crystal; however, it could also be integrated into the tip of a scanning probe microscope 14 for position-dependent measurements, which are well established in magnetometry, or into a nanodiamond 15 for integration with other materials or biological samples. Alternatively to the SnV, other D 3d Symmetrical defects such as silicon or germanium defects and other inversion-symmetrical defects in other materials, for example in silicon, can be used as local probes 11. To demonstrate the nonlinear sensor principle, a single SnV, generated by ion implantation and annealing, is used. Determination of charge trap positions on the plane of the atomic lattice

[0100] Probe 20 and its surroundings are in Fig. Figure 5 illustrates the sensor capability. To demonstrate this capability, the time-varying quasi-static electric field caused by the charging and neutralization of crystal defects in the surrounding lattice 13 under laser irradiation 22 is analyzed. Based on the recorded field strength for different charge distribution configurations, the position of the surrounding crystal defects can be extracted with lattice-scale resolution.

[0101] If all traps 12 are neutral, the total field at the position of the local probe 20 is zero and the optical transition of the SnV is undisturbed. A charged trap 12 induces an electric field. It→, which strongly shifts the energy of the optical transition according to Eq. 1. If a single elementary charge is located near probe 20, the C transition is shifted by more than its own linewidth, leading to a spectral jump (jumps, spectral jumps, charge state change, state change) (cf. Fig. 2) The magnitude of the spectral shift can be determined by comparison with the unperturbed case. The addition of both resonances in a spectrum results in a unique optical fingerprint with two peaks.

[0102] To capture spectra 62 (see Fig. 6) The fluorescence of sensor 20 is measured under photoluminescence excitation (PLE) with a narrowband laser. The charge-induced electric field is extracted from the spectral shift. Knowledge of the local field and the use of the polarizability allow the trap-probe distance to be determined.

[0103] For N charged traps 12 near the probe 20, the electric fields add up to It'→ and the individual charges cannot be directly separated. To distinguish the 2 N To distinguish charge states, the strongly shifted PLE spectra 62 (photoluminescence emission spectra, PLE line scans, PLE line scans, scan, PLE scan, PLE spectrum) are repeatedly recorded. The traps 12 are randomly ionized and neutralized by laser irradiation. Complex trap distributions can be analyzed by sampling a large number of configurations.

[0104] In addition to the nearby charges 12, which cause significant spectral line shifts, the numerous randomly distributed traps in the distant environment also contribute. These distant traps exhibit fluctuating charge states, resulting in a fluctuating electric field. δEs→ This leads to an inhomogeneous broadening. Consequently, the density of the charge traps ρ can trap within grid 13, the linewidths can be determined by measuring the traps. It is found that traps can be resolved with subnanometer resolution. For trap densities ρ trap Approximately 0.3 ppm can be detected with volumes of 150 3 Å are possible. Fluctuating charge traps at larger intervals mainly contribute to the inhomogeneous broadening.

[0105] To fully calibrate the electrometer, the nonlinear response to external fields is taken into account, which causes a mutual dependence of the various external field components. For example, the effective Stark shift caused by two charges is not equal to their sum. This phenomenon enables high resolution but makes the analysis of the recorded fingerprints very complex. Therefore, a theoretical database of simulated spectra is created for a variety of discrete charge positions at near and far trap densities using Eq. 1.

[0106] The complex experimental four-peak fingerprint from Fig. 6 can be analyzed quantitatively as follows. Experimentally determined polarizabilities are used. By comparing the experimental and simulated fingerprints, several possible trap configurations (charge trap configuration, charge state configuration, state configuration, charge trap state configuration) are found. Of these possible configurations, the most plausible one is identified through specific physical considerations.

[0107] The most likely configuration of Trap 12 nearby consists of a permanent Ebias→, which is generated, for example, by a permanently ionized trap 12, and two additional traps 12 that cause spectral jumps. The spectral peaks (peaks) in Fig. 6. Designations are assigned based on the charge state of the two additional traps 12 nearby ○○,○⊙,⊙○,⊙⊙, where ○ represents an uncharged trap (neutral charge trap) and ⊙ a charged trap (ionized charge trap). Subsequently, the position of these charge traps 12 up to an azimuthal angle is determined using Monte Carlo simulations. The relative Stark displacements corresponding to the distances of the adjacent traps r1 = 8(1)Å, r2 = 11(2)Å, r3 = 26(3)Å ( Fig. 7) correspond, and a remote charge trap density of 74(22) ppm is extracted.

[0108] In Fig. Figure 5 shows a schematic representation of a crystal lattice 13 with a tin vacancy (SnV) 21 and lattice defects. The charges localized in this case 12 cause a Stark shift in the energy levels of the atom sensor probe 20. From very near to far, the spectral effect of an elementary charge can be categorized as follows: a >30 GHz spectral shift detectable by photoluminescence spectroscopy, a ~GHz shift detectable by photoluminescence excitation spectroscopy (PLE), and inhomogeneous broadening detectable by PLE. Charges in the very far region have negligible effects.

[0109] In Fig. Figure 6 shows a plot of the integrated spectrum 61 (multimodal spectrum) and a simulated spectrum 60 with the peaks assigned to the charge-trap states (trap states, state) and a plot of the photoluminescence emission spectra 62 as a function of the Stark shift. Above in the Fig. Figure 6 shows an integrated multimodal PLE spectrum 61, acquired with the SnV sensor 20 (blue) and modeled with Monte Carlo simulations (integrated spectrum 61 with error bars representing the statistical standard deviation) to determine a nearby charge trap configuration (states above the peaks, ⊙ and O represent ionized and neutral traps 12, respectively) and the surrounding charge density. Below in the Fig. Figure 6 shows time-resolved photoluminescence emission spectra 62 as well as an SnV level scheme.

[0110] In Fig. Figure 7 shows a representation of the relative positions of the charge traps 12 and their probability distribution with respect to the SnV probe 20, and a table indicating the charge trap states and the position of the identified charge traps 12. On the left are the identified charge trap configurations, their relative (optimal) positions, and their probability distribution with respect to the SnV probe 20. Due to the direction-independent calibration of the sensor 20, the distributions resemble a donut shape. On the right is a diagram indicating the charge trap states and the position of the identified traps 12. Dynamics of the charge

[0111] To identify the position of charge traps 12, accumulated spectral fingerprints were used, which comprised the integrated spectrum 61 for the entire set of charge states. UC={○○,○⊙,⊙○,⊙⊙,SnV−2}, including the dark state SnV -2 , reproduce. The comparison of individual electrometer readout events, i.e., individual PLE line scans between different charge configurations within UC enables access to time-resolved charge transfer dynamics.

[0112] The charge state changes are represented by a simplified charge transfer diagram (see below). Fig. 8) interpreted: charge traps 12, which later became known as multivacancy complexes V nThe charge traps 12, which can be identified under laser illumination, can be ionized by two different processes: negative charge, which occurs when trap 12 captures an electron transported from the valence band, leaving a positively charged hole in the band; and positive charge, which occurs when an electron is transported from trap 12 into the conduction band. The generated holes and transported electrons then diffuse and recombine with other charge traps 12, resulting in an overall charge-neutral environment. The event ○○ → ○⊙ is called ionization, and the reverse case ○⊙→○○ is called a neutralization event. The charge transfer pattern is consistent with the time-resolved correlation measurements performed, assuming that charge events are triggered by single-photon processes.

[0113] To characterize the local charge environment and dynamics, the transition probabilities 92 of the charge states p(i → j) and the conditional transfer rates (jump rate 93, state change rate, charge state change rate) Γ are determined. ct (i → j) between charge states i and j of the near traps 12, wherein i,j∈UC introduced. p(i → j) and Γ are introduced. ct (i → j) extracted from histograms 90, which were created based on the charge transfer events and the intervals between them (see Fig. 9). Furthermore, the lifetimes of each configuration are defined as τ(i).

[0114] In Fig. Figure 8 shows a schematic representation for SnV of the ionized and neutral lattice defects (V). x,y) shown in the band gap. Ionization occurs when either an electron from the valence band is transported into the charge trap 12 or an electron is transported from the trap into the conduction band by an illumination field. Neutralization occurs when the trap 12 captures either a hole from the valence band or an electron from the conduction band.

[0115] In Fig. Figure 9 shows example histograms 90 that illustrate how long the charge remains in a charge-trap state before transitioning to another state, and a table of jump probabilities 92 p(i → j) and jump rates 93 Γ ct (i → j) to the corresponding spectral jumps 91 i → j are shown. The example histograms 90 show how long the resonance remains in one charge state before transitioning to another. The data are fitted to a Poisson distribution to estimate an average time. The time values ​​can be derived from the sensor data in Fig. 6. The experiment is performed under 0.5 nW 619 nm light, with a 2 µW (CW power) blue 450 nm pulse of 4 ms duration applied between line scans. p(i → j) and Γ ct (i → j) represent conditional spectral jump probabilities 92 and rates 93, respectively, where i,j are the initial and final charge state configurations. Missing rates are due to insufficient data points. Γ s is the sampling rate. The uncertainties are estimated from the overlap of the individual peaks for p(i → j) and the 95% confidence intervals derived from the fits for Γ ct (i → j) were extracted.

[0116] The analysis begins with the quantification of the smallest jump probabilities p(i → j). The occurrence of a charge exchange event, taking into account the current line scan time of 5 seconds, given by p(○⊙→⊙○)=0.03(1), suggests an unlikely direct transfer between the two nearby traps. Furthermore, the occurrence of a two-trap charging event p(○○→⊙⊙)=0.03(1) is also unlikely, indicating that these events are not correlated.

[0117] Furthermore, the relationship between the reinitialization of the bright SnV charge state SnV -2 → SnV -1 and the charge states of trap 12. The probabilities p(SnV -2 → ○⊙) = 0.61(12) and p(SnV -2 → ○○) = 0.38(9) are close to the corresponding peak intensities in the spectrum 61 (0.63(5) and 0.31(3)), which may indicate that the trap states are not correlated with the charge state of the SnV.

[0118] The following compares the ionization and neutralization rates for a single case 12, Σ X=○,⊙ Γ ct (○X → ⊙X) / 2 = 0.075(1) Hz or ∑ X=○,⊙ Γ ct (⊙X → ○X) / 2 >> Γ s = 0.2 Hz, where Γ s The scan rate is [missing information]. The more than 3-fold higher ionization rate may reflect the different physical mechanism compared to neutralization. The ionization rates of the other case 12 change abruptly over time: for the line scans 0-250 Γ ct (○○ → ○⊙) = 0.07(2) Hz and 250-500 Γ ct (○○ → ○⊙) >>Γ s = 0.2 Hz. The trend is reversed for the neutralization rate. This change in rates 93 is attributed to discrete changes in the trap environment. Furthermore, the different ionization rates, Γ ct {(○○ → ○⊙})=0.09(1) Hz and Γ ct(⊙○ → ⊙O) = 0.19(4) Hz, observed under the same illumination laser field, either indicate large variations in the local electrostatic potentials in a ~1 nm range that alter the charge dynamics, or the presence of multiple charge trap types. Further investigations could differentiate between the various V n They can be distinguished.

[0119] Furthermore, the total lifetime of the charge states τ(i), which provides a reference point for experiments requiring spectral stability, is determined and interpreted. τ(○⊙) = 2.3(1) s and τ(○○) = 4(1) s are found, which correspond approximately to the duration of a line scan. The measurement procedure includes a blue 445 nm charge initialization pulse between each line scan, accompanied by continuous orange 619 nm laser illumination. From these timescales, it is evident that the blue laser is the primary driver for changes in the charge-trap states ( Fig. 20) which suggests that the stability of the trap states can be maintained during optical operations resonant with SnV transitions. Since the trap states are stable for much longer than the measured SnV ionization time of 50 ms and the spin coherence time of about 1 ms, albeit not deterministically, the emitter can still act as an optically coherent spin-photon interface. Evaluation of spectral dispersion

[0120] The spectral dynamics induced by charge transfer are extremely detrimental to applications in quantum technology. Spectral diffusion, a term that describes the probabilistic nature of the observed spectral dynamics, leads to optical decoherence, which in turn results in reduced entanglement fidelity in quantum network nodes.

[0121] Knowing the nonlinear sensitivity of the quantum electrometer to charge noise, predictions are now made about how a specific charge distribution influences the spectral properties of a color center. Based on the model, an overview is given of the inhomogeneous broadening caused by a specific charge trap density ρ. trap is caused. The details of the calculation are described in the sections below.

[0122] First, the bulk case will be considered (see below). Fig. 10) considered and surface charge traps are considered ρtraps The effects of two different surface geometries, planar and cylindrical, were analyzed. It was found that an implantation depth of d > 21 nm and a cylinder with a radius of r > 45 nm ensure that the surface charges do not degrade the spectral properties of an SnV color center, with a linewidth broadening of less than 1%. Such broadening results in 90% interference visibility and more than 87% entanglement fidelity. Similar estimates can be made for any defect with known polarizability. Control measurements of spectral diffusion as a function of the illumination field are included in the supplementary materials.

[0123] Due to the estimated minimum harmful distances, SnVs and similar color centers are well suited for integration into nanostructures, increasing photon collection efficiency and providing tailored emission properties for quantum information applications via the Purcell effect.

[0124] In Fig. Figure 10 shows plots of the inhomogeneous broadening of the SnV zero-phonon line due to bulk and surface charges. The inhomogeneous broadening of an SnV line with a lifetime-limited linewidth of 35 MHz is shown as a function of ρ. trap The linewidth distribution is represented in ppm units in a bulk diamond. The brightness levels in the plots indicate the linewidth distribution. The mean and variance of the distribution are represented by the white dots and error bars. The inhomogeneous broadening is shown as a function of the distance of a SnV to a planar surface and the surface trap density. ρtraps is defined as the fraction of surface grid sites. The dashed lines show the threshold values ​​of 1% and 10% of the broadening compared to the lifetime-limited linewidth of 35 MHz. The inhomogeneous broadening of a SnV located centrally in a cylinder with radius r is a function of ρtraps. The dashed lines represent 1% and 10% widening, respectively. Identification of material properties: Double vacancy formation

[0125] Based on the electrometer's ability to quantify charge trap density, the investigation of material properties is extended, and the sensor data are combined with additional simulations. In particular, the physical origin of charge traps 12 in the implanted diamond is determined. For a sample with less than 1 ppb of nitrogen and boron and even lower lattice defect concentrations, the estimated charge trap density of 74(22) ppm must originate from damage caused by the Sn ion implantation and the subsequent annealing process. The ion implantation creates Frenkel pairs: a pair consisting of a single vacancy V1 and a dislocated interstitial carbon atom. During annealing, V1 is n mobile and can form gap complexes, a process that is not well understood and is an active area of ​​research (cf. Fig. 11).

[0126] Here, the V1 to double vacancy V2 conversion yield is estimated using a kinetic Monte Carlo simulation in combination with a simple stochastic diffusion model.

[0127] The density V2 is used as a proxy for higher-order vacancy complexes V. n Considered. Annealing to up to 1100 °C primarily converts V2 into V3 and V4. In fact, wavelength-dependent spectral diffusion and jumps occur (cf. Fig. 21) observed, which indicate different ionization energies of the multiple trap types. The estimated density of V2 serves both as an approximation of an order of magnitude and as an upper limit for the total density of the charge trap 12. ρ V2 = 40.0(2.1) ppm is compared with the experimentally estimated trap density of ρ Exp = 74.1(22.5) ppm compared. Due to charge neutrality, the total charge density ρ would be Sim = twice the density of V2 with ρ Sim = ρ V2× 2 = 80.0 (4.2) ppm. The small deviation is attributed to a reduction in the density of V. n compared to the V2 estimate.

[0128] Understanding the origin of charge traps 12 also provides a clear path to generating optically noise-free group 4 vacancy defects in diamonds. Single-peak fingerprints, which are based on a low V n -Density is indicated more frequently in samples annealed at high pressure and high temperature (HPHT) at 2000 °C, which is consistent with electron spin resonance measurements.

[0129] Spectral jumps have already been observed for group IV vacancy defects. A comparison of the V n -Density for the atom types Si, Ge and Sn and different implantation energies ( Fig. Figure 12 shows that Si implantation leads to the lowest V2 density. This observation is consistent with the more frequent reports of spectrally stable SiV compared to SnV, which can now be explained by the analysis that heavier ions increase V. n -cause densities.

[0130] In Fig. Figure 11 shows a schematic representation of the formation of double-charge traps (V2) in the crystal lattice 13 during an annealing process. A spatial distribution of the single vacancies (V1) generated by 400 keV Sn implantation, predicted by SRIM simulations, is shown. Furthermore, the formation of V2 during annealing at 800 °C is shown. At higher temperatures, V1 begin to diffuse. V1 then either migrates to the interfaces, recombines with interstitial carbons, or forms V2. The distribution of V1 and V2 near the damage channel caused by the Sn implantation is also shown.

[0131] In Fig. Figure 12 shows plots of the simulated densities of the double-charge traps V2 as a function of the single-charge trap V1 implantation yield (% of participating V1, estimated by SRIM simulations) for three different species: tin, germanium, and silicon. A lower yield of V1 is attributed to recombination with interstitial carbons. The implantation energies were chosen to achieve an average implantation depth of 100 nm. Densities of V2 for 100 keV implantation energy are shown. The error bands shown represent the statistical standard deviation. Overview of the Monte Carlo simulation

[0132] The following is an overview of the general methodology for simulating single and multimodal spectra 60 ( Fig. 6) given. The simulations begin with the uniform distribution of charge traps 12 within a given volume or surface. For multimodal spectra 61, such as the one in Fig. As shown in Figure 6, the distribution of the charge traps 12 is divided into two categories: near-range traps 12 and far-range traps. Near-range traps 12 are positioned at fixed locations, while far-range traps are distributed with a fixed density within a predetermined volume. The SnV -1 Probe 20 is always located at the origin of the coordinate space.

[0133] Once a spatial trap configuration has been created, a single iteration of the Monte Carlo simulation can be performed. This consists of assigning charges to the trap locations (charging the traps 12). A fixed number of charges 12 are distributed under the assumption of charge neutrality: -e + e Σ i q i = 0 with elementary charge e and charge state qi ∈ {-1,0, +1}. The field strength at the location of the SnV -1 will then become: E→=∑iE→(qi,r→i), where r→i the position of a trap 12 is and E→(qi,r→i) The electric field of a point charge in the medium is chosen to adequately reflect the boundary conditions for solving Maxwell's equations. The nonlinear Stark shift Δ Stark according to the size of the field E→(q,r→i) is calculated using Eq. 1, where It=|It→| E s and the parameters Δµ = 6.1 × 10 -4 GHz / ( MV / m) 2 , Δα = -5.1 × 10 -5 GHz / ( MV / m) 2 , Δβ = -5.5 × 10 -8 GHz / (MV / m) 3 and Δγ = -2.2 × 10 -10 GHz / (MV / m) 4Unless explicitly stated otherwise, the procedure is repeated 1000 times, and for spectrum 61, which corresponds to the distribution of Stark shifts, the following applies: S(ω)=1N∑nLγ(ω−ΔStark,n), where N is a normalization constant (max S(ω) = 1), n ​​is the simulation step index, and L γ (ω) is a Lorentzian line profile with a half-width γ = 35 MHz, which corresponds to the lifetime-limited linewidth of the SnV -1 This corresponds to the assumption that there is neither an additional increase in performance nor a reduction in lifespan due to Purcell reinforcement. Relative sensitivity to electric fields

[0134] The sensitivity of the relative electric field δε = ΔE / E s given ρ trap can be calculated by applying ΔE according to the smallest spectral shift Δ Starkcan be solved according to a modified Rayleigh criterion as described below.

[0135] ΔE is calculated in a two-stage process: First, the expected inhomogeneously broadened linewidth in the presence of an electric field is determined. It→ (see Fig. 13) simulated, which is generated either by a charged near trap 12 or by a non-neutral charge state of the entire spatial trap configuration. The total field at the sensor position can be divided into two components: E→=Es→+δEs→, where δEs→ a fluctuating electric field that is generated by the varying charge states of the remote trap configuration.

[0136] In Fig. 13. A plot of the inhomogeneous broadening as a function of the local bias field E is shown. s shown. The line width decreases with increasing E. s or ρ trap to.

[0137] The average value of the nonlinear Stark shift is given by 〈Δstark〉==Δα(Es2+σ2). Its variance is σΔstrong==Δα2(4Es2σ2+2σ4) (assuming that δEs→ (normally distributed with variance σ). The expressions show that a field induces both a discrete spectral shift and a quasi-permanent dipole moment, leading to an inhomogeneous broadening of the lines depending on the quantities E. s and σ leads.

[0138] In the second step, ΔE is calculated for a given ρ. trap calculated using a modified Rayleigh criterion: Two spectral peaks originating from different fields E s and It' Line shapes originating from two individually standardized shapes are considered separable if the sum of these shapes is equal to the sum of the two shapes derived from them. E→=Es→+δEs→ and E→=Es'→+δEs→ result in a contrast of at least 26.3% between their local maxima.

[0139] For Fig. 7 will Es→=(0,0,Es) chosen. To determine 〈Δ Stark For the inhomogeneously widened line width, a Monte Carlo simulation is used, as described in the simulation overview. The traps that δEs→ generated, were produced with a fixed density ρ trap placed in a conical volume z > 0 with an opening angle of 45°, mimicking the anisotropic distribution of the traps produced by implantation and annealing (see e.g. Fig. 5 and Fig. 6) The conical volume was capped at z = 30 nm. A spherical volume of 2.5 nm was left free of trap 12 to reduce the occurrence of exaggerated multimodal spectral features.

[0140] The for Fig. The 3 required average line widths are calculated using γFWHM=ασhom+(bσhom2+σinhom2)1 / 2, where σ hom and σ inhom The half-width of the Lorentz and Gaussian contributions to the Voigt profile are α = 0.5346 and b = 0.2166. In total, the Gaussian and Lorentzian components of 100 different spatial trap configurations are determined at a specific ρ. trap averaged. For each ρ trap 2500 randomly generated charge states are used to simulate a single spectrum 60. The averaged spectral profiles correspond to E→=Es→+δEs→ and E'→=Es→+δEs→ are then used to determine used with the Rayleigh criterion.

[0141] Finally, the in Fig. The relative sensitivity shown in Figure 3 is calculated by using δε = ΔE / E s for a given ρ trap is divided. resolution

[0142] To determine the spatial resolution Δr=|r→−r'→|, where r→−r→' Since there are two different positions of point charges, the same calculation is performed as for the relative sensitivity of the electric field. However, it is additionally assumed that the charges generate electric fields: E→(q,r→)=qi4πε0εrr→r3, where ε0 is the permittivity of the vacuum and ε r = 5.5 is the relative dielectric constant of diamond. The use of the bulk expression and the neglect of surface contributions is justified due to the column dimensions, r > 40 nm ( Fig. 4) if the SnV is located on the axis of symmetry of the column. In Fig. 4. The resolution of sensor 20 in the presence of a constant static field will be E→r0 shown, which is generated by a negatively charged trap 12 at a fixed location, r→0=(0;0;0,8) nm. As described in the previous section, Fig. 4. created in a two-stage process: First, the expected spectral profiles for a given ρ were calculated. trap and E→=E→(−1,r0→)+E→(−1,r1→)+δEs→ The resolution was calculated using the Rayleigh criterion.

[0143] The position vector r→1=(0,0,d) will be in a line with r→0 The averaged profiles are then used to determine the smallest resolvable distance. Δr=|r→−r'→| to determine from the spectral profiles, using the fields Ebias→=E→(−1,r0→)+E→(−1,r1→)+δEs→ and Ebias→=E→(−1,r0→)+E→(−1,r1→)+δEs→. Multimodal spectra

[0144] The most probable trap configuration is determined in three steps. First, the spectral positions of the (in this case) four peaks observed in the measured multimodal spectrum 61 are determined to identify the near traps 12 that generate the Stark shifts observed in the experiment. Next, the predetermined positions of the near traps 12 are fine-tuned using an optimization procedure that draws on a comprehensive collection of simulated spectra 60. Finally, an objective function (χ) is used to determine the optimal position of the near traps 12. 2 -Test) the most probable near-field configuration by comparing the simulated spectra 60 with the experimental observations. Modeling the glow

[0145] A kinetic Monte Carlo simulation of the annealing process was performed, in which an initial distribution of single vacancies was calculated using SRIM for a specific set of implantation parameters. Subsequently, a spatial distribution of double vacancies was calculated by randomly moving the single vacancies along the fcc diamond grid until they encountered another single vacancy and formed a double vacancy. sample

[0146] The sample used (E001) is an electronic diamond (element 6) grown by chemical vapor deposition (CVD). The sample was first purified in a boiling triacidic solution (H₂SO₄:HNO₃:HClO₄, 1:1:1) and then in Cl₂ / He and O₂ / CF₃. 24 The surface was etched to remove organic contaminants and structural defects. Subsequently, Sn-(spin-0) ions with a fluence of 5 × 10⁻⁶ were removed. 10 atoms cm -2and implanted into the diamond with an implantation energy of 400 keV, corresponding to a penetration depth of 100 nm, as estimated by SRIM simulations. The formation of the SnV color centers was then achieved by annealing the diamond at a temperature of 1050 °C for approximately 12 hours in a vacuum (pressure 7.5 × 10⁻⁶). -8 mbar).

[0147] The nanopillars were fabricated by a combination of electron beam lithography and plasma etching. First, 200 nm of Si3N4 were deposited onto the diamond surface using an inductively coupled plasma (ICP) system. After coating the sample with 300 nm of electrosensitive resist (ZEP520A), pillars with nominal diameters from 180 nm to 340 nm were exposed in 40 nm increments using electron beam lithography. Following development, the pattern was transferred to the Si3N4 layer using a reactive ion etching plasma (RIE) (10 sccm CF4, RF power = 100 W, P = 1 Pa) and subsequently etched into the diamond using an ICP process in O2 plasma (80 sccm, ICP power = 750 W, RF power = 200 W, P = 0.3 Pa). The remaining nitride layer was finally dissolved in a buffered HF solution. Optical setup and experimental details

[0148] The sample is cooled to 4 K in a closed-loop helium cryostat (Montana s50). A confocal scanning microscope is used to locate and optically address nanopillars with SnV. The SnV is initialized with a blue diode laser at 450 nm (Thorlabs LP450-SF15 or Hübner Cobolt 06-MLD). Non-resonant measurements are performed with a green diode laser at 520 nm (DLnsec). PLE spectra were measured with a spectrometer (Princeton Instruments HR500) and a CCD camera (Princeton Instruments Excelon ProEM:400BX3). The photons collected by the cryogenic setup are coupled into a fiber and counted using avalanche photodiodes (Excelitas SPCM-AQ4C or SPCM-AQRH). The experiments are controlled using the Qudi software package.

[0149] A highly tunable laser at 619 nm (Sirah Matisse, DCM in EPL / EG solution) and an SHG laser source (TOPTICA SHG DLC PRO) are used for PLE scans. The frequency of the resonant excitation laser is scanned across the C-junction of an SnV center, and the phonon sideband of the fluorescence is captured. The analyzed measurement ( Fig. 6) was under P = 0.5~nW << P sat The scans were recorded to minimize power spread and SnV ionization. A 4 ms interval of 2 µW (average CW power) blue laser irradiation was performed between each line scan. Temporal analysis of sensor data

[0150] As described, emitters with inversion symmetry can be used to investigate aspects of charge dynamics near the emitter. Details of the long-term PLE scan data analysis used to estimate the lifetime of the nearby charge configuration and the switching rates are presented below.

[0151] Wavemeter correction: During scanning, the laser frequency is controlled by applying an external voltage signal. The laser frequency is monitored via a pick-off path directed at a wavemeter. The PLE spectra are initially recorded as voltages and fluorescence signals. The voltages can then be converted into frequencies by matching the timestamps. All nonlinear frequency changes occurring during the scan are thus accounted for.

[0152] Binning: Individual scans are mapped to a frequency axis by selecting a single line scan and then frequency binning. If multiple data points fall into the same bin, they are averaged. If a bin remains empty, the average of the previous and the next bin is used.

[0153] Histograming of scans: The binned scans are summed and normalized to create histograms for PLE spectra 62.

[0154] Configuration identification: A peak finder algorithm (MATLAB: findpeaks) is used to identify the frequencies of the (four) peaks. These peaks are then labeled and used to calculate the spectral position corresponding to a specific charge configuration of Nahfallen 12.

[0155] Configuration ranges: The state configurations are separated by assigning a spectral range to each central peak position. These ranges can be derived by means of half the spectral distance between two adjacent peaks.

[0156] Scan-wise peak detection: The same peak finder algorithm is used for each individual scan to find peaks.

[0157] Scan-wise configuration identification: The identified peaks are then assigned to a charge state configuration based on their central frequencies.

[0158] Determination of brightness durations: A brightness duration is determined by the time that a peak value is associated with the same charge configuration until a change occurs. Each brightness duration is recorded along with the changes in the charge state configuration.

[0159] Histograming of brightness durations: The brightness durations are summarized in histograms 90 according to the frequency with which they were observed, in order to extract average lifetimes and switching rates 93.

[0160] Probability 92 of a charge state change p(i → j): The frequency with which a spectral jump 91 from one charge state i to another j has occurred is recorded. It is then normalized to the total number of jumps from configuration i to obtain a probability. There are two factors that can limit the quantification of uncertainties. First, jump events depend on the individual identification of the peak positions per line. The implemented peak finder algorithm locates the maximum of a line for each scan. Due to spectral scattering, it is not possible to fit each individual line and extract a central frequency uncertainty. Second, there are in the integrated spectrum 61 in Fig. 6. Overlaps of individual spectral peaks. Although a cutoff position in the middle of the peaks was chosen, some of the identified peaks might actually belong to the tail of the neighboring spectral peak rather than to the identified position. Therefore, an overall uncertainty factor is assigned by calculating the overlap of the individual integrated fits of each peak. These factors are then multiplied by the extracted probabilities.

[0161] Poisson fit: The histograms are converted into probability densities and then fitted to a Poisson distribution. After fitting, the histogram and the fit are scaled back to the original occurrences. The brightness durations are then converted into real time units by the duration of a single scan.

[0162] Lifetime τ(i) and determination of the conditional spectral jump rate 93 Γ ct(i → j): The mean values ​​of the Poission distribution fittings and their uncertainties are given as lifetimes of the near-charge configurations or their inverse as state transition rates between the configurations. Simulation details: Multimodal spectra

[0163] The following describes the simulation of the multimodal spectrum in Fig. Section 6 is presented in detail. It is described that there is a spatial trap configuration that affects the experimental data in Fig. 6 can reproduce.

[0164] The process for determining the most probable trap configuration can be divided into three main steps. First, the four peaks observed in the measured multimodal spectrum 61 are used to determine the positions of near traps 12 that produce Stark shifts consistent with the experimental observations. This first step provides a rough estimate of the near trap positions 12. Next, an optimization procedure is applied to fine-tune the predetermined positions of the near traps 12. By optimizing the relevant parameters, a comprehensive collection of simulated spectra 60 is generated. Finally, using the objective function (χ²), 2The large dataset of simulated spectra 60 (test), used during the optimization process, analyzes the most probable configuration of the near traps 12. This objective function serves as a measure of the agreement between the simulated spectra 60 and the experimental observations. By comparing the calculated spectra 60 with the measured data, the configuration that best agrees with the experimental results can be determined. Each step is described in detail below.

[0165] The four peaks of the measured spectrum 61 in Fig. 6 are used as a reference to estimate the position of a loaded near trap 12 relative to the SnV using the following equation: Δstrong=−ΔμEs−12ΔαEs2−13!ΔβEs3−14!ΔγEs4.

[0166] It is assumed here that the scenario with three traps 12 contributing to the multimodal spectrum 61 is the most likely. Trap 12, which occurs at r→2=(0,0,r2) The trap located at position {○○,○⊙,⊙○,⊙⊙} is assumed to be permanently charged. The charge state of the other two traps 12 is then given by {○○,○⊙,⊙○,⊙⊙}, where the left circle represents a trap 12 at position {○○,○⊙,○⊙}. r→1 and the right circle a trap 12 at position r→3 An empty circle represents a neutral trap 12, while a filled circle indicates a trap 12 with a negative charge. The peaks corresponding to each charge state are shown in Fig. 6 shown. The negative charge, which is located at a distance r→2 The location of the SnV increases its response to distant charges and produces the observed inhomogeneous broadening. The choice r→2=(0,0,r2) This is not universally valid, but it can be assumed due to the anisotropy expected from the implantation procedure. Furthermore, including the position would r→2 to increase the free parameter space by adding two more degrees of freedom.

[0167] The arrangement of the three proximity traps is restricted to one plane, further reducing the complexity of the problem. The starting positions r→1,r→2,r→3 are approximated by solving the following system of equations: Δ○○=−Δα2E(−1,r→2)2 Δ○⊙=−Δα2[E(−1,r→2)+E(−1,r→1)]2 Δ⊙○=−Δα2[E(−1,r→2)+E(−1,r→3)]2 Δ⊙⊙=−Δα2[E(−1,r→2)+E(−1,r→1)+E(−1,r→3)]2.

[0168] The positions are parameterized according to: r→1=r1[cos(θ1),0,sin(θ1)] r→3=r3[cos(θ3),0,sin(θ3)].

[0169] The equations above can be solved for r1(θ1), r3(θ1) and θ3(θ1). The relative displacements Δ ○○ ,Δ ○⊙ ,Δ ⊙○, Δ ⊙⊙ are estimated from the central peak positions using a fitting procedure, with the integrated spectrum in Fig. 6 is fitted simultaneously with four Voigt profiles.

[0170] The fine-tuning of the near-trap positions in the second step is again carried out using a Monte Carlo simulation in combination with an optimization procedure. For the optimization procedure, the distant traps are randomly placed in a conical volume z > 0 nm with an opening angle of 45° and a fixed density ρ. trap The volume is distributed to mimic the non-isotropic distribution of traps expected in implantation damage. The volume is capped at 30 nm. A volume r is used. q< 2.5 nm for the arrangement of the near-charge traps 12. It is assumed that one charged trap is connected to the total field E→=∑iE→(qi,r→i), contributes E→(q,r→)=qi4πε0εrr→r3, where e is the elementary charge and q i a charge state with q i ∈ {-1,0, +1}, ε0 is the dielectric constant of free space and ε r = 5.5 is the relative dielectric constant of diamond.

[0171] For each choice of ρ trap , r2 and θ1, a Monte Carlo simulation of the spectral fingerprint is performed.

[0172] To adequately account for the charge state of the near traps 12, they are assigned a probability p. i The probabilities were charged according to the relative peak heights in each individual simulation step. The following probabilities p i were used: p ⊙⊙ = 0.041 , p ⊙○ = 0.017, p ○⊙ = 0.63 and p ○○ = 0.31.

[0173] Optimizing trap positions for a given ρ trap , r2 and θ1 are achieved by minimizing the χ 2 -Function with: ∑iχ(θ,i)=∑n=0,iN[on(θ,i)−En,i]2En, The algorithm for simplicial homology global optimization (shgo) is used. An implementation of the shgo algorithm provided by the Python library SciPy is employed. In Eq. S10, θ = [a, b, p], where a and b fine-tune as follows: r1' = ar1 and r3' = br3.

[0174] The spectrum is divided into three parts, denoted by i ∈ {○○, ○⊙,⊙○+⊙⊙}. For each part, the respective single and double Voigt profile fits are used for comparison with the simulated spectra 60 using Eq. S10. In Eq. S10, E n,iThe expected counts in the nth bin, determined by binning the (normalized) single and double Voigt profiles, fitted to the measured spectrum 61, into 170 equal bins over an interval containing the profile with a width of 4 GHz. 0 n (θ,i) is the number of expected counts of the respective i for the simulated spectrum in the nth bin.

[0175] Finally, the values ​​χ 2 , r1', r3' summarized in tabular form for ρ trap ∈ [35,100] ppm, (Δ ⊙⊙ ∈ [0.5; 1.7] GHz) and θ1 ∈ [0; 0.6] rad. 500 iterations of optimization over different spatial configurations of the remote traps for each value of ρ trap , r2 and θ1 are performed. Only the 50 lowest values ​​of χ are considered. 2 (the others are considered outliers) are used and a weighted averaging is used to determine 〈χ. 2 > carried out.

[0176] The 68% confidence interval for ρ is calculated. trap , (Δ ⊙⊙ ) and θ1 by min{(χ 2 )} + 3.5 determined. The results are in Fig. 6 and Fig. 7 shown. The one in Fig. 6 and Fig. The statistical errors shown in Figure 7 result from all simulated spectra within the 68% confidence interval. Effects of noise

[0177] The in Fig. The relative sensitivity to electric fields shown in Figure 3 depends on how well the peak frequency of a spectral peak can be determined. The determination of the peak position is affected by uncertainties caused by noise other than the stochastic shifts of the C junction. Sources of such noise can be dark counts of the detector or unwanted background fluorescence. The signal-to-noise ratio (SNR) required to determine the peak position is determined by the frequency of the peak position shown in Figure 3. Fig. To enable the 3 relative sensitivities shown, an estimate is made. It is initially assumed that α dominates the sensor's response to the interaction with an electric field, so that the relative Stark shift according to Eq. S1, which arises from two differently resolvable electric fields E1 and E2, becomes the following equation: |δω|=α2|E12−E22| =αδ∈E12,

[0178] Here, the definition of the relative sensitivity of the electric field δε = |E1 - E2| / E1 is used, and it is assumed that E1 + E2 ≈ 2E1. The normalized uncertainty is given as A = |δω| / γ hom defined, where the homogeneous linewidth of the SnV γ hom A = 35 MHz was chosen as the reference. A is the smallest Stark displacement difference that must be resolved to achieve a relative electric field sensitivity of δε.

[0179] In Fig. 14 shows the normalized uncertainty for three values ​​of δε, which are representative values ​​from Fig. The uncertainty normalized to the homogeneous linewidth for three different values ​​of the relative electric field sensitivity is δε = 1, 4, 7 · 10⁻⁵. -7 For the range of relevant field strengths, it is determined that 2.5 · 10 -5 < Λ ≤ 10 -4 This applies. To understand the normalized uncertainty, the normalized uncertainty of the central peak position δω0 / γ is used. hom a spectral fitting with a centered Voigt profile V(ω - ω) o0 γ hom , σ) with ω0 = 0 of a Lorentzian component γ hom and simulates a Gaussian component σ in the presence of noise. If δω0 / γ homIf the value resulting from the adjustment does not exceed the threshold required by Λ, it is assumed that the corresponding relative sensitivity of the electric field can be achieved. Fig. Figure 15 shows the result of the simulations. The Gaussian component of the Voigt profile is calculated according to σ. norm = σ / γ hom normalized. SNR=10log10(A2 / δnoise2) calculated, where the amplitude of the Voigt profile A=1 and δnoise2 The amplitude of the white noise is: S(ω) = V(ω,γ) hom ,σ) + δ noise .

[0180] Fig. Figure 15 shows the required SNR as a function of σ normThe uncertainty extracted from the fit as a function of the SNR and the Voigt profile component are both normalized to the homogeneous linewidth. Although the requirements are demanding, they do not represent a fundamental limitation of the proposed sensor. For the multimodal spectrum in Fig. 6. The normalized uncertainties lie between 10 -2 ≤ Λ < 7 · 10 -1 The unfavorable A in the experiment is mainly due to experimental shortcomings and does not represent a fundamental limitation of the sensor principle.

[0181] Even if Λ in the implementation does not meet the simulated requirement to generate the simulated limit of the relative sensitivity of the proposed electrometer, it is sufficient for the claimed angstrom resolution of the sensor. A similar estimate of the normalized sensitivity as a function of the relative resolution δε can be obtained. r= (r1 - r2) / r1, making similar assumptions as above (r1 + r2 ≈ 2r1), so that Λ=2δεra2αλ(1rbias2r12+1r14), where α = 1 / 4πε0ε r It is determined that 18 < Λ < 166 for δε r = 1, r bias = 10 Å and r1 ∈ (10,30) Å, which far exceeds the stated relative fitting uncertainties. Most likely spatial trap configuration

[0182] The integrated multimodal spectrum in Fig. 6 can arise from different spatial charge configurations, which can lead to identical results. However, the possible spatial charge configurations can be narrowed down.

[0183] The integrated spectrum in Fig. Figure 6 shows four peaks. The two simplest configurations that produce such a spectrum are: A) three traps 12, where one trap 12 is permanently charged and the other two are in the states [○○,○⊙,⊙○,⊙⊙], or B) four near traps 12, where one trap 12 is permanently charged and the other three are in the charge states [○○○, ○○⊙,○⊙○,⊙○○]. In both cases, a bias field / permanently charged trap 12 is required to explain the inhomogeneous broadening of the right peak. There are many more trap configurations that could produce the same features, but these are less likely because they require increasingly more traps 12, with only a subset of all possible charge state combinations contributing to the observed spectrum. Of the two scenarios, scenario A) requires the fewest additional assumptions.

[0184] The strongest argument for A) is the rate p(○○ →⊙⊙) = 3(1)%. If the traps are assumed to ionize independently with a probability P, then the corresponding rates for B) are p(○○○ →⊙○○) ≈ P. However, this is one of the least likely processes. Scenario A) would require two ionization events on the order of P. 2 This is much closer to the observation. The same argument can be made for p(○⊙→⊙⊙) = 33(6)%. For B), the corresponding event would be p(○⊙○→⊙○○) ≈ P 2 , which is unlikely. However, the event of single ionization p(○⊙→⊙⊙) is more probable and therefore more consistent with the two-trap scenario.

[0185] The bias field to which the sensor is exposed is estimated by positioning a constantly ionized charge trap such that the inhomogeneous broadening of the simulations matches the observed linewidths. The simulations yield a bias field that causes a spectral shift of 1.27(0.4) GHz. This result is compared with the integrated spectrum 61 for lines between 0 and 200 from the spectrum in Fig. 6 compared and evidence of a small blue-shifted peak with a spectral shift of 1.24(2) GHz compared to the ○○ peak was found (cf. Fig. 16). Fig. Figure 16 illustrates the experimental estimation of the bias field on the sensor using a background-subtracted integrated spectrum of the line scans between 0 and 200 as in Fig. Figure 6 shows that the fit centered at 1.24 GHz indicates the existence of an additional charge trap 12 that is ionized most of the time. This experimentally demonstrates the existence of a third charge trap 12 that is ionized most of the time. Analysis of the inhomogeneous linewidth using Monte Carlo simulations and experimental data independently confirms the estimated magnitude of the bias field. This agreement also shows that the simulations can reproduce the charge environment and are able to detect traps that do not dynamically change their charge on the timescales of the distant traps. Glow

[0186] The formation of V2 is understood as a consequence of implantation damage and the annealing process: Implantation damage occurs during the collision cascade in the diamond lattice, which decelerates the implanted ion. Collisions with energies above the displacement threshold (≈ 37.5–47.6 eV, much lower than typical implantation energies) displace carbon atoms and generate Frenkel pairs: a pair consisting of V1 and a dislocated carbon atom located at an interstitial site. After implantation, an annealing process is carried out to generate the color center through vacancy diffusion and to repair the lattice damage. At temperatures above 600 K, the interstitial carbon becomes mobile, and at 800 K, the V1 exhibits a high degree of mobility. Consequently, during annealing, the interstitial carbon can either recombine with the V1 or diffuse away from the damage site and eventually leave the sample via the interfaces.The V1, which is not recombined with the interstitial carbon, can form an immobile V2, vacancy clusters, or together with the implanted ion, a color center.

[0187] The model starts with a single mobile species (V1) and considers the formation of V2 without multiple-vacancy complexes. Since multiple species are not considered, the assignment of different jump frequencies is omitted. The initial number N and the 3D distribution of V1 after implantation are estimated using an SRIM simulation. It is assumed that a certain percentage of V1 is not consumed by interstitial carbon, which is denoted as the yield in % of non-recombinant Frenkel pairs (V1 yield in Fig. 11 and Fig. 12), a range of V2 concentrations is found which in Fig. Figure 12 shows the three atomic G4V species Si, Ge, and Sn and different implantation energies. The distribution of V2 in the sample is estimated using a kinetic Monte Carlo simulation. In each time step of the kinetic simulation, V1 can make a random step along one of the adjacent lattice sites. When two V1s are adjacent, they form a static V2 that no longer diffuses. The initial distribution of V1 is estimated using SRIM. For each implantation energy, 50,000 implantation events for a given atomic species and implantation energy are used to determine the probability distribution p(z) of V1 as a function of the depth z, measured relative to the diamond surface (001). The p(z) values ​​are then used to realize the spatial distribution of V1 after a single implantation event.The V1 atoms are distributed along a narrow damage channel with a rectangular cross-section of 2a × 2a on the diamond lattice according to p(z). The loss of V1 atoms that do not contribute to the formation of V2 atoms through recombination with interstitial carbon atoms is a fixed percentage due to the reduction in the original amount of V1, as determined in the SRIM simulation. Bulk cargoes

[0188] Based on the model, an overview of the charge trap densities and the resulting inhomogeneous broadening is given, along with specific threshold values, 90% interference visibility, and >87% entanglement fidelity. First, a Monte Carlo simulation is used to determine the linewidth distributions for a given trap density p. A carbon density of ρ is assumed. C = 8 / a 3In the bulk, an isotropic distribution of traps 12 in the vicinity of the SnV is assumed at a given density ρ. For each ρ, 500 spatial trap configurations are considered, each generating individual spectra tapering to a peak for ρ ∈ (1,100) ppm. Equations S9 and S8 are used to calculate the spectra. Surface charges

[0189] The surface density for both the semi-infinite half-space and the cylindrical geometry, given in ppm, is expressed in terms of a carbon density of ρ. c = 2 / a 2[(001)-plane] calculated. For the semi-infinite half-space, the traps 12 are randomly arranged on a square with a side length of 100 nm. The cylindrical surface has a height of 100 nm. The simulation of the inhomogeneous linewidth was performed in both cases using the Monte Carlo method with 5000 different charge configurations for a single spatial configuration of traps 12. The electrostatic fields of a point charge on a surface are also used, taking into account the corresponding boundary conditions. The electric field of a charge located on the surface of the semi-infinite half-space is: E→(q,r→q)=q2πε0(εr+1)r→qrq3.

[0190] For the cylindrical surface, a diamond cylinder with radius R is assumed, extending to z = ±∞. Band bending is not considered, which can be advantageous for eliminating surface noise through shielding. Shielding by free charge carriers is also neglected because the significant reduction in sensitivity to charge noise, which would be expected even with moderate shielding lengths of a few tens of nanometers, is not observed. Control tests: Verification of emissions from a single transition

[0191] The sensor can be verified to determine whether the multimodal spectral fingerprint originates from a single transition. Four characterization measurements at zero magnetic field are provided to rule out Zeeman splitting, demonstrating that the signal originates from a single source and a single transition. Distribution of jump distance

[0192] For the 19 characterized emitters, jump distances ranging from a few hundred MHz to several GHz were determined. In the investigated samples, either one or two different jump processes, or combinations thereof, were found, which correspond perfectly with the number of estimated lattice defects. The distribution of these distances is shown in Fig. 17 shown on the left. Fig. Figure 17 on the left shows the spectral hopping regions of characterized emitters. Non-hopping emitters were stable during the linewidth scans, which took place over various time periods ranging from minutes to one hour. The error bars show the 95% confidence intervals of the central frequency spacings extracted from the data.

[0193] The existence of unknown levels with quasi-forbidden transition rules therefore seems unlikely, since the jump distances appear to be random for each emitter. PL spectrum

[0194] In Fig. Figure 17 shows a photoluminescence spectrum of E1 with an -850 GHz split between C and D transitions. The photoluminescence emission spectrum measured under 520 nm excitation light at 4 K is shown according to Fig. Figure 17 in the middle shows a typical SnV spectrum with recognizable spectrometer-limited peaks, which represent the C- (between the levels |1〉-|3〉, Fig. 6) and D- (|2〉-|3〉) transitions. Since they are approximately 850 GHz apart, it can be stated with certainty that several peaks from the PLE scan do not correspond to these transitions. Measurement of autocorrelation

[0195] The autocorrelation measurements presented in the control experiments for the single-photon ionization charge dynamics model originate from the emitter under investigation. The probability that multiple emitters contribute to the spectrum is determined by an autocorrelation measurement with g. (2)(0) = 0.12(9) < 0.5 close to the theoretical expected value of g (2) (0) = 0 made improbable. Rabi frequencies of different resonances

[0196] Rabi oscillations between the levels |1〉 and |3〉 (C transition) of an SnV are demonstrated at emitter E2 at two different resonance frequencies before and after a spectral jump event. Fig. Figure 17 on the right shows Rabi frequencies of emitter E2 at different power levels from both resonances. The values ​​are extracted from a damped oscillation function at different resonant excitation powers (between levels |1〉 and |3〉). The data points were recorded before and after a spectral step, and thus at different frequencies. The uncertainties and error bars represent 95% confidence intervals extracted from the data. The detailed view shows Rabi oscillations observed at the higher-frequency resonance with a power of 45.5 nW. The oscillations are achieved by resonance excitation after a green stabilization pulse. The data after the rise time of the resonance laser are fitted to a damped oscillation function. After repeating the measurement at different power levels, a slope of [value missing] was obtained for the lower-frequency resonance. 20.9(9)HznW, for the higher frequency a slope of 21.2(1.8)HznW and for the combined dataset a slope of 21.0(5)HznW on a linear Frequency-Power-Line. The fact that the slopes for three data sets remained within the adjustment error range strongly suggests that the dipole moment did not change between the spectral jumps and that the same transition is being addressed between the two measurements. Demonstration of ionization processes via single-photon processes using autocorrelation measurements

[0197] One of the events that can occur during laser irradiation is the transition of group IV vacancy (G4V) emitters to a dark state. This manifests as shoulder-like bundling features around the antibundling drop in autocorrelation measurements. Applying the assumption of a one-photon process from the model used, a linear power dependence is found for both hole creation / capture and electron promotion. These experiments show that the charge transfer picture is consistent with the photon statistics measurements. The analysis is based on the derivation of the autocorrelation function and the rate equations.

[0198] The system is assumed to have three levels, where level 1 is the ground state, level 2 is the excited state, and level 3 is a non-radiating shelving state, which is designated as G4V. -2 is referred to as such a system. (2)With a non-zero background, the following equation applies: g(2)=1+p2[1−(1+a)exp(−ττa)+a exp(−ττb)], where p determines the contribution of the background, τ a The anti-bunching time is the time that refers to the sink at 0 delay, τ b The bunching time determines the shoulders around the anti-bunching decay, and the parameter α is related to the transition rates. To verify the model, g (2) Measurements from an SnV center at different power levels (P) were fitted to this equation and the parameters extracted. To predict the transition rates (k InitialFinal The following performance relationships are then assumed: • At k 12 (incoherent excitation) a linear dependence on the power 'δP' is assumed, since it is a one-photon process in which an electron transitions from the ground state into quasi-continuous phononic bands of the excited state. • k 21 (Spontaneous emission) is modeled with a constant rate 'Γ'. • At k 23 (Shelving) a linear power dependence 'αP' is assumed, since this process is known to be a one-photon process that transports electrons from the valence band into an excited G4V. • k 31 Deshelving is also modeled as linearly proportional to the power 'βP': Here, hole provision is assumed to be a one-photon process that occurs through the promotion of an electron from the valence band to a V n is triggered. So far, this rate has been modeled with a saturation curve, which is due to the limited amount of contributing V. n can be traced back to this. However, in this case, the Monte Carlo simulations indicate a V that is too high. nDensity increases, so saturation can occur. Therefore, a linear model can capture the data well. A saturation curve can mimic a linear relationship at low power levels, and both models can perform consistently across different ranges.

[0199] The bundling time τ b , is related to the transition rates by the following equation: τb=1k31+k23k12k12+k21

[0200] If k 12 as much larger than k 21 - as expected with higher performance - is assumed, then k strives for 12 / (k 12 + k 21 ) against 1. Consequently: τb=1k31+k23=1(α+β)P

[0201] This shows that τ b effectively through the total rate of k 31 and k 23 is determined at higher power levels. When a 1 / x model is applied to the extracted data τ b in Fig. When adjusted to 18, it becomes apparent that the model captures the data well, and α + β is extracted as 7.5(1) kHz / µW. The total charge cycle rate of 1 MHz at ~150 µW also appears reasonable, as it is assumed that the charge transfer process is slower than the spontaneous emission or excitation.

[0202] To estimate the rate coefficients separately, the α parameter can be determined, which can be calculated using the following equation: a=k23k31+k12+k21=αβδPδP+Γ.

[0203] At high power levels, the α parameter asymptotically reaches the value α / β. Fig. Eq. S17 presents the extracted α values ​​from the measurements of a saturation curve, where the fit asymptotically approaches 0.40(3). From this relationship in Eq. S17, the shelving and deshelving rates at each power can be derived with α = 2.2(2) kHz / µW and β = 5.4(2) kHz / µW. Since the assumption of linear power dependence agrees with the observed data, it is assumed that single-photon processes are the main cause of the charge dynamics in the sample.

[0204] In Fig. Figure 18 shows plots of the extracted parameters from the autocorrelation measurements for emitter E1. The error bars represent 95% confidence intervals derived from the fits. These measurements on the left demonstrate that shelving and deshelving processes can be modeled as single-photon events. The bunching time at different power levels is indicated. The gray dots are excluded from the calculation because they do not behave according to the approximated model at low power levels and exhibit large errors. The solid line represents the fit to a 1 / (cP) function. In the box in Fig. Figure 18 on the left shows selected example measurements. On the right, the parameter 'a' is plotted at different power levels. The solid line represents the fit to a saturation curve. Interaction between charge trap and illumination field

[0205] The properties of the laser can influence spectral diffusion. Since the illumination triggers ionization events in the sample, it is shown that the interactions and observed phenomena are consistent with the existence of charge traps. Position dependence of the stabilization laser and measurement of the subdifference drift

[0206] A particular characteristic of the ZPL of a SnV is that the spectral line drifted in correlation with the laboratory's climate control cycle. Simulations are performed to reproduce the periodic changes and the inhomogeneous broadening of the determined PLE measurement. These simulations involve introducing a periodic misalignment of the laser by varying the far-charge densities involved.

[0207] The blue stabilizing laser is assumed to have a Gaussian intensity distribution in the z-direction that oscillates over time: I(z,t)=I0e−[z−z0(t)]2 / 2σ, where I0 is the peak intensity of the laser at the focal point, σ is the focal length and z0(t)=a sin(ωt).

[0208] The amplitude a, which describes the extent of misalignment due to temperature fluctuations in the system, is unknown. The frequency ω = 2π / T corresponds to a T = 10 min cycle. The Monte Carlo simulation is performed according to the steps described above, with the field generated by an ionized trap specified as follows: E→(q,r→)=qi4πε0εrr→r3.

[0209] Twelve random traps with a density of ρ = 22.7 ppm are distributed in a cubic volume with an edge length of 100 nm. The trap density accurately reproduces the inhomogeneously broadened linewidth of approximately 103 MHz and the... Fig. 17 for a power-broadened homogeneous linewidth of ≈ 88 MHz. The probability of a trap participating in ionization is assumed to be given by P(t) = P(z, t) + P0, where P(z, t) ∝ I(z, t) and P0 = 0.1 is a constant background ionization probability. For the Monte Carlo simulation of the inhomogeneous linewidth, 2500 different charge configurations are used at each time step t. Very good agreement with the results is obtained for a laser with a focal spot width of FWHM = 240 nm. (σ=FWHM / 22log(2)) and a vibration amplitude of a = 200 nm. The results are in Fig. 19 can be seen.

[0210] To further confirm the model, a long-term PLE scan was performed ( Fig. 19) and the xyz control of the confocal microscopy setup is used to optimize the fluorescence signal. By monitoring changes in the spectral line, a drift of approximately 200 MHz is measured over a period of 3 hours, corresponding to a shift of approximately 50 nm according to the position optimizer. Reorienting the setup restores the original position of the resonance, further supporting the hypothesis.

[0211] Spectral drift relationships of ~0.2 MHz / nm and ~4 MHz / nm for Fig. are extracted. This means that, depending on the surrounding charge density, it would be reasonable to estimate a MHz / nm equivalent of the laser position drift relative to the emission mean frequency. Such a spectral test could prove useful for estimating the position drift below the diffraction limit. It has been shown that chirped pulses from an EOM can sample a range of 200 MHz in less than one second. Therefore, using a spectral approach would also allow for a higher bandwidth, exceeding the readout rates of fluorescence intensity-based systems.

[0212] Overall, a SnV or, more generally, an emitter with inversion symmetry can be used to temporally resolve the involved remote charge trap density at any given time. By correlating the central frequency, spatial drifts in experimental systems can be tracked.

[0213] In Fig. Figure 19 shows plots illustrating the influence of laser misalignment on PLE spectra. The left plot simulates the temporal change in the central position and linewidth of the C transition caused by a periodic change in the orientation of the charge-state stabilization laser, which can result from temperature variations in the experiment. A power-broadened homogeneous linewidth of FWHM is shown. hom = 88 MHz (left line) assumed and an inhomogeneous linewidth of FWHM hom A frequency of 103.3 MHz (extracted from the fit using a Voigt profile, right line) was determined for the specified parameters of the charge-state polarization laser. The right plot shows an example PLE measurement demonstrating a drift in the resonance frequency. After optimizing the xyz position of the sample and the laser spot, the central frequency returns to its original position. Methods for stabilizing the emitter

[0214] The spectral properties of the emitters are also investigated using various methods for charge stabilization with blue laser light, in order to understand its interaction with the V n to investigate. Fig. Figure 20 shows PLE scans and spectra using two different stabilization methods with a charge stabilization laser at 450 nm and 300 nW average power. In the first scheme, continuous (CW) laser light is used during each PLE scan (continuous stabilization). The second is a pulsed scheme: before each PLE scan, the sample is irradiated with a 4 ms blue laser pulse (pulsed stabilization). The PLE scans were performed at emitter E1 with a resonant power of 0.7 nW, which is below the saturation power (> 20 nW) and also low enough to avoid ionization during the scan.

[0215] Fig. Figure 20 shows the two resonance peaks (~1.4 GHz apart), which are also present in each individual line scan. The individual PLE scans of the pulsed scheme in Fig. Figure 20 shows that both resonances correspond to two different spectral positions of the C transition, which is attributed to the Stark shift according to Eq. S1, caused by two different charge configurations of the ionized V n is caused near the SnV. With the resonance laser, a quasi-continuous fluorescence signal with the full inhomogeneous linewidth can be observed. Due to the continuous stabilization, the charge state of the surroundings is adjusted with a spectral jump rate Γ SH » G scan cyclically changing, which is much higher than the PLE scan rate, resulting in two recognizable peaks in individual PLE scans.

[0216] In Fig. Figure 20 shows plots of the photoluminescence excitation of the carbon junction under different charge stabilization schemes at emitter E1. During the scans, hopping between two different resonances is observed. The resonance laser has a power of 0.7 nW and the blue laser has a power of 300 nW. The spectra were calculated using Voigt profiles. The uncertainties represent 95% confidence intervals extracted from the spectra. In the left plot, the blue laser illuminates the sample continuously at 450 nm while the resonance laser measures. The continuous operation of the blue laser results in hopping that is faster than a single line scan, causing both peaks to be observed in each individual scan. In the right plot, a 4 ms blue laser pulse is sent at the beginning of each scan.Without the help of the blue laser, the transition between the two resonances is slower, but still present due to the laser being in resonance with the C junction.

[0217] Another clear signal for the increased ionization of V n The more pronounced inhomogeneous broadening of the resonance lines during continuous stabilization is a key finding. 450 nm CW light results in more charge traps in the vicinity contributing to the generation of the fluctuating electric field at the emitter's position during each scan. Just as predicted in the Monte Carlo simulation, increased charge trap activity leads to enhanced inhomogeneous broadening. Wavelength dependence of the stabilization laser

[0218] An indication that charge dynamics and the occupation of nearby traps play a role in the spectral jump phenomena arises from the comparison of charge stabilization with blue (450 nm) and green lasers (520 nm). Fig. Figure 21 shows the PLE spectra of emitter E2, recorded under the same resonance and stabilization laser powers, exhibiting a single peak with the green laser, while a smaller second peak (albeit weak) can be observed when the blue laser is used. Blue laser irradiation has been shown to be more efficient for charge-trap ionization. This suggests that the blue laser activates a previously inaccessible charge trap, leading to the new discrete spectral jump. Spectroscopy of charge-trap transition rates could help determine the ionization energies for individual charge-trap types. For example, it is possible, albeit only qualitatively, to observe a faster-switching fluorescence signal within the PLE acquisition resolution with the blue laser at each individual line, resulting from rapid spectral jumps.

[0219] In Fig. Figure 21 shows plots of the photoluminescence excitation (PLE) of the carbon transition under different colored stabilization schemes of emitter E2. The carbon laser had a power of 1 nW. The spectra were generated using bimodal Voigt profiles. The uncertainties represent 95% confidence intervals extracted from the spectra. In the left plot, the green laser is continuously switched on at 500 nW at 520 nm while the resonance laser scans. Continuous fluorescence of smaller peaks was sometimes observed. The secondary peak was not observed in this configuration. The spectra were recorded using a Voigt profile. In the right plot, the blue laser is continuously switched on at 500 nW at 450 nm while the resonance laser scans. The blue laser generates a spectral jump that leads to a secondary peak. The spectrum was recorded using a bimodal Voigt profile. Power dependence of the stabilization laser

[0220] Extended resonance excitation of SnVs leads to a transition to a dark state. This has been linked to a change in the charge state through the ejection of an electron from the valence band. A hole-capture process induced by blue or green lasers can return the SnV to its bright state. Using higher powers or longer illumination times increases the probability of charge state stabilization and re-emission.

[0221] This is made possible by the ionization or charging of the defects around the quantum emitter, which act as charge / hole donors. As a result, the illumination alters the charge distribution around the color center, leading to spectral diffusion. Therefore, charge stabilization and inhomogeneous broadening become competing effects that must be optimized for high-quality emission.

[0222] In Fig. 22 This conflict of objectives is demonstrated using a measurement at emitter E14. At a power of 7000 (375) nW, bright lines are observed for 30%, 9 / 30 (23%, 7 / 30) of the time, and a histogramed linewidth of 871 (204) MHz is obtained. Since charge traps 12 play such a crucial role in stabilizing the bright state, a competition arises between spectral diffusion and the efficiency of charge state stabilization η. bright expected. The ideal V n-Density (or more generally the density of hole donors) can then be achieved by a compromise between minimizing spectral diffusion and maximizing η bright be determined.

[0223] In Fig. Figure 22 shows plots comparing different stabilization pulse powers during illumination of emitter E14. Both measurements were performed under 0.5 nW resonance laser excitation. Two different blue laser powers of 375 nW and 7000 nW were used. Higher powers resulted in a broadened inhomogeneous linewidth and more pronounced spectral drifts. The spectra were recorded using a Voigt profile. The uncertainties represent 95% confidence intervals extracted from the spectra. The two left-hand plots show the measured fluorescence for each cycle while sampling the laser frequency. The two right-hand plots show histogram counts for linewidth determination using a Voigt profile.

[0224] Furthermore, the contribution of the blue laser to spectral diffusion was determined as a function of its power. Fig. Figure 23 shows measurements of emitter E20, i.e., sample E014, which had the same manufacturing parameters as E002 (five times the dose of sample E001), but with an additional sulfur co-implantation step. It is clearly evident that higher blue laser light powers lead to a more pronounced broadening, exhibiting a certain degree of saturation, which in turn is consistent with the Monte Carlo simulations.

[0225] In Fig.Figure 23 shows a plot comparing different stabilization powers at emitter E20. The measurements were performed on a different sample with a five times higher sulfur implantation dose and co-implanted with sulfur. All measurements use the same resonance excitation power of 5 nW, while varying the power of the continuous blue stabilization laser. As the blue laser power increases, the linewidth widens and reaches an asymptotic limit. The inset shows a magnification of the lower powers to better illustrate the saturation trend. The error bars are the 95% confidence intervals, which are strongly influenced by background fluorescence caused by the high blue laser powers.

[0226] The features disclosed in the foregoing description, the claims and the drawing can be important for the realization of the various embodiments, both individually and in any combination.

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