DE102020118699A1 - Method and device for examining a sample with spin-dependent fluorescence - Google Patents

Abstract

Methods and devices for examining samples which emit spin-dependent fluorescence are disclosed. The spin-dependent fluorescence is measured and/or the measurement is evaluated using information about the time-dependent course of the fluorescence.

Description

The present application relates to methods and devices for examining a sample with spin-dependent fluorescence.

In quantum technology, spin systems can serve as so-called quantum bits, with a spin state corresponding to a value of the quantum bit. A candidate for such spin systems are defect centers such as nitrogen vacancy centers (NVC for short) in a diamond structure, which have spin states with a long coherence time. Such systems are sometimes also referred to as color centers. The spin state of such defect centers can be manipulated, for example, using microwave fields or magnetic fields and then read out optically. Such defect centers can also be used as probes in microscopy, as is the case, for example, in the German patent applications DE 10 2019 119 213.7 and DE 10 2019 119 212.9 is described by the applicant.

A level scheme of a nitrogen vacancy center is in 1 shown. the 1 shows a ground triplet state ³ A ₂ and an excited triplet state ³ E, each having three possible spin states |0>, |+1> and |-1>.

The splitting between the spin levels |+1 > and |-1> each depend on an applied magnetic field. A transition from the spin state |0> to the state 1+1> or |-1> can take place, for example, via microwave radiation, as indicated by an arrow 10, or through the influence of a magnetic field.

From the ground state ³ A ₂ , an excitation into the excited state ³ E can take place, for example by means of optical excitation, as illustrated by arrows 11 . For example, a green laser with a wavelength of 532 nm can be used for this excitation. A radiant transition into the ground state can then take place from the excited state ^3E , as indicated by arrows 12 . The wavelength of this optical emission is 637 nm for the transition between the spin states |0> and is also in this order of magnitude for transitions between the spin states |+1> or between the spin states |-1>. Due to spin conservation and the spin of a photon being 0, a transition can only occur between corresponding states, i.e. from spin |+1> to spin |+1>, from spin |-1> to spin |-1> or from spin | 0> to spin |0>.

In addition, a transition can occur from the excited state ³ E to a metastable state ¹ E as represented by an arrow 13, this transition being non-radiative. From the state ¹ E there is then a transition to a state ¹ A ₁ , with this transition light having a significantly longer wavelength, namely 1042 nm, being emitted, so that this light is normally not included in a detection of the fluorescence according to the arrows 12 is detected. From the ¹ A ₁ state, the system then returns to the ground state ³ A ₂ with spin |0> by a nonradiative transition.

The probability of the transition from state ³ E to state ¹ E according to arrow 13 is higher for the spin states |+1> and |-1> than for the spin state |0>. This means that the optical emission according to the arrows 12 for the spin states |+1> and |-1> is lower than for the spin state |0>.

this is in 2 shown. the 2 shows normalized fluorescence intensity versus spin angle, where spin angle expresses a proportion of spin |+1> or |-1> to a proportion of spin |0> states in a sample. If the spin angle is denoted by phi, a corresponding state Ipsi> can be expressed as |psi> = cos (phi/2) |0> + sin (phi/2) |1>, where cos is the cosine function and sin is the sine function.

In the 2 shows a curve 20 a behavior for so-called integrated detection, while a curve 21 shows a behavior for a so-called "gated" detection (more precisely also referred to as time-gated detection or time window detection), wherein in both cases the fluorescence for a spin angle of π, corresponding to spin states |+1> and |-1>, is smaller than for a spin angle of 0 or 2π, corresponding to a spin state |0>. In the case of the integrated detection according to the curve 20, the fluorescence signal is integrated over an entire period of time in which fluorescence is present, while in the case of gated detection it is only detected over a limited period of time.

At intermediate spin angle values, some nitrogen vacancy centers in a sample exist in a |0> spin state and others in a |+1> or |-1> spin state. In the case of integrated detection according to curve 20, a contrast between the minimum and maximum of the curve is 0.25, while the contrast for gated detection according to curve 21 is 0.65 in the example shown.

For excitation, in one approach, a continuous wave (cw) laser can excite the nitrogen vacancy centers throughout to fluoresce. At the same time, the spin state is manipulated, for example by irradiation len appropriate microwave pulses or by applying magnetic fields. The intensity of the fluorescence signal, which is integrated over a certain period of time, then provides information about the spin state. The disadvantage of this approach is that the laser used to excite the fluorescence perturbs the spin state while it is being manipulated, for example, by microwave pulses. This spin state perturbation can severely reduce the performance of a system based on nitrogen vacancy centers. If the nitrogen vacancy centers are used to measure magnetic fields, for example, this reduces the sensitivity.

In another approach, pulsed reading, the manipulation of the spin and the irradiation of a laser to read the spin are separated in time. The process of such a measurement is in the 3 shown. A curve 30 schematically shows laser irradiation over time, and a curve 31 microwave irradiation over time. First, there is a first pump pulse 32 with a duration t1. Following this first pump pulse, the spin is manipulated using a microwave pulse 34 . In addition or as an alternative to the microwave pulse, another type of manipulation, for example magnetic manipulation, of the spin can also take place. A duration of the microwave pulse 34 is tm. tl and tm can be on the order of 1 μs, for example.

A further laser pulse 33 for reading out the spin state takes place after the microwave pulse 34, which can also have a duration t1 or a duration that deviates therefrom.

the 4 shows examples of fluorescence signals over time associated with the pulsed readout of the 3 are producible. Curve 41 shows the course of the fluorescence over time after the start of the read-out pulse (pulse 33 of 4 ), this beginning being indicated by an arrow 35 in the 3 is marked and t = 0 in the 4 is equivalent to. A curve 41 shows an example for the spin state 0>, and a curve 42 shows the profile for the spin state |−1>. The curve for the |+1> spin state would be similar to the curve for the |-1> spin state.

As can be seen, the difference in intensity between curves 41 and 42 decreases over time. If now over the entire time period (e.g. 0 to 1000 ns in 4 ) is integrated, there is then a relatively small difference between the integrated intensities, as is also the case in curve 20 of 2 you can see. Therefore, gated detection is used in many cases. Here an integration only takes place in a certain time window, which in 4 indicated by the reference numeral 40. The measured signal is then only integrated in this time window. This results in a clearer difference between different spin states, as is also shown by curve 21 of FIG 2 is clarified. The integrated intensity can then be compared to one or more threshold values, for example, in order to infer a spin state.

• Generell sind derartige Fluoreszenzsignale sehr schwach, und somit verrauscht, beispielsweise durch Poisson-Rauschen. Um trotzdem mit entsprechender Sicherheit auf den Spin-Zustand schließen zu können, muss in vielen Fällen das Signal über viele Durchläufe (Präparation des Spin-Zustandes und nachfolgendes Auslesen) gemittelt werden, um somit durch Mittelung das Rauschen zu reduzieren. Dies erhöht jedoch den Zeitaufwand für Messungen. Alternativ kann auch eine Verbesserung der Detektionseffizienz angestrebt werden. Allerdings sind herkömmliche Messvorrichtungen hier schon weitgehend optimiert, weswegen weitere Verbesserungen in der Detektionseffizienz durch verbesserte Hardware nur bedingt möglich bzw. mit großem Aufwand verbunden sind.

The following problems arise with the conventional approaches as presented above:

• In general, such fluorescence signals are very weak and are therefore noisy, for example due to Poisson noise. In order to be able to infer the spin state with a certain degree of certainty, in many cases the signal must be averaged over many runs (preparation of the spin state and subsequent readout) in order to reduce the noise through averaging. However, this increases the time required for measurements. Alternatively, an improvement in the detection efficiency can also be sought. However, conventional measuring devices are already largely optimized here, which is why further improvements in the detection efficiency through improved hardware are only possible to a limited extent or are associated with great effort.

In the case of gated detection, the suitable selection of the time window 40 then also represents a problem. If the time window is selected too short, too few photons are detected and the noise relative to the signal is thus increased. If the time window selected is too long, the result is that the signal is also integrated at times when signals 41 and 42 do not differ or differ only slightly. As a result, no additional information is obtained through further integration, but photons continue to be collected, which contribute to the overall noise with their Poisson noise, but no relevant signal, which indicates the signal-to-noise ratio , short SNR) deteriorated.

Such gated detection can also be used in the case of continuous excitation. In this case, the time window is not selected in relation to the switching on of the laser, because it is on continuously, but in relation to the microwave pulses radiated in or other manipulation of the spins. The problem is otherwise similar here.

It is therefore an object to provide methods and devices with which the measurement of spin-dependent fluorescence can be improved, for example a signal-to-noise ratio nis for the determination of a spin state can be improved.

A method according to claim 1 and a measuring device according to claim 13 are provided. The dependent claims define further embodiments.

According to the invention, a method for examining a sample is provided, comprising: measuring a spin-dependent fluorescence from the sample, and evaluating the measurement of the spin-dependent fluorescence, the measuring and/or the evaluating taking place using information about the time-dependent course of the spin-dependent fluorescence.

Information about the course of time means that not only the integral is used over a period of time, but is actually used in the measurement or evaluation of how the fluorescence signal decreases, decreases or otherwise develops over time. By using information about the course over time, this information is additionally available and can be used to improve the measurement or to evaluate the measurement.

The information about the spin-dependent course can be based on properties of fluorescence-emitting components of the sample, for example on decay rates of (spin) states of such components

Additionally or alternatively, the information about the time-dependent profile can be based on calibration measurements of the sample in a first spin state and a second spin state that is different from the first spin state. This does not rule out the possibility that other spin states are present and involved. The information can then also be based on calibration measurements of the sample in a third spin state, which is different from the first and second spin state, etc.

The sample may contain nitrogen vacancy centers in a diamond structure, e.g., as the fluorescence-emitting components mentioned above.

Performing the measurement using information about the time-dependent history can calibrate a measuring device used for the measurement based on the information.

Thus, calibrating the measuring device can include calibrating a beginning of an integration of a signal obtained during measurement relative to a beginning of a laser pulse for exciting the sample on the basis of a beginning of an increase in the spin-dependent fluorescence.

In this way, for example, timing jitter can be reduced, i.e. inaccuracies or noise that result from a time offset between the start of the measurement and the laser pulses.

Evaluating the measurement using the information about the time-dependent course include obtaining information about a spin state of the sample based on the information about the time-dependent course.

In other words, in this case, use is made of the fact that different spin states not only have different fluorescence intensities, but also the temporal progressions differ, ie information about the spin state is contained in the information about the temporal progression.

Evaluating the measurement using the time-dependent history information may include weighting the measurement with a weighting function based on the time-dependent history information.

By choosing a weighting function, an improvement in the signal-to-noise ratio can be achieved compared to using a time window in gated detection.

The sample can have one or more fluorescence centers, each fluorescence center being in a first spin state or in at least one second spin state, and the weighting function being a function of a time-dependent course of a fluorescence intensity for the first spin state and a time-dependent course is the fluorescence intensity for the at least one second spin state.

gegeben sein, wobei I_|0>(t) der zeitliche Verlauf für den ersten Spin-Zustand, I_|±1>(t) der zeitliche Verlauf für den zweiten Spin-Zustand und c ein Normierungsfaktor ist.The weighting function w(t) can be given by $$w\left(t\right)=c\frac{I_{|0>}\left(t\right)-I_{|\pm 1>}\left(t\right)}{I_{|0>}\left(t\right)+I_{|\pm 1}\left(t\right)}$$

be given, where I _|0> (t) is the time profile for the first spin state, I _|±1> (t) is the time profile for the second spin state and c is a normalization factor.

gegeben sein.The normalization factor c can be $${\left[{\displaystyle \underset{0}{\overset{\infty }{\int }}\frac{I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)}{I_{|\pm 1}\left(t\right)+I_{|0>}\left(t\right)}}\mathrm{i.e}t\right]}^{-1}$$

be given.

The sample may have one or more fluorescence centers, eg the nitrogen vacancy centers mentioned above, each fluorescence center being in a first spin state or in a second spin state, and the information about the time-dependent course includes a time-dependent course of a fluorescence intensity for the first spin state and a time-dependent profile of the fluorescence intensity for the at least one second spin state.

• einen Detektor zum Messen einer spinabhängigen Fluoreszenz von der Probe, und
• eine Steuer-/Auswerteeinrichtung zum Steuern der Messung der spinabhängigen Fluoreszenz und zum Auswerten der Messung, wobei die Vorrichtung eingerichtet ist, die Messung und/oder das Auswerten der Messung unter Verwendung einer Information über den zeitabhängigen Verlauf der spinabhängigen Fluoreszenz durchzuführen.

According to the invention, a measuring device for examining a sample is also provided, comprising:

• a detector for measuring a spin-dependent fluorescence from the sample, and
• a control/evaluation device for controlling the measurement of the spin-dependent fluorescence and for evaluating the measurement, the device being set up to carry out the measurement and/or the evaluation of the measurement using information about the time-dependent course of the spin-dependent fluorescence.

The device can further comprise a light source for exciting the sample.

The device may further comprise a microwave emitter and/or a magnetic field device for manipulating a spin state of the sample.

The device can be set up to carry out one of the methods described above.

A computer program will also be provided, e.g. on a tangible storage medium, with which the evaluation of the measurement based on the information about the time-dependent course (e.g. weighting) is carried out according to the methods described above.

• 1 ein Niveauschema eines Stickstoff-Fehlstellen-Zentrums,
• 2 Fluoreszenzintensitäten für verschiedene Spinwinkel bei verschiedenen Detektionsarten,
• 3 Signale zum gepulsten Auslesen eines Stickstoff-Fehlstellen-Zentrums,
• 4 Beispiele für Fluoreszenzkurven,
• 5 ein Blockdiagramm einer Vorrichtung gemäß einem Ausführungsbeispiel,
• 6 ein Flussdiagram zur Veranschaulichung von Verfahren gemäß mancher Ausführungsbeispiele,
• 7 schematische Darstellungen zeitabhängiger Fluoreszenz zur Veranschaulichung mancher Ausführungsbeispiele, und
• 8 eine Gewichtungsfunktion gemäß einem Ausführungsbeispiel im Vergleich mit Gated-Detektion.

Various exemplary embodiments of the present invention are explained in more detail below. Show it:

• 1 a level scheme of a nitrogen vacancy center,
• 2 Fluorescence intensities for different spin angles with different types of detection,
• 3 signals for pulsed readout of a nitrogen vacancy center,
• 4 examples of fluorescence curves,
• 5 a block diagram of a device according to an embodiment,
• 6 a flowchart to illustrate methods according to some embodiments,
• 7 schematic representations of time-dependent fluorescence to illustrate some embodiments, and
• 8th a weighting function according to an embodiment compared to gated detection.

Various exemplary embodiments are explained in detail below. These embodiments are provided for illustration only and are not to be construed as limiting. Thus, a description of an embodiment having a plurality of features (components, steps, processes, elements, etc.) should not be construed as implying that all of those features are necessary, as other embodiments may have fewer features and/or alternative features. In addition to the features explicitly described here, other features can also be provided, for example features of conventional measuring devices and methods for measuring spin-dependent fluorescence. Thus, apart from the use of fluorescence time course information, as detailed below, the measurement can be made in a conventional manner using conventional apparatus, and these conventional components will not be discussed in detail.

Features of different exemplary embodiments can be combined with one another unless otherwise stated. Variations and modifications that have been described for one of the exemplary embodiments can also be applied to other exemplary embodiments and are therefore not explained in more detail.

In the following description, nitrogen vacancy centers in diamond are used as an example of samples or components of samples showing spin-dependent fluorescence. However, the techniques described below are also applicable to other cases where spin-dependent fluorescence occurs, such as other defect centers. Examples of this are silicon vacancies in SiC, as in D. Reidel et al., "Resonant addressing and manipulation of silicon vacancy qubits in silicon carbide", arXiv1210.0505v1, or defects in 2D materials, as in A. Gottscholl et al., "Room Temperature Initialization and Readout of Intrinsic Spin Defects in a Van der Waals Crystal", arXiv:1906.03774.

In the following it is assumed as an example that fluorescence differs between 2 spin states, eg |0> and |±1|. The one shown here However, the techniques and approaches presented above, which use information about the time-dependent course of fluorescence, are also applicable to systems and samples in which three or more different spin states with different fluorescence behavior are present.

the 5 FIG. 12 shows a measuring device according to an exemplary embodiment, which is set up to measure a spin-dependent fluorescence from a sample 54. FIG. The sample 54 can have nitrogen vacancy centers as fluorescence centers, for example.

The device of 5 has a laser 51 for optically exciting the sample 54 and a detector 53 for detecting fluorescence from the sample 54 . The laser 51 can be, for example, a laser with a wavelength of 532 nm, for example a Nd:YAG laser. The detector 53 can be any type of detector set up to detect a wavelength corresponding to the fluorescence of the sample 54 (in the range of 637 nm for nitrogen vacancy centers), for example a semiconductor-based detector. Any conventional laser 51 and detector 53 used for such fluorescence measurements can be used.

Furthermore, the measuring devices include a microwave emitter 52 for manipulating the spin of the sample 54, for example the nitrogen vacancy centers. Instead of the microwave emitter 52 or in addition thereto, manipulation can also take place, for example, by means of a magnetic field that is generated with a corresponding magnetic field generating device (e.g. coils, permanent magnets, external magnetic field to be measured, etc.).

A control/evaluation device 50, hereinafter referred to as control device 50 for short, controls the laser 51 and the microwave emitter 52 and receives the signals from the detector 53. Apart from the use of information about the time-dependent course of the fluorescence described below, this control can and evaluating the signals obtained from the detector 53 in a conventional manner as in the conventional approach explained at the outset. The controller 50 can be implemented, for example, by means of a computing device such as a computer or a microcontroller that is programmed accordingly. However, it can also be implemented in other ways, for example using special hardware components such as application-specific integrated circuits (ASICs).

The use of information about the time course of the fluorescence is described below with reference to FIG 6 until 8th explained in more detail.

6 shows a flow chart of a method, as for example by means of the device 5 can be implemented.

While the method is presented as a sequence of steps, this is not meant to be limiting and, as will be explained in more detail below, some of the steps or acts illustrated may be performed concurrently, or one act may modify another act. Also, steps may be performed in a different order than shown.

In step 60 the spin-dependent fluorescence of a sample is measured. For example, as explained above, spins of the sample, for example from nitrogen vacancy centers, can be manipulated by means of microwave radiation and/or magnets and read out by means of laser radiation and a detector.

At 65 the measurement is evaluated. The term evaluation is to be understood in general terms and refers to any processing of the raw data supplied by a corresponding detector such as detector 53 . Such an evaluation can, for example, include an integration of the raw data. Furthermore, the evaluation can include determining the spin state of a sample, for example by comparing integrated data with one or more threshold values.

At 61, the measurement at 60 is modified to be performed using information about the time-dependent course of the spin-dependent fluorescence, and/or the evaluation of the measurement at 65 is modified to be performed using such information. Examples of the modification at 61 are given at 62-64. These various measures can be implemented in combination with one another or individually in various exemplary embodiments.

At 62, a measuring device used, for example the measuring device of 5 , calibrated on the basis of the information about the time-dependent course. For example, in conventional methods, as under 4 explained, the time window 40 at the beginning of the laser pulse 33 of 3 started. Depending on the setup, this can lead to a so-called timing jitter, for example due to runtime effects (e.g. if the actual start of the laser pulse does not coincide with a nomi nally beginning based on a control signal).

In exemplary embodiments, the information about the course over time can now indicate, for example, when the increase in the fluorescence signal actually begins, and the time window 40 can be started at this beginning. In other words, the actual increase indicates when the laser pulse actually begins, which can deviate from a time stored in a controller, for example due to runtime effects. Thus, the beginning of the time window 40 can be adjusted accordingly, which can reduce timing jitter.

At 63, the information about the time-dependent profile is used to infer the spin state. To make this clear, the 7 the fluorescence intensity over time, a curve 70 showing the intensity I for spin |0> and a curve 71 showing the intensity I for spin |+1> or spin |-1>. The curves essentially correspond to 7 the curves of 4 , where the curves of the 7 are shown without noise.

As in 7 As can be seen, the curve 70 first rises and then falls, while the curve 71 first rises, then falls and then rises again, ie has a minimum. From a minimum over time it can be concluded that the spin |+1> or |-1> is present or at least dominates to such an extent that a minimum occurs. This information can be used, for example, to check the plausibility of a conventional measurement.

If the conventional evaluation of a fluorescence signal by integration shows, for example, that a spin state |0> is present, but on the other hand the information about the time profile shows that a minimum is present, this can indicate an incorrect measurement. It can also be checked in this way whether fluorescence is actually measured from an expected defect center (e.g. nitrogen defect center). If a measured course of the fluorescence over time deviates greatly from typical courses for spin states, this can indicate an error in the measurement.

At 64, the measurement is weighted for evaluation. The integral over the measured fluorescence is not simply formed as in conventional methods or, in the case of gated detection, the integral over a specific time window (which can be seen as a simple weighting independent of the course over time, namely, for example, a weight +1 during the time window and a weight of 0 outside the time window), but the weighting function is chosen as a function of time. An example of how such a weighting function can be obtained is explained further below. Before this explanation, various options for obtaining the information about the course over time are discussed.

A first possibility is through calibration measurements by bringing the sample into known spin states and then measuring the time course of the fluorescence in each case. For example, when used as a magnetic field measuring device, a known magnetic field can first be used that polarizes the sample into a spin |0> or into a spin |+1> or |-1>, and then the time profile can be measured in each case . The measures mentioned above can then be carried out on the basis of these time curves if unknown spin states are measured later, e.g. to measure unknown magnetic fields. The advantage of this approach is that no precise knowledge of the dynamics of the sample, for example the nitrogen vacancy centers, is required. In addition, the measuring device can also be calibrated in another way during this measurement.

In other exemplary embodiments, the information about the course over time can be derived from previous knowledge about the respective sample, for example the respective defect center such as nitrogen vacancy center, for example from previously known decay rates, transition probabilities or the like for the various transitions of the 1 . This has the advantage that less measurement time is required.

These two approaches can also be combined. For example, some parameters of a system with measuring device and sample can be known with sufficient accuracy, for example transition probabilities/decay rates, while other parameters such as the power of a laser used or coupling efficiencies can vary greatly. For this approach, some data can be measured and then the open parameters can be fitted to the actual measurement data using a physical model.

Now an example for the determination of a weighting function (64 at 6 ) explained in detail on the basis of information about the course over time. In this case, the information about the time profile is the time profile of the fluorescence signals for spin |0> and spin |+1>, as shown in curves 70 and 71 of FIG 7 is shown. The fluorescence intensity versus time for spin |0> is hereinafter referred to as I _|0> (t) (corresponding to curve 70) and the intensity for the spin State |±1> is described with I _|±1> (t). t denotes the time.

For example, in a general sample, the spin of each defect center has a certain probability λ in the spin state |0> and correspondingly with the probability 1 - λ in the spin states |+1> or |-1>. The fluorescence signal over time I _Iλ> (t) is given by $$I_{\lambda }\left(t\right)=\lambda I_{|0>}\left(t\right)+\left(1-\lambda \right)I_{|\pm 1>}\left(t\right)$$

ist. Ein Schätzer ist dabei ein Funktional, mit dem die Intensität I über der Zeit so ausgewertet werden kann, dass der Spin-Zustand durch λ ausgedrückt, bestimmt werden kann. Ein Schätzer, der zu einem guten Signal-Rausch-Verhältnis SNR führt, hat zudem die Eigenschaft, dass seine Varianz Var[S(I)] klein ist, was bedeutet, dass mit hoher Zuverlässigkeit ein Wert bei oder nahe λ bestimmt wird.The goal now is to find an estimator S such that the expectation value of the estimator is $$E\left[S\left(I\right)\right]=\lambda$$

is. An estimator is a functional with which the intensity I can be evaluated over time in such a way that the spin state, expressed by λ, can be determined. An estimator that leads to a good signal-to-noise ratio SNR also has the property that its variance Var[S(I)] is small, which means that a value at or near λ is determined with high reliability.

For the exemplary embodiment discussed here, it is assumed that the estimator S is a linear functional. In other embodiments, non-linear functionals can also be used. In the case of a linear functional, the most general form of the estimator is given by $$S\left(I\left(t\right)\right)=O+{\displaystyle \underset{0}{\overset{\infty }{\int }}w\left(t\right)I\left(t\right)\mathrm{i.e}t}$$

where w(t) is the weighting function sought for the weighted measurement and o is a real number as an offset parameter. The above formula (3) essentially means that the integral of the intensity over time is not simply evaluated as in conventional approaches, but rather an integral over the weighted intensity over time is evaluated.

The measurement of the fluorescence signal will always be subject to noise. Assuming Poisson noise, the variance Var[l(t)] is proportional to the intensity I(t) of the measured signal.

At the same time, it can be assumed that the covariance Cov of the fluorescence signal between different points in time disappears, $$\text{cov}\left(I\left(t_1\right),I\left(t_2\right)\right)=0\text{f}\ddot{\text{and}}\text{<figure-callout id="1" label="right t" filenames="DE102020118699A1\_0021.png,DE102020118699A1\_0025.png" state="{{state}}">right</figure-callout>}{t}_{}{}_1\ne t_2$$

This assumption is valid for practically relevant measurements in a good approximation. It states that the probability of detecting a photon at time t ₁ is independent of the probability of detecting a photon at time t ₂ . There is the so-called anti-bunching effect, according to which a defect center cannot emit another photon immediately after emitting a photon. However, the influence of this effect is negligible for practically relevant measurements.

If only a single defect center is considered, 200,000 photons per second are detected in a good measurement setup. This corresponds to one photon per 5000 ns. Consequently, no more than one photon can be expected in each measurement run (in which fluorescence is measured for perhaps 200 ns). The measurement is therefore only useful and meaningful if it is averaged over many measurement runs. However, after the start of a new measurement process, the system forgets everything about the past (the spin is reinitialized again). As a result of this initialization, the correlations between the measurement runs disappear, i.e. the covariance between two measurement runs is 0.

In the case of ensembles with many defect centers, there is a significantly stronger signal, so that averaging over many measurement runs does not necessarily have to be carried out. However, this strong signal is due to the fact that many defect centers are measured simultaneously. In most cases, one can assume that fluorescence from two different defect centers is statistically independent of one another, which again corresponds to a covariance of 0.

In order to fulfill the condition stated in formula (2), the weighting function must fulfill the following property: $$S\left(I_{|\pm 1>}\left(t\right)\right)-S\left(I_{|0>}\left(t\right)\right)={\displaystyle \underset{0}{\overset{\infty }{\int }}w\left(t\right)\left[I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)\right]}\mathrm{i.e}t=1$$

Using formulas (3), (4) and (5), this results in the variance of the estimator $$\text{Var}\left[S\left(I\left(t\right)\right)\right]\sim {\displaystyle \underset{0}{\overset{\infty }{\int }}{w}^2\left(t\right)I\left(t\right)\mathrm{i.e}t}$$

$$\text{unter der Nebenbedingung}{\displaystyle \underset{0}{\overset{\infty }{\int }}w\left(t\right)\left[I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)\right]}dt=1$$

Consequently, the following optimization problem arises: $$\text{minimize}{\displaystyle \underset{0}{\overset{\infty }{\int }}{w}^2\left(t\right)I\left(t\right)\mathrm{i.e}t}$$

$$\text{under the condition}{\displaystyle \underset{0}{\overset{\infty }{\int }}w\left(t\right)\left[I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)\right]}\mathrm{i.e}t=1$$

To solve this problem, I(t) has to be determined. Since according to formula (4) Var(I(t))-I(t), I(t) can be used to model the ignorance about the system before making the measurement in terms of Bayesian statistics. In this specific case, ignorance about the system before the measurement is carried out means that the spin or λ is not known before the measurement.

One possible choice is to assume that the ignorance about the spin state is maximal, which means that 50% of the time the system is in the spin state |0> and the other 50% of the time it is in the spin state | ±1>. this leads to $$I\left(t\right)=\frac{I_{|\pm 1>}\left(t\right)+I_{|0>}\left(t\right)}{2}$$

If more is known about the measurement or the system, a weight other than 50% can also be selected here. Equation (9) gives the intensity I(t) assuming that each spin state exists with a probability of 50%.

kann man das Optimierungsproblem gemäß Formel (8) wie folgt schreiben minimiere (wlw), unter der Nebenbedingung $$\begin{array}{r}{}_{\text{minimiere}{\langle w|w\rangle }_I}\\ {\langle w|\frac{I_{|\pm 1>}-I_{|0>}}{I}\rangle }_I=1\end{array}$$

Using the scalar product <f ₁ |f ₂ > _| for two functions f ₁ (t)|f ₂ (t) according to $${〈{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="DE102020118699A1\_0021.png,DE102020118699A1\_0025.png"\; state="\{\{state\}\}">f</figure-callout>}}_1|f_2〉}_I:={\displaystyle \underset{0}{\overset{\infty }{\int }}{f}_1\left(t\right)f_2\left(t\right)I\left(t\right)\mathrm{i.e}t}$$

one can write the optimization problem according to formula (8) as minimize (wlw), under the constraint $$\begin{array}{r}{}_{\text{minimize}{〈w|w〉}_I}\\ {〈w|\frac{I_{|\pm 1>}-I_{|0>}}{I}〉}_I=1\end{array}$$

This optimization problem now has a simple geometric interpretation: the search for w(t) corresponds to the search for the shortest connection vector in the norm given by the scalar product according to formula (10) between the origin and a plane. The plane is described by the constraints and has the normal vector $$\frac{I_{|\pm 1>}-I_{|0>}}{I}$$

This means that the connection vector mentioned above must be parallel to the normal vector of the plane.

With appropriate normalization, the result for the weighting function w(t) is $$w\left(t\right)=\frac{I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)}{I_{|\pm 1}\left(t\right)+I_{|0>}\left(t\right)}\cdot {\left[{\displaystyle \underset{0}{\overset{\infty }{\int }}\frac{I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)}{I_{|\pm 1}\left(t\right)+I_{|0>}\left(t\right)}\mathrm{i.e}t}\right]}^{-1}$$

kann allgemein als Normierungsfaktor c angesehen werden.The factor $${\left[{\displaystyle \underset{0}{\overset{\infty }{\int }}\frac{I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)}{I_{|\pm 1}\left(t\right)+I_{|0>}\left(t\right)}\mathrm{i.e}t}\right]}^{-1}$$

can generally be regarded as the normalization factor c.

According to the formula (12), the weighting function w(t) can be determined if the time profile of I _|±1> (t) and I _|0> (t) is available as information about the time profile.

This then results in the signal-to-noise ratio SNR _w for this weighting function w(t) $${\left[SN{R}_w\right]}^2\sim {\left[{\displaystyle \underset{0}{\overset{\infty }{\int }}{w}^2\left(t\right)I\left(t\right)\mathrm{i.e}t}\right]}^{-1}$$

To illustrate the effect of using such a weighting function, a comparison is now made with a conventional gated detection approach. For this purpose, the fluorescence signals of the 7 used. On this basis, according to formula (12), the weighting function w _opt (t), a weighting function that corresponds to conventional gated detection and is referred to here as w _gated (t), is determined. The time window for gated detection is determined in such a way that the signal-to-noise ratio is maximized. The weighting function w _opt (t) is given in 8th represented by a curve 80, the weighting function w _gated (t) by a curve 81, i.e. the window here ranges from 0 to a little over 250 ns, after which the weighting function w _gated (t) assumes the value 0, i.e. the time window is over.

A comparison of the signal-to-noise ratios based on equation (13) results $$\frac{{\text{SNR}}_w^2{}_{{}_{\text{opt}}}}{{\text{SNR}}_w^2{}_{{}_{\text{gated}}}}=116.9\%$$

This means that the square of the signal-to-noise ratio with the weighting function based on the information over time is 17% higher than the best possible signal-to-noise ratio ² in conventional gated detection. This 17% corresponds to a signal improvement that would be possible with 17% additional measurement time or 17% improved detection efficiency. In addition, this improved signal processing is relatively easy to implement with software and does not require any special hardware, especially since most measuring devices anyway count photons with high time resolution.

The time profile of fluorescence signals I(t) depends on various parameters, including the laser power and thus the saturation parameter. 9 shows the expected signal improvement (improvement of SNR ² ) versus the saturation parameter. As can be seen, an improvement of 25% is possible for small laser powers and by 22%, but at least 14%, for high powers. Since it is difficult to increase detection efficiency through hardware improvements and measurement time is valuable, such increases are a great gain in practice.

As already mentioned, the techniques described above can be used in various applications in which a spin-dependent fluorescence is detected, for example in microscopes for research applications or sensors, for example for measuring magnetic fields. As already explained, the above embodiments only represent examples and are not to be construed as limiting. For example, by assuming other probabilities across the system or by using a non-linear functional as described above, other weighting functions can also be achieved that can be adapted to a particular application.

QUOTES INCLUDED IN DESCRIPTION

This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• DE 102019119213 [0002]
• EN 102019119212 [0002]

Claims (17)

Method for examining a sample (54), comprising: measuring a spin-dependent fluorescence from the sample (54), and evaluating the measurement of the spin-dependent fluorescence, wherein the measuring and/or the evaluating takes place using information about the time-dependent course of the spin-dependent fluorescence . procedure after claim 1 , where the information about the spin-dependent course is based on properties of fluorescence-emitting components of the sample. procedure after claim 1 or 2 , wherein the information about the time-dependent history is based on calibration measurements of the sample (54) in a first spin state and a second spin state different from the first spin state. Procedure according to one of Claims 1 until 3 , where the sample contains nitrogen vacancy centers in a diamond structure. Procedure according to one of Claims 1 until 4 , wherein carrying out the measurement using information about the time-dependent curve comprises calibrating a measuring device used for the measurement on the basis of the information. procedure after claim 5 , wherein the calibration of the measuring device comprises calibrating a start of an integration of a signal obtained during measurement relative to a start of a laser pulse (33) for exciting the sample (54) on the basis of a start of an increase in the spin-dependent fluorescence. Procedure according to one of Claims 1 until 6 , wherein evaluating the measurement using the information about the time-dependent course comprises obtaining information about a spin state of the sample (54) based on the information about the time-dependent course. Procedure according to one of Claims 1 until 7 , wherein the evaluating of the measurement using the information about the time-dependent curve comprises weighting the measurement with a weighting function which is based on the information about the time-dependent curve. Procedure according to one of Claims 1 until 8th , wherein the sample has one or more fluorescence centers, each fluorescence center being in a first spin state or in a second spin state, and wherein the weighting function is a function of a time-dependent course of a fluorescence intensity for the first spin state and a time-dependent course of the fluorescence intensity for the second spin state. procedure after claim 9 , where the weighting function w(t) is given by $$w\left(t\right)=c\frac{I_{|0>}\left(t\right)-I_{|\pm 1>}\left(t\right)}{I_{|0>}\left(t\right)+I_{|\pm 1}\left(t\right)}$$

Where I _|0> (t) is the time profile for the first spin state, I _|±1> (t) is the time profile for the second spin state and c is a normalization factor. procedure after claim 10 , where the normalization factor c is $${\left[{\displaystyle \underset{0}{\overset{\infty }{\int }}\frac{I_{|\pm 1>}\left(t\right)-I_{|0>}\left(t\right)}{I_{|\pm 1}\left(t\right)+I_{|0>}\left(t\right)}\mathrm{i.e}t}\right]}^{-1}$$

given is. Procedure according to one of Claims 1 until 11 , wherein the sample has one or more fluorescence centers, each fluorescence center being in a first spin state or in a second spin state, and wherein information about the time-dependent course includes a time-dependent course of a fluorescence intensity for the first spin state and a time-dependent course of the fluorescence intensity for the second spin state. Measuring device for examining a sample (54), comprising: a detector (53) for measuring a spin-dependent fluorescence from the sample (54), and a control/evaluation device (50) for controlling the measurement of the spin-dependent fluorescence and for evaluating the measurement, the device being set up to carry out the measurement and/or the evaluation of the measurement using information about the time-dependent course of the spin-dependent fluorescence. device after Claim 13 , further comprising a light source (51) for exciting the sample (54). device after Claim 13 or 14 , further comprising a microwave emitter (52) and/or a magnetic field device for manipulating a spin state of the sample (54). Device according to one of Claims 13 until 15 , wherein the device for carrying out the Procedure according to one of Claims 1 until 12 is set up. Computer program with a program code that, when executed on a computing device, causes the evaluation of the measurement using the information about the time-dependent curve according to the method according to one of Claims 1 - 12 is carried out.

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