Heralded initialization of charge state and optical transition frequency of diamond tin-vacancy centers

Diamond Tin-Vacancy centers have emerged as a promising platform for quantum information science and technology. A key challenge for their use in more complex quantum experiments and scalable applications is the ability to prepare the center in the desired charge state with the optical transition at a pre-defined frequency. Here we report on heralding such successful preparation using a combination of laser excitation, photon detection, and real-time logic. We first show that fluorescence photon counts collected during an optimized resonant probe pulse strongly correlate with the subsequent charge state and optical transition frequency, enabling real-time heralding of the desired state through threshold photon counting. We then implement and apply this heralding technique to photoluminescence excitation measurements, coherent optical driving, and an optical Ramsey experiment, finding strongly improved optical coherence with increasing threshold. Finally, we demonstrate that the prepared optical frequency follows the probe laser across the inhomogeneous linewidth, enabling tuning of the transition frequency over multiple homogeneous linewidths.


I. INTRODUCTION
In the past decade, color centers in diamond have become a leading platform for quantum networking experiments [1][2][3].The first demonstrations relied on the Nitrogen-Vacancy (NV) center, ranging from the first loophole-free Bell test [4] to a multi-node network experiments [5,6].However, the NV center suffers from a low Debye-Waller factor and strong spectral diffusion close to surfaces, making its optical interface inefficient.Group-IV vacancy centers emerged as a favourable alternative due to their high Debye-Waller factor [2,7,8] and inversion symmetry [9], resulting in first-order insensitivity to charge noise [10] and thus compatibility with nanophotonics integration [11,12].Pioneering experiments showing basic network node operation in a dilution refrigerator have been performed using the silicon-vacancy (SiV) center in nanophotonic devices [13][14][15].More recently, the negatively charged Tin-Vacancy (SnV − ) center in diamond has attracted significant interest thanks to a high quantum efficiency [7,11,16] and significant spin-orbit coupling, which allows for operation at elevated temperatures compared to the SiV center [7,17,18].In recent experiments, the integration of SnV centers into nanophotonic devices [19][20][21][22] and coherent SnV spin qubit control have been demonstrated [23,24].
The optical transition frequency of the SnV − after the repump is in general not the same as before (spectral diffusion), possibly caused by the capture or release of nearby charges in the repump process or by the direct impact of the pump excitation on the charge environment [25].These processes pose two challenges for future use in quantum protocols: i) the charge state repump is probabilistic, leading to initialization errors, and ii) spectral diffusion hinders efficient optical spin initialization and readout and causes reduced photon indistinguishability, which negatively impacts key protocols requiring photon interference such as remote entanglement generation [26].In this work, we overcome these challenges by realizing heralded initialization into the desired charge state and pre-set the optical transition frequency.

II. EXPERIMENTAL SETUP
A simplified level structure of the SnV center in the negative charge state (SnV − ) is shown in Fig. 1(a).In the absence of a magnetic field, the ground and optically excited states consist of spin-degenerate orbital doublets, leading to four optical transitions.Of main interest for a spin-photon interface is the Zero-Phonon Line (ZPL) transition at 619 nm, linking the lowest-branch ground and optically excited state.Besides the ZPL path, photon emission can be accompanied by the excitation of vibronic modes (phonon-side band emission, PSB).
Our main investigation focuses on an SnV − center (labeled SnV − A) in an IIa <111>-oriented diamond, where Sn-ions are implanted ∼1 nm below the surface.Subsequently, overgrowth of the diamond by chemical vapor deposition [27] results in SnV − centers ∼550 nm below the surface.All experiments on SnV − A are performed in an optical confocal set-up at 4 K (see Supplemental Material [28] for experimental set-up details, which includes [29,30]).Fig. 1(b) shows the second-order correlation function, g (2) , of the PSB emission of the SnV − center under continuous resonant excitation.We find g (2) (0) = 0.10 ± 0.02 without any background subtraction showing that the light indeed originates from an individual emitter.

III. DYNAMICS OF CHARGE STATE AND RESONANCE FREQUENCY
We investigate the SnV − center by performing photoluminescence excitation (PLE) scans, where a resonant laser of 3 nW is scanned at ∼1.3 GHz/s over the optical transition while recording the PSB emission.In this experiment a conditional repump is used: we apply a repump pulse in case the peak photon counts detected during the PLE is below a pre-set threshold, see pulse sequence in Fig. 1(c).
Fig. 1(d) shows 1000 consecutive resonant scans.We identify three different regimes, that we label by color on the right for a subset of scans.Red indicates that the optical transition is found near zero detuning ('on resonance') and the photon count threshold is met.
This condition constitutes the desired state.Green indicates scans with counts below the threshold, indicating the emitter has gone into the dark state.A 515 nm repump pulse of 50 ms and 1 µW is applied prior to the following scan.It can be seen that the repump pulse indeed brings the emitter back to the bright SnV −charge state with good probability, often accompanied by a shift of the resonant frequency of the emitter.We highlight scans with orange in which the threshold of counts is met, but the detected resonance is significantly detuned, >100 MHz ('off resonance').Importantly, we find that the SnV − exhibits high spectral stability both in the on-resonance and off-resonance conditions, up to the point that ionization occurs.

IV. PROBE PULSES FOR CHARGE STATE AND RESONANCE CONDITION DETECTION
Motivated by the observed spectral stability before ionization, we explore the possibility of using photon counts during a resonant probe pulse as a heralding signal for the successful preparation of the SnV center in the negative charge state with its optical transition at a desired frequency.To gain quantitative insights into the predicting capabilities of such heralding signal, we implement the pulse sequence shown in Fig. 2(a).A 515 nm 'repump' pulse is followed by two identical resonant laser pulses, named here 'Pulse 1' and 'Pulse 2'.The sequence in Fig. 2 (cos(ωτ) + 3γ 4ω sin(ωτ)), obtaining a g (2) (0) = 0.10 ± 0.02, without background correction.(c) Pulse sequence for the conditional PLE measurements, where we apply a repump pulse in case the maximum number of photon counts detected during a single frequency step is less than 1.5 times the mean number of photons detected.(d) The fluorescence of 1000 PLE scans taken in ∼1.3 GHz/s over the optical transition.The state of the emitter is estimated from the counts detected during each scan.If the emitter is flagged as dark, an off-resonant 515 nm pulse is applied before the following scan.
In Fig. 2(b) we plot in log-scale the distributions of the photons detected during Pulse 2, C 2 , as a function of the number of photons detected during the preceding Pulse 1, C 1 , for three different resonant laser powers.For the lowest power (top panel), we find an almost perfect correlation between C 1 and C 2 .This observation implies that the number of photons scattered by the SnV − center during these pulses is dictated by their charge state and their instantaneous detuning from the laser frequency.By increasing the resonant laser power (middle and lower panel), we observe a change in the distribution of photon counts.As expected, the mean number of photon counts is increased.In addition, while the correlation between C 1 and C 2 is still present, we can see the effect of ionization, resulting in vertical and horizontal regions of uncorrelated photon distributions.The vertical band is due to ionization during Pulse 2 after several photons have already been detected.The horizontal band mainly corresponds to cases where ionization occurred during Pulse 1; those cases could lead to an incorrect heralding signal and should thus be minimized.
Having confirmed that the probe signal strongly correlates to the state of the SnV − center after the probe, we now use this to condition our data set to cases where the SnV − is on resonance with the probe laser (i.e. a high number of photon counts in the detection window).As shown in Fig. 2(c), if we condition on C 1 > 100, the photon count distribution of Pulse 2 follows a Poisson distribution centered around 110 counts, while the reverse conditioning shows a broader, lower-counts distribution mixed with a peak near zero counts.The thresholding approach demonstrated here allows to filter the desired bright state condition of the color center out of the statistical distribution of possible charge-resonance states.Tighter thresholding can be done at the expense of a decrease in efficiency, as shown in Fig. 2(d).For instance, for the threshold value of 100 used above, we observe a success probability of passing the threshold of 33%.
Similarly to the analysis above, we study the effect of the repump laser (see pulse sequence in Fig. 2(e)) by plotting the number of photons detected during Pulse 4, C 4 , as a function of the number of photons detected in the probe pulse (C 3 ) preceding a pump pulse, see Fig. 2(f).For weak repump pulses (top panel), some correlation between the probe and pump signals is visible, as the repump in this case does not significantly affect the SnV center and its environment.For sufficiently strong repump pulses (middle and lower panel), no correlations are observed, showing that the state following the repump pulse is independent of the state before the repump.This is confirmed by the histograms shown in Fig. 2(f), where we plot the counts distribution of C 4 of the data of the middle panel of Fig. 2(f) for the 2 shaded areas.We see that the distributions are similar for low and high counts detected in Pulse 3.
Using again the data of the middle panel of Fig. 2(g), we estimate how efficiently the repump re-initializes the SnV − in the negative charge state if it was in the dark state before.For this, we set a threshold of 20 counts to distinguish between the desired charge state and the dark state.Conditioning on a dark state being detected on Pulse 3, the probability of detecting a bright state on Pulse 4 reaches about 75%.

V. OPTICAL RABI DRIVING
Next, we investigate the correlation between probe pulse counts and the SnV − optical coherence.We apply the pulse sequence as shown in Fig. 3(a), where the repump and probe pulse are now followed by 500 repetitions of a 30 ns resonant pulse used to drive optical Rabi oscillations.Fig. 3(b) shows a histogram of the number of photons detected during the probe pulse, where 3 peaks are present.We allocate the instances of high detected photon counts (rightmost peak) to the emitter being in the 'on resonance' state.The instances of the middle and left peak instead correspond respectively to the 'off-resonant' and 'dark' cases.Based on this, we divide the histogram into four parts, as highlighted by the shaded background colors of Fig. 3(b) corresponding to the 3 peaks described above plus an intermediate region between the center and rightmost peak.Fig. 3(c) shows time traces of the detected photons during the 30 ns resonant readout pulse conditioned on the four threshold intervals.Each curve reveals coherent driven oscillations with different amplitude, frequency, and decay times.As expected, by thresholding for higher probe counts we obtain higher count rates in the readout, as we are selecting for cases where the SnV − is on resonance with the driving laser.By fitting these curves with an exponentially damped sine function we extract the Rabi frequency and decay time of the oscillations.These values are summarized in Fig. 3(d), showing that the fitted decay time (frequency) increases (decreases), consistent with the SnV − being closer to resonance for an increasing number of detected photons in the probe pulse.These results demonstrate a clear relation between the probe counts and the measured coherence.

VI. REAL-TIME HERALDING OF CHARGE STATE AND OPTICAL TRANSITION FREQUENCY
In the experiments so far, the conditioning on probe pulse counts was done in post-selection.For scalable applications in quantum protocols, it is key that the selection is done in real-time i.e. before quantum protocols are run [5,6,31,32].In the following, we implement live thresholding on the probe counts using the programmable logic of a fast microcontroller (running on a 10 µs clock cycle, see Supplemental Material [28]) and use this as a charge resonance check (CRC) routine to herald the desired charge-resonance state before each experimental run.
The CRC sequence (see Fig. 4(a)) starts with a resonant probe pulse and live counting.Below we report on an implementation using two threshold values instead of just one, which allows more freedom in trading off heralding efficiency (rate) and accuracy.In the case that the number of counts detected during the resonant probe pulse is below C repump , an off-resonant 515 nm repump pulse is applied, followed by a resonant probe pulse.In case the counts detected during the probe pulse are above C repump but below C pass , the resonant probe pulse is applied again.C repump probes whether the emitter is in the correct charge state and the threshold C pass functions to filter for instances that the emitter is not on resonance with the driving field.This procedure is repeated until the threshold C pass is met.
We first implement the CRC in conjunction with PLE scans to show its effect on spectral diffusion and ionization, see Fig. 4(b).The CRC repump and probe pulses are of the same power and duration as in Fig. 3. Fig. 4(b) depicts two panels with 250 PLE scans each.Before every scan, a CRC is performed with a (C pass , C repump ) threshold of (50, 10) and (110,10) counts for the left and right panel respectively.
For a low CRC threshold, C pass = 50, the SnV − resonant frequency shows spectral jumps less frequently compared to a high CRC threshold, C pass = 110, but jumps with higher magnitude.Due to the lower threshold, enough photons can be scattered to pass the CRC even when the SnV − is off-resonance.As a result, these off-resonant cases affect the PLE experiment, while the repump pulse is applied only once the emitter is dark.
With higher CRC thresholding, more repump cycles are required to reach a configuration where the SnV − detuning to the driving laser is small enough to scatter more photons than the threshold value, C pass .This leads to more frequent spectral jumps of the resonance frequency but the jumps are of significantly lower magnitude.It can be seen how this improves the effective spectral diffusion probed by our experiment by looking at the distribution of SnV − resonance frequencies in the PLE scans (top panels of Fig. 4(b)).Here we have filtered for the resonance of the other emitter.In Fig. 4(c), we show the standard deviation of the distribution in the top panel of Fig. 4(b) as a function of the CRC threshold, C pass .A clear trend towards a single-peaked distribution and lower variance is visible for higher thresholds (see Supplemental Material for the PLE scans [28]).We note that employing a CRC threshold C pass < 50 resulted in too few repump pulses to reliably determine the repump-induced spectral diffusion.
In addition, we applied the CRC on a different SnV (SnV − B) which is embedded in a nanophotonic waveguide (we refer to [22] the device and experimental setup details).When setting a high C pass , we observe similar stable lines as for SnV − A, see Fig. 4(d) and Supplemental Material for more PLE scans using different CRC thresholds [28].Furthermore, we show on SnV − B that the CRC can be employed to tune the heralded optical transition frequency.In Fig. 4(d), we step the frequency of the resonant laser during the CRC about every 30 scans, while using a high C pass .The resonant peak center detected in the subsequent PLE follows the frequency set-point indicated by the red solid lines as shown in Fig. 4(d).In Fig. 4(e) we plot the mean center frequency of the individual scans for the different laser detuning setpoints.This experiment shows that using CRC heralding we can tune the emitter >100 MHz, which is several times larger than the measured mean single-scan (homogeneous) linewidth of 31 MHz.The effective tuning range of this method is determined by the inhomogeneous (or spectral-diffusion-limited) linewidth (which can be measured by setting the CRC  threshold to zero), as the probability for the repump pulse to bring the optical transition to more detuned frequencies decreases rapidly.

VII. OPTICAL RAMSEY EXPERIMENT USING REAL-TIME HERALDING
Finally, we directly probe the coherence of the optical transition for different CRC thresholds, by performing Ramsey interferometry experiments using the pulse sequence depicted in Fig. 5(a).First, coherence between the ground and optically excited state is created with an optical π/2 pulse.After letting this state evolve for a time τ we apply a second π/2 to map the remaining coherence onto populations that we read out by integrating the fluorescence in a 5 ns window after the second π/2-pulse.This signal is then normalized to twice the fluorescence measured for a mixed state (i.e. for large τ).
We run this experiment for different delays τ and phase differences ϕ of the pulses.The resulting data is shown in Fig. 5(b), where the dependence of the readout signal on τ (x-axis value) and ϕ (plot color) is shown for a C pass of 10, 60 and 110 counts in the left, center and right panel, respectively, and a fixed C repump = 10.For increasing CRC threshold C pass we observe both a higher contrast of the oscillations, as well as a slower decay of this contrast with increasing τ.
We extract a quantitative measure for the coherence between the ground and excited state by fitting the phase dependence for each τ to a sine function [20].The amplitude of the sine is plotted in Fig. 5(c) as a function of τ.From a Gaussian fit to the data we determine the dephasing time T * 2 of the optical transition.For the CRC threshold C pass = 10 we obtain a T * 2 of (4.3 ± 1.7) ns, where the large uncertainty is a consequence of the low contrast.For a high CRC threshold of C pass = 100 we determine a T * 2 = (6.3± 0.4) ns.This is, to our knowledge, the highest measured optical T * 2 for an SnV − center to date.This demonstrates that implementing a CRC can mitigate the effects of spectral detuning leading to an increase in optical coherence time, which is key to improve photon interference experiments.

VIII. CONCLUSION AND OUTLOOK
The ability to reliably prepare color center qubits in the desired charge state at a set optical transition frequency, as demonstrated here, is a key requirement for efficiently running complex quantum experiments as well for future quantum technologies.Taken together with recent diamond SnV center demonstrations of nanophotonic integration [19], spin qubit control, and coherence beyond a millisecond [23,24], our results complete a quantum control toolkit for scaling current single-center experiments.Compared to the experimentally more mature diamond Nitrogen-Vacancy center [4,5,31,32] and diamond Silicon-Vacancy center [14,15,33,34], the SnV center adds the combination of compatibility with nanophotonic integration and the relatively high quantum efficiency and operating temperature, making it a compelling platform for future exploration of multi-qubit quantum networking and quantum computing protocols.

IV. CRC OPTICAL RAMSEY INTERFEROMETRY MEASUREMENTS
Additional data to Fig. 5 of the main text.We sweep the CRC threshold, C pass , while keeping C repump = 10.For C pass = 1, we implement C repump = 1, which is effectively equivalent to not implementing a CRC sequence but instead use a conditional repump, where we only repump once the emitter is in the dark state.

FIG. 2 .
FIG. 2. (a) The pulse sequence used for the data in (b), consisting of an off-resonant pump pulse followed by two identical resonant probe pulses (1 and 2).(b) 2D histogram of photon counts C2, as a function of C1 for increasing resonant laser powers (10 nW, 100 nW, 200 nW) and a fixed duration of 50 µs.(c) Histogram of C2 conditioned on C1 above or below a threshold of 100 counts of the data of the middle panel of (b).(d) The probability of passing the threshold used for heralded bright state initialization, the error bars fall within the data points.(e) The pulse sequence used for the data in (f), consists of two identical resonant probe pulses (3 and 4) with an off-resonant pump pulse in between.(f) 2D histogram of photon counts C4, as a function of C3 for increasing repump duration and powers (50 µs at 10 µW, 500 µs at 100 µW, 750 µs at 200 µW).(g) Histogram of C4 conditioned on C3 being a low or high number of counts.

FIG. 3 .
FIG. 3. (a) The pulse sequence used for the Rabi driving experiment conditioned on the probe pulse counts (Repump: 500 µs, 100 µW, Probe: 500 µs, 100 nW, Rabi pulse: 30 ns at 17.5 nW).(b) Histogram of the photon counts detected during the probe pulse.(c) Time-resolved histograms of photon counts during Rabi driving, conditioned on the number of photons detected in the preceding probe pulse.Solid lines are exponential decaying sine fits to the data.(d) The decay times and Rabi frequencies were obtained by fitting the time traces in panel (c), including the error of the fits.

FIG. 4 .
FIG. 4. (a) The real-time logic pulse sequence for the CRC used to herald the charge-resonance state of the SnV.(b) Bottom: The fluorescence of 300 PLE scans each taken in ∼1.3 GHz/s over the optical transition of SnV − A, preceded by a CRC for a threshold Cpass of 50 (left) and 110 (right) counts and a threshold Crepump = 10.We attribute the second reddetuned resonance detected to another nearby emitter.Top: The distribution of the fitted centers of the individual scans, filtered for the bright emitter.(c) The standard deviation of the centers of the individual fitted scans as a function of the CRC threshold.The error bar is the standard error of the standard deviation.(d) The fluorescence of PLE scans each taken in ∼1.3 GHz/s over the optical transition of SnV − B, preceded by a CRC for different resonant frequencies indicated by the red vertical lines.(e) The emitter's mean central frequency as a function of the set laser frequency, showing the shift of the SnV − center's emission by CRC conditioning.The error bar is one standard deviation over the repetitions shown in panel (d).

CRC N 2 2 FIG. 5 .
FIG. 5. Optical Ramsey experiment conditioned on CRC.(a) Pulse sequence used for the data in (b) and (c) (see Supplemental Material for further details [28]) (b) The counts detected during an integration window after the second π/2pulse for a set Crepump of 10 and different Cpass, for different phases of the second π/2-pulse, normalized to twice the counts detected in a mixed state.(c) Contrast decay envelopes for different CRC thresholds, Cpass, and a fixed Crepump of 10.The fitted envelopes show in an increase of the T * 2 from (4.3±1.7)ns for a low threshold,Cpass, to T * 2 =(6.3±0.4)ns for the highest Cpass = 100.The error bars are fit errors.

FIG
FIG. S1.Confocal set-up V. CRC LINESCANSAdditional data to Fig.4of the main text.
FIG. S4.CRC linescan additional data of an in a waveguide embedded SnV − B. Bottom: The fluorescence of 300 PLE scans each taken in ∼1.3 GHz/s over the optical transition of SnV − A, preceded by a CRC for various threshold Cpass and a fixed threshold Crepump = 10.Top: The distribution of the fitted centers of the individual scans.
(a) is repeated 10, 000 times in our experimental runs.