Method and apparatus for analysing a measurement signal emitted by a spin-based quantum system

Abstract

The invention relates to a method and an apparatus for evaluating a measurement signal (5') emitted by a spin-based quantum system (4), comprising: exciting the spin-based quantum system (4) by means of pulsed excitation light (13; 220); alternately subjecting the spin-based quantum system (4) to a first and a second magnetic field pulse sequence (211; 212), wherein one of the first and second magnetic field pulse sequences (211; 212) comprises two π-pulses, and the other of the first and second magnetic field pulse sequences (211; 212) comprises one π-pulse and one π / 2-pulse; detecting the measurement signal (5') emitted by the spin-based quantum system (4); integrating the measurement signal (5') over an integration window (231) which includes a signal time of a light pulse (222) of the pulsed excitation light (13; 320) between the first magnetic field pulse sequence (211) and the second magnetic field pulse sequence (212) and between the second magnetic field pulse sequence (212) and the first magnetic field pulse sequence (211), in order to obtain a first and a second signal value; and determining a measurement value from the first and the second signal value.

Description

[0001]R.410057 Description Title Method and apparatus for evaluating a measurement signal emanating from a spin-based quantum system. The present invention relates to a method and an apparatus for evaluating a measurement signal emanating from a spin-based quantum system. Background of the invention To measure very small magnetic field strengths, quantum-based or optically pumped magnetometers are particularly suitable as sensors. Such magnetometers often utilize optically pumped and optically detected magnetic resonances (ODMR). This exploits the fact that, under the influence of an external magnetic field, the energy levels of certain spin states of unpaired electrons split, the so-called Zeeman effect.The splitting of energy levels results in altered relaxation transitions from excited states, which can then be measured, for example, by optical excitation and frequency-dependent detection of the resulting fluorescence radiation or by observing optical properties such as light absorption. The magnetic field strength can then be deduced from the measured optical parameters. Sensor crystals with excitable defect centers can be used for such quantum-based magnetic field sensors. Typically, diamonds are used that are homogeneously covered with negative nitrogen vacancy centers (NV-R.410057-). 2 -The preparation of the quantum state is achieved via optical excitation and interaction with a static magnetic field and a dynamic magnetic field, i.e., a microwave field. For measuring very small magnetic field strengths, quantum-based magnetic sensors based on nitrogen vacancy centers are known, for example, from DE 102018220234 A1 or DE 102018214617 A1. In this process, the information stored in the spin system is read out optically by detecting the spin-state-dependent fluorescence rates of the NV center. Therefore, the accuracy is limited, among other things, by the signal-to-noise ratio of the optical readout method of the NV center. A measurement method that can be used in this context is based on quantum mechanical superposition states. A typical protocol is, for example, Free induction decay (FID, also called Ramsey protocol) or the Hahn echo.In this process, a quantum mechanical superposition state is generated using a microwave pulse, which is then freely evolved for one evolutionary time. The state oscillates around an existing magnetic field at its natural frequency (Lamor frequency), and the phase between this oscillation and the microwave, which provides information about the magnetic field, is measured at the end. A typical pulse train (FID) is... − ^ − ^. A laser pulse first initializes a spin state |ms = 0>. The first ^ ^-pulse prepares the superposition state 1 / √2 (|ms = 0> + |ms = ±1>). Subsequently, a temporal development ^ takes place, in which a phase is collected due to the frequency difference between the laser precision and the microwave. This ^ phase difference is then transferred with the last ^-pulse into a population difference, which can then be read out. A ^ ^ ^-pulse is a microwave pulse that rotates the Bloch vector in the Bloch sphere by ^ = 90° around an axis the y-axis. R.410057 -3 - For such pulsed measurement protocols in quantum sensors, the contrast of a measurement can be increased by inverting the measured signal in a second measurement. This can be achieved by extending the second pulse by a half-rotation (→). Since the difference between the signals can now be calculated, this is one way to double the contrast. However, the fidelity of the signal is - und desThe pulses differ, meaning the additional rotation by ^ reduces the achievable contrast in the measurement signal, making a direct comparison of the measurement signals difficult and reducing the performance gain. Extending the second ^^ pulse to ^ leads to a lengthening of the measurement sequence and thus to a deterioration of sensitivity. Furthermore, the different lengths of the measurement sequences either create additional dead time (if the lengths of the measurement sequences are matched) or the different duty cycles can lead to problems in the signal output as well as instabilities in the hardware (e.g., different laser behavior in the individual measurement sequences due to different thermal equilibrium being established).Disclosure of the Invention: According to the invention, a method and a device for evaluating a measurement signal emanating from a spin-based quantum system are proposed, comprising the features of the independent claims. Advantageous embodiments are the subject of the dependent claims and the following description. In detail, excitation of the spin-based quantum system by pulsed excitation light comprises alternately exposing the spin-based quantum system to a first and a second series of magnetic field pulses, wherein one of the first and second series of magnetic field pulses contains two pulses and the other contains a pulse and a second series of magnetic field pulses. 4 -^ contains. The − ^-pulse in the Bloch sphere rotates the Bloch vector by ^ − ^= −90° around the y-axis, thereby transforming the x-component of the Bloch vector into the -z-component and vice versa; the y-component remains unchanged. The magnetic field pulses are pulses of a magnetic field oscillation. Typical frequency values ​​of such oscillations, which are used to excite spin-based quantum systems, lie in the high-frequency range. The abbreviation "HF" is also used for the term "high frequency" in the following. The frequency of the high-frequency field (HF field) depends on the quantum system to be excited, i.e., on the energy difference (which corresponds to a frequency) between the quantum mechanical states of the quantum system between which transitions are to be induced. Typical frequencies can lie in the microwave range, e.g., between 300 MHz and 300 GHz or between 300 MHz and 1 THz. The quantum system can, for example,An NV center in a diamond, where the ground state is a triplet in which (without an external magnetic field) there is an energy difference corresponding to 2.87 GHz between spin 0 (|ms = 0>) on the one hand and spin +1 or -1 (|ms = ±1>) on the other. Such NV centers in diamonds can be used, for example, as quantum sensors.The method further comprises acquiring the measurement signal emanating from the spin-based quantum system, integrating the measurement signal over an integration window containing a signal time of a light pulse of the pulsed excitation light between the exposure of the spin-based quantum system of the first magnetic field pulse sequence and the exposure of the spin-based quantum system of the second magnetic field pulse sequence to obtain a first signal value, and integrating the measurement signal over an integration window containing a signal time of a light pulse of the pulsed excitation light between the exposure of the spin-based quantum system of the second magnetic field pulse sequence and the exposure of the spin-based quantum system of the first magnetic field pulse sequence to obtain an R.410057 -. 5 -to obtain a second signal value. In other words, a signal value is obtained after each magnetic field pulse sequence and before the next magnetic field pulse sequence. Finally, a measured value is determined from the first and second signal values. The invention makes it possible to reduce the disadvantages described above for differential measurements with two magnetic field pulse sequences. With a negative pulse, i.e., a rotation operation with the opposite sign, the same effect as with a positive pulse can be achieved, but with the same quality. By replacing the second pulse of the first pulse in one of the two magnetic field pulse sequences with a negative pulse, an extension of the measurement sequence and thus a deterioration of the sensitivity is avoided. Furthermore, the first and second magnetic field pulse sequences have the same length. There is no difference in the length of the measurement sequences.This prevents problems with the operating cycle, such as fluctuations in the light source due to varying cool-down times. The overall sequence length is minimized because no additional time is required for inversion (typically, a ^-pulse is three times longer than a ^-pulse). Each measurement step has the same length, enabling constant-frequency data output without additional pauses. Due to the identical pulse length, the quality factor of the inverted pulse is identical to that of the ^-pulse, allowing for simple subtraction of the numbers without an offset. Furthermore, a ^-pulse generally has a higher quality factor than longer pulses because inhomogeneities in the external magnetic field (background field) and the magnetic field pulse lead to an exponential decrease in quality factor with longer pulse durations.^ In embodiments of the invention, the − ^-pulse is generated with a phase shift of the magnetic field oscillation by an angle ∆φ to the ^ ^-pulse, wherein ∆φ = 180° or wherein ∆φ depends on the R.410057 -. 6 - The measured value is specified, in particular such that the measured value or the contrast is maximized. In the Bloch sphere diagram, the phase shift changes the axis around which the Bloch vector is rotated. Assuming that a -Puls den If the Bloch vector rotates by 90° around the y-axis, then a pulse shifted by 180° (notation chosen here: ^^^^° pulse) rotates the Bloch vector around the -y-axis. Furthermore, for example, a -Puls den ^ ^ ^^°The Bloch vector around the x-axis and a 180° pulse rotate the Bloch vector around the x-axis. A phase shift of 180° is technically easy to implement and essentially corresponds to the phase shift required to generate an opposite direction of rotation in the Bloch sphere. On the other hand, to always generate the maximum sensitivity of the measurement signal, the phase of the 180° pulse can be adjusted more finely to always be within the range of maximum sensitivity. This allows the determination of the magnetic field-induced frequency shift, and thus of the magnetic field itself, not only by adjusting the microwave frequency but also by adjusting the phase relationship of the measurement pulses (feedback loop). This has the advantage that the microwave frequency resolution can be chosen to be coarser, which offers advantages in terms of costs (cheaper components) as well as development / application (fewer microwave fields need to be calibrated).(has a lower calibration error of the microwave intensity). Advantageously, a ^ ^ pulse and / or a −^ ^ is used. -Puls das The spin-based quantum system switches between two spin states selected from a state |ms = 0>, a state |ms = ±1>, and a superposition state 1 / √2 (|ms = 0> + |ms = ±1>).^ In embodiments of the invention, the − ^-pulse is generated using a phase shifter as a discrete component, a switch network, R.410057 - 7 -Individual phase paths (one fixed phase per path) are selected via switches or generated by direct synthesis of the RF pulses (or by mixing a synthesized signal with an RF source in an (IQ) mixer network, where the phase of the pulses is set directly during synthesis). In embodiments of the invention, the pulse is generated using a setup with a high-frequency source and one or more mixers (in particular so-called IQ mixers, in-phase and quadrature), which modulate a modulation frequency onto the signal of the high-frequency source. By changing the phase of the modulation frequency, the phase of the generated signal can ultimately be adjusted. In embodiments of the invention, a measured value is determined from the first and second signal values ​​by forming a quotient of the difference between the first and second signal values ​​and the sum of the first and second signal values.This allows for increased contrast. For example, this results in the following calculation formula: ^^^^^^^^^^^^^^^^^^^ = 2 (^^^^^^+ − ^^^^^^−) / (^^^^^^+ + ^^^^^^−) where ^^^^^^^^^^^^^^^^^^^: measured value ^^^^^^+, ^^^^^^-: first and second signal values. Furthermore, normalization to the sum of the first and second signal values ​​compensates for fluctuations in the signal value, leading to increased robustness against fluctuations in the excitation power density. This increases the robustness of the system and allows a sensitivity of the sensor system comparable to a system with two photodiodes, which achieves such fluctuations by balancing the photodiode signal, without requiring such a balancing circuit. R.410057 -. 8 -Further advantages and embodiments of the invention will become apparent from the description and the accompanying drawing. The invention is schematically illustrated in the drawing with reference to exemplary embodiments and is described below with reference to the drawing. Brief description of the drawings: Figure 1 schematically shows a device for generating a measurement signal from a signal emanating from a spin-based quantum system according to an embodiment of the invention in a block diagram. Figure 2 shows a sequence for a pulsed ODMR measurement according to an embodiment of the invention. Embodiment(s) of the invention: Figure 1 schematically shows a device 100 for evaluating a measurement signal 5' emanating from a spin-based quantum system 4 according to an embodiment of the invention in a block diagram.The device 100 comprises an excitation light generation device 12 for generating pulsed excitation light 13 and a field generation device 2 for generating a magnetic field 3, and the spin-based quantum system 4, which is to be excited by the excitation light 13 and the magnetic field. In embodiments, the spin-based quantum system 4 can comprise a sensor crystal with color centers, in particular a diamond with nitrogen-defect centers. Other types of spin-based quantum systems can also be advantageously used within the scope of the invention. R.410057 -. 9 -The field generation device 2 is configured to generate a magnetic field 3, in particular a high-frequency field (HF field), and more specifically a microwave field with a desired frequency and pulse length. The device 100 further comprises a measuring device 6 for detecting the measurement signal 5' emanating from the spin-based quantum system 4 in order to obtain a raw signal 7, which is transmitted to a computing unit 8. In certain embodiments, the measurement signal 5' emanating from the spin-based quantum system 4 is a fluorescence signal or light signal. Accordingly, the measuring device 6 can, for example, comprise one or more photodiodes or a photodiode measurement arrangement. The computing unit 8 is configured to evaluate the raw signal 7 and control the field generation device 2. An exemplary measurement process is illustrated in Figure 2. Figure 2 shows...2 a profile 210 of the microwave field 3, a profile 220 of the excitation light 13, and a profile 230 of integration windows. Pulsed ODMR experiments conventionally include an initial light pulse (especially a laser pulse) 221 for spin polarization (especially in the state |ms = 0>), a magnetic field pulse sequence 211 for spin manipulation, and a light pulse (especially a laser pulse) 222 for spin readout via the fluorescence intensity (readout pulse). The fluorescence (photon number n) for NV centers in diamonds is time-dependent and different for the spin states |ms = 0> (so-called bright state) and |m = ±1> (so-called dark state). For longer illumination (t > 500 ns), both curves show the same steady-state intensity, which is determined by the ratios of the different transition rates of the intercombination and can conventionally be used to determine a reference value. R.410057 -. 10 -If the initial state is |ms = 0>, a higher photoluminescence intensity is initially observed, which then drops to the intensity of the steady state because a portion of the population is trapped in the metastable singlet state due to remaining intercombination. For an initial state |ms = ±1>, the intensity rapidly drops to a low level due to rapid intercombination into the singlet state. Since the singlet state preferentially decays to the ground state |ms = 0>, the intensity recovers towards the steady-state value within the lifetime of the metastable state (∼ 250 ns). The difference between the two curves, or a normalized difference, can be conveniently used to read out the spin state. To determine such a difference, a measurement with |ms = 0> and a measurement with |ms = ±1> are necessary.These measurements are made possible in embodiments of the invention by different magnetic field pulse sequences 211 and 212, wherein a first (here 211) of the first and second magnetic field pulse sequences contains a first pulse, a magnetic field to be measured that is present during a time evolution, and a second pulse, and the other (here 212) of the first and second magnetic field pulse sequences contains the pulse, the magnetic field to be measured that is present during the time evolution, and the negative pulse. In the image of the Bloch sphere in the rotating frame approximation, the time evolution causes the coherent superposition state to perform a rotation in the equatorial plane, wherein the angle of the rotation corresponds to the time integral between 0 and τ of the product of detuning Δν and time t.The detuning Δν is here the frequency difference between the frequency of the applied microwave field νMW and the resonance frequency ν0→1 for the transition from bright state |ms = 0> to dark state |ms = ±1>.Δ^ = ^^→^ − ^^^ R.410057 -. 11 -This frequency is determined by the Zeman effect through the applied magnetic field. The last pulse of each of the different magnetic field pulse sequences flips the spin state either to |ms = 0> or to |ms = ±1>, so that both states can be measured alternately and combined to obtain measured values. For evaluation, the measurement signal can be integrated using an integration window 231 containing a signal time point of a light pulse to obtain a signal value, and using an integration window 232 containing a reference time point of the light pulse to obtain a reference value. To read out the spin state at the end of the sequence with high accuracy, it is crucial to detect the first fluorescence photons after the laser is switched on, before the NV center is repolarized to |ms = 0>.Furthermore, it is specifically provided that the integration window containing the reference time of the light pulse of a previous measurement simultaneously represents the integration window containing the signal time of a light pulse of the subsequent measurement. In other words, for a continuous output of measured values, the measured value at time (N+1) can be formed from the signal value at time (N+1) and the signal value at time (N) with continuously changing signs. The following calculation formula results: ^^^^^^^^^^^^^^^^^^^^(^+1) = [(−1)^ ^^^^^^^ + (−1)^+1 ^^^^^^^+1] / (^^^^^^^ + ^^^^^^^+1) where: ^^^^^^^^^^^^^^^^^^^(^+1): Measured value at time N+1^^^^^^^+1: Signal value or reference value at time N+1^^^^^^^: Signal value or reference value at time N R.410057 -. 12 -This allows for a higher bandwidth of measurement data to be provided. Furthermore, the sensitivity of the sensor is improved by a factor of up to √2 (square root of 2). Normalization to (^^^^^^^ + ^^^^^^^+1) is optional and can also be omitted. The frequency shift caused by the magnetic field, and thus the magnetic field, can be determined not only by adjusting the microwave frequency, but also by adjusting the phase relationship between the ^-pulse and the −^-pulse. By phase-adjusting the −^-pulse, any desired phase can be sensitively read out. Here, it is advantageous to adjust the rotation axis in the Bloch sphere for the rotation caused by the −^-pulse so that it is shifted by 90° + ∆φ relative to the first ^-pulse to ensure maximum sensitivity to phase changes. This has the additional advantage that the differential signal (^^^^^^^^^^^^^^^^^^^(^+1)) reflects a change in phase sign, i.e.In the differential measurement scheme, the measurement signal is 0 when the phase is exactly compensated (difference between two single measurement pulses and one −^ ssungen with one each). ^ ^^°^^^ ^ ^^°^^^ -pulse, if the phase shift corresponds to ∆φ). This is a measurement using differential calculation. From the difference, a deviation of the phase in the measurement from the specified phase φ can be calculated. This then allows the adjustment of the specified phase φ of the last pulse. A deviation of the phase generates a sign-preserving deviation in the measurement signal and can thus be used as a feedback input for control and tracking of the resonant frequency. A typical measurement can proceed as follows: • Measurement of the differential measurement signal with phase φ R.410057 - 13 -• Adjustment of the phase φ+90° of the readout pulse to compensate for the zero deviation of the differential signal by a factor: φNew = φold+k*SignalDiff. • Only for large frequency deviations (reduction of pulse performance due to excessive frequency difference between microwave and resonance) does the microwave frequency need to be readjusted. The 90° phase shift is required to maximize the change in the measurement signal due to a phase change (the phase from the detuning is translated into the measurement signal using -cos(), which is why a 90° phase shift of every second π / 2 pulse is advantageous, as a change in detuning then leads to a maximum signal change at this operating point). The second π / 2 pulse in every second individual measurement (S(N+1)) is additionally phase-shifted by 180° (corresponding to a negative sign) to minimize the influence of detuning on the measured individual signal. invert.It is also possible to create a coherent state between |ms = +1> and |ms = -1> (double quantum state (DQ)). This has several advantages. However, the method mentioned above can also be applied to such coherences. E A typical pulse sequence in this context is: ^ –^ – ^ ^°^^ ^ ^^^ The first pulse generates the DQ (|ms = 0> → |ms = +1> + |ms = -1>). Subsequently, a temporal evolution ^ occurs, during which a phase is collected. This phase difference is then transferred to the |ms = 0> state with the last pulse, which can then be read out. Here, the phase of the second pulse can be adjusted for both the differential measurement scheme and phase tracking. Typical implementations of such ^ pulses include: R.410057 - 14 -- Composite pulses (π / 2 pulse on one transition (e.g., |ms = 0> → |ms = +1> and a π pulse on the other transition (e.g., |ms = 0> → |ms = -1>)). - Simultaneous and equal driving of both transitions

Claims

R.410057 - 15 -Claims 1. Method for evaluating a measurement signal (5') emanating from a spin-based quantum system (4), comprising the steps: Exciting the spin-based quantum system (4) by a pulsed excitation light (13; 220), alternately exposing the spin-based quantum system (4) to a first and a second magnetic field pulse sequence (211; 212), wherein one of the first and second magnetic field pulse sequences (211; 212) contains two ^ ^-pulses, and the other of the first and second magnetic field pulse sequences (211; 212) contains one ^-pulse and one −^ ^ ^-pulse, acquiring the measurement signal (5') emanating from the spin-based quantum system (4), integrating the measurement signal (5') via an integration window (231) containing a signal time of a light pulse (222) of the pulsed excitation light (13;320) between the exposure of the spin-based quantum system (4) of the first magnetic field pulse sequence (211) and the exposure of the spin-based quantum system (4) of the second magnetic field pulse sequence (212) to obtain a first signal value, integrating the measurement signal (5') over an integration window (232) containing a signal time of a light pulse (222) of the pulsed excitation light (13; 320) between the exposure of the spin-based quantum system (4) of the second magnetic field pulse sequence (212) and the exposure of the spin-based quantum system (4) of the first magnetic field pulse sequence (211) to obtain a second signal value, determining a measured value from the first and the second signal value.

2. Method according to claim 1, wherein the -^ ^-pulse is generated with a^ phase shift of 180° to the ^-pulse.; R.410057 - 16 -3. A method according to claim 1, wherein the -^ ^-pulse is generated with a ^ phase shift relative to the ^-pulse that depends on the determined measurement value.

4. A method according to any of the preceding claims, wherein the −^ ^-pulse is generated using a phase shifter or a switch network that switches off individual phase paths via switches.

5. A method according to any of the preceding claims, wherein the −^ ^-pulse is generated by changing a phase of a modulation frequency, the ^-pulse, and the −^ is modulated onto the ^ ^-pulse.

6. A method according to any of the preceding claims, wherein the pin-based quantum system (4) comprises a sensor crystal with color centers, in particular a diamond with nitrogen-vacancy centers.

7. A method according to any of the preceding claims, wherein the magnetic field of the first and second magnetic field pulse sequence is a microwave field. 8.A method according to any one of the preceding claims, wherein the measurement signal (5') emanating from the spin-based quantum system (4) is a fluorescence signal or a light signal.

9. A method according to any one of the preceding claims, wherein determining a measured value from the first and the second signal value comprises: forming a quotient of a difference between the first and the second signal value and a sum of the first and the second signal value.

10. A device (100) for evaluating a measurement signal (5') emanating from a spin-based quantum system (4), comprising: R.410057 - 17 -the spin-based quantum system (4), an excitation light generation device (12) for generating pulsed excitation light (13; 320), a field generation device (2) for generating a magnetic field (3; 310), wherein the spin-based quantum system (4) is arranged in the magnetic field (3; 310), a measuring device (6) for detecting the measurement signal (5') emanating from the spin-based quantum system (4), wherein the device (100) is configured to carry out a method according to one of the preceding claims.

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