Real-Time Charge Initialization of Diamond Nitrogen-Vacancy Centers for Enhanced Spin Readout

TL;DR

This paper introduces a real-time control technique to deterministically initialize the charge state of diamond NV centers at room temperature, significantly improving spin readout fidelity and speed for quantum sensing applications.

Contribution

The authors develop a real-time control method that achieves near-perfect charge initialization fidelity, enabling faster and more accurate NV center spin readout compared to traditional steady-state methods.

Findings

Charge initialization fidelity reaches 99.4%

Experiment speed increases by a factor of two

Achieves a magnetic sensitivity of 1.3 nT/Hz^{1/2}

Abstract

A common impediment to qubit performance is imperfect state initialization. In the case of the diamond nitrogen-vacancy (NV) center, the initialization fidelity is limited by fluctuations in the defect's charge state during optical pumping. Here, we use real-time control to deterministically initialize the NV center's charge state at room temperature. We demonstrate a maximum charge initialization fidelity of 99.4$\pm$0.1% and present a quantitative model of the initialization process that allows for systems-level optimization of the spin-readout signal-to-noise ratio. Even accounting for the overhead associated with the initialization sequence, increasing the charge initialization fidelity from the steady-state value of 75% near to unity allows for a factor-of-two speedup in experiments while maintaining the same signal-to-noise-ratio. In combination with high-fidelity readout based on spin-to-charge conversion, real-time initialization enables a factor-of-20 speedup over traditional methods, resulting in an ac magnetic sensitivity of 1.3 nT/Hz$^{1/2}$ for our single NV-center spin. The real-time control method is immediately beneficial for quantum sensing applications with NV centers as well as probing charge-dependent physics, and it will facilitate protocols for quantum feedback control over multi-qubit systems.

Figures

Equations

$$p(n|s),$$

$$F_{{\mathrm{NV}}^{-}}=(1-{ϵ}_T)(1-{ϵ}_D),$$

$${ϵ}_{\mathrm{T}}=\frac{{\sum }_{n\ge \nu }(1-P_{-})p(n|0)}{{\sum }_{n\ge \nu }{P}_{-}p(n|-)+(1-P_{-})p(n|0)},$$

$${ϵ}_D=1-e^{-{\tau }_{\mathrm{delay}}{\Gamma }_{\mathrm{Ion}}}.$$

$$\bar{n}={\left(\sum _{n\ge \nu }{P}_{-}p(n|-)+(1-P_{-})p(n|0)\right)}^{-1}.$$

$$⟨S_i⟩=⟨{\tilde{S}}_i⟩F_{{\mathrm{NV}}^{-}}+⟨ϵ⟩(1-F_{{\mathrm{NV}}^{-}}),$$

$$\mathrm{SNR}=\frac{\left|⟨S_0⟩-⟨S_1⟩\right|}{\sqrt{{\sigma }_0^2+{\sigma }_1^2}},$$

$$\xi =\frac{\mathrm{SNR}}{\sqrt{{\tau }_I+{\tau }_O+{\tau }_R}},$$

$${\tau }_I=({\tau }_{\mathrm{pump}}+{\tau }_{\mathrm{overhead}}+{\tau }_{\mathrm{probe}})\bar{n},$$

$$\mathrm{Speedup}={\left(\frac{\xi }{{\xi }_{\mathrm{baseline}}}\right)}^2.$$

Full text

††preprint: AIP/123-QED

The accelerating pace of quantum technology is evident in the advancement of quantum sensors [1] and the emergence of quantum networks [2]. Critical to these developments have been solid-state spin qubits based on semiconductor defects, due to their optical interface [3], compatibility with integrated technologies [4], and wide selection of host materials [5]. The most well-known example is the nitrogen-vacancy (NV) center in diamond [6, 7], which has enabled pivotal advances in quantum sensing [8, 9, 10, 11, 12, 13, 14] and quantum information processing [15, 16, 17].

One limitation to the performance of NV-center qubits is imperfect initialization into the oft-desired negative charge state (NV-). Optical pumping with 532 nm light produces a steady-state statistical charge distribution; typically the probability to prepare the NV- state is around 75% [18, 19], although it can be much lower for defects close to surfaces [20]. This probabilistic steady-state initialization (SSI) hampers spin readout by decreasing contrast and increasing readout noise [7], and it limits the fidelity of quantum gate operations of coupled spin systems utilizing the NV center as an ancilla [21, 18]. Existing techniques to improve the charge initialization fidelity include doping electrically [22] or chemically [23], and multi-color optical pumping [24]. In addition, many experiments utilize post selection to filter out the noise [25, 26, 27, 28, 24, 20]. These techniques either impose strict constraints on materials and device design or require elongated experimental runtime. At cryogenic temperatures, deterministic initialization protocols based on real-time feedback have been essential for entanglement generation and quantum error correction using NV centers due to their long measurement times [29, 30, 16], however these techniques have not been adapted for quantum sensing applications where the duration of each measurement cycle drastically affects the overall sensitivity.

Here, we use real-time feedback to control an NV center’s charge-state initialization fidelity at room temperature, and we demonstrate improved spin readout efficiency and sensitivity [Fig. 1]. A model for the stochastic initialization procedure allows for the selection of near-unity initialization fidelity into either charge state, or an arbitrary intermediate charge distribution. We measure the influence of charge fidelity on the spin readout signal-to-noise ratio (SNR) for two readout techniques, traditional photoluminescence (PL) and spin-to-charge conversion (SCC). Our comprehensive model allows for the optimization of initialization and readout parameters for quantum control experiments of arbitrary durations. The real-time initialization (RTI) protocol improves the spin readout efficiency and reduces the time required for experiments; in combination with SCC readout, we demonstrate a factor-of-20 speedup as compared to traditional methods.

A schematic of the experiment is shown in Fig. 1(a). The traditional portion of the setup consists of the lasers, microwave sources, diamond device, and photon-counting electronics. The sample is an electronics grade type-IIa synthetic diamond (Element Six) which has been irradiated with $2\text{\,}\mathrm{MeV}$ electrons ($10^{14}$ $\mathrm{cm}$-2) and annealed at $800^{\circ}$C for 1 hour in forming gas. A solid immersion lens aligned to a single NV center was fabricated using focused-ion-beam milling to increase collection efficiency [24]. Imaging and optical control is performed with a home-built room-temperature scanning confocal microscope with three excitation sources. A continuous-wave $532\text{\,}\mathrm{nm}$ laser (Gem 532, Laser Quantum), referred to as “green,” is gated by an acousto-optic modulator (AOM) in a double-pass configuration; it is used for optical pumping and traditional PL readout. An amplitude modulated $635\text{\,}\mathrm{nm}$ laser diode (MLD 06-01 638, Cobolt), referred to as “red,” is used for charge readout and SCC. A continuous-wave $592\text{\,}\mathrm{nm}$ laser (VFL-592, MPB Communications, Inc.), referred to as “orange,” is gated with an AOM and is used for SCC. A $115\text{\,}\mathrm{G}$ magnetic field is aligned along the NV axis to distinguish the $m_{s}=\pm 1$ states. A lithographically-defined loop-antenna surrounding the solid immersion lens is driven by an amplified (ZHL-16W-43-S+, Mini Minicircuits), amplitude modulated (ZASWA-2-50DR, Mini Circuits), continuous-wave signal generator (SG384, Stanford Research Systems), which allows for ground-state spin control.

The NV charge state is determined to a high accuracy by utilizing a wavelength that excites the NV- zero phonon line of $637\text{\,}\mathrm{nm}$ but not NV0 zero phonon line of $575\text{\,}\mathrm{nm}$. Example histograms of photon counts arising from 75,000 charge readouts are shown in Figure. 1(b) for both the steady-state NV- population of $75.3\pm 0.4\%$ and a higher fidelity initial population of $98.6\pm 0.2\%$. The benefit of this elevated initialization fidelity can be seen in the ground-state Rabi nutations in Fig. 1(c), where the higher fidelity charge state exhibits higher brightness and contrast.

We implement real-time control by linking our timing electronics, which consist of an arbitrary waveform generator (AWG, AWG520 Tektronix) and data acquisition (DAQ, National Instruments) system, with the fast digital logic of a field programmable gate array (FPGA, Virtex-7 Xilinx); refer to Figure 1(a) for the full system overview. In the initialization control loop, the AWG outputs a sequence consisting of a green pump and red charge probe in an repeating loop; when the FPGA detects that a preset photon detection threshold has been reached duing the charge probe, it sends an event signal to advance the AWG out of its loop and continue with the other predefined measurements. The time it takes from detection of the final photon to the halting of the initialization procedure is $\tau_{\mathrm{delay}}=$550\text{,}\mathrm{ns}$$, which consists of the detector delay ($30\text{\,}\mathrm{ns}$), the AWG delay ($500\text{\,}\mathrm{ns}$), and the red laser delay ($20\text{\,}\mathrm{ns}$).

We model the charge probe process using a photon distribution model accounting for transitions between NV- and the neutral (NV0) charge state [28, 31, 32]. The model assumes that the charge dynamics of the NV center can be reduced to a two-state system with emission rates $\gamma_{-}{}$ and $\gamma_{0}{}$, and charge transition rates for ionization (negative to neutral, $\Gamma_{\mathrm{Ion}}$) and recombination (neutral to negative, $\Gamma_{\mathrm{Rec}}{}$); see Fig. 2(a). We determine these rates as a function of power by measuring the photon distributions during a time bin that allows for about one ionization event to occur and fitting to the model [33]. Since the charge readout powers used in this work are below the saturation regime, the emission rates scale linearly with laser power while the ionization and recombination rates scale quadratically with power [18, 19].

The control parameters governing the charge probe process are the laser power (Pprobe), maximum duration ($\tau_{\mathrm{probe}}$), and the photon threshold ($\nu$) that breaks the initialization loop [Fig. 2(a)]. Given these three parameters, the model provides the expected photon distributions for the negative or neutral charge state configurations,

[TABLE]

where $n$ is the number of photons detected during $\tau_{\mathrm{probe}}$ and $s=-$ or [math] signifies the initial charge state; see Fig. 2(b) for an example.

The distributions allow us to calculate two critical metrics for RTI: the NV- charge fidelity ($F_{\mathrm{NV}^{-}}$) and the average attempts ($\bar{n}$) required for successful initialization. The initialization fidelity is governed by two terms,

[TABLE]

where $\epsilon_{T}$ is the threshold error and $\epsilon_{D}$ is the delay error. The threshold error is the probability that NV0 leads to a threshold reaching event and is given by

[TABLE]

where $P_{-}$ is the probability that the NV center was initially in NV- prior to the charge probe. The delay error is the probability that an ionization event occurred during the electronic delay time and is given by

[TABLE]

The average attempts to initialize is given by

[TABLE]

As an ensemble average, $\bar{n}$ takes continuous values.

Fig.  2(c) outlines the experimental decision tree in the real-time initialization procedure. A charge pump-and-probe sequence is repeatedly played out by the AWG until the FPGA detects a threshold-reaching event. The green pump pulse is set to $500\text{\,}\mathrm{\SIUnitSymbolMicro W}$ and $500\text{\,}\mathrm{ns}$ to quickly repump the charge without incurring significant overhead; we vary $P_{\mathrm{probe}}$ and $\tau_{\mathrm{probe}}$ to optimize the performance. In order to verify our model, we measure $F_{\mathrm{NV}^{-}}$ and $\bar{n}$ as a function of $P_{\mathrm{probe}}$ as shown in Figs. 2(d) and (e). We extract $F_{\mathrm{NV}^{-}}$ by performing a subsequent charge measurement and fitting to the photon distribution model, and determine $\bar{n}$ from the time it takes to record 105 threshold reaching events.

The measurements of $F_{\mathrm{NV}^{-}}$ are generally consistent with our model. We attribute the minor discrepancy between the measured values of $\bar{n}$ and the model predictions to minor variations in the steady-state charge population imposed by the control sequence. The model assumes an initial NV- population of $P_{-}=75\%$ prior to each probe, however We neglect this higher-order effect since it has the beneficial affect of decreasing $\bar{n}$ for the control parameters we employ.

The relative contribution of the two error sources in the charge initialization fidelity depend on the power. At very low powers, $\epsilon_{T}$ is dominant and $F_{\mathrm{NV}^{-}}$ is limited by the signal-to-background ratio of the charge readout process. At higher powers, $\epsilon_{D}$ is dominant due to the quadratic scaling of the ionization rate with power. Therefore, when designing an experiment utilizing RTI, it is crucial to minimize the control delay time. For a threshold of 1 photon, the maximum achievable fidelity is $98.6\pm 0.2\%$ at low powers [Fig. 2(d)].

To verify that RTI preserves the ground state spin properties, we measured the coherence times for a Ramsey ($T_{2}^{*})$ and Hahn echo ($T_{2}$) measurement, as well as the spin relaxation time ($T_{1}$) [33]. We observe a $\sim 16\%$ increase in $T_{2}^{*}$ when utilizing RTI, which could be due to ionization of nearby substitutional nitrogen donors [34], but we detect no statistically significant difference in $T_{2}$ or $T_{1}$.

We now consider the effect of the initial $F_{\mathrm{NV}^{-}}$ on the spin readout SNR. Generally, the observable for a spin measurement of an NV center follows the form

[TABLE]

where $\braket{S_{i}}$ is ensemble-averaged value of the observable $S$ for the spin state $i$, $\braket{\tilde{S}_{i}}$ is the expectation value of the observable for spin state $i$ given an initial NV- state, and $\braket{\epsilon}$ is an error in the observable which is due to the NV center residing in NV0 during the readout. The single-shot SNR for spin readout is then given by

[TABLE]

where $\sigma_{i}$ is the standard deviation associated with $\braket{S_{i}}$ [7].

To make quantitative comparisons between readout techniques, the physical observable and its accompanying statistical model must be incorporated into equation (7). For PL readout [Fig. 3(a)], the signal is the average number of detected photons during the first $250\text{\,}\mathrm{ns}$ of $532\text{\,}\mathrm{nm}$ illumination and thus obeys Poissonian statistics. For SCC readout [Fig. 3(b)], the signal is the probability of detecting NV- following the conversion, and it obeys Binomial statistics.

Figure 3(c) details the measurement timing diagram that allows for the characterization of spin SNR as a function of $F_{\mathrm{NV}^{-}}$. Following initialization with an arbitrary $F_{\mathrm{NV}^{-}}$, the spin state is either left in the polarized $m_{s}=0$ state, or flipped to the $m_{s}=-1$ state with a $40\text{\,}\mathrm{ns}$ microwave $\pi$-pulse. We estimate the value of $\braket{S_{i}}$ from repeated measurements using both traditional and SCC readout techniques. We also measure the spin SNR for the traditional SSI consisting of $2\text{\,}\mathrm{\SIUnitSymbolMicro s}$ of $532\text{\,}\mathrm{nm}$ illumination. We separately optimize PL and SCC readout parameters to ensure a fair comparison between the techniques [33]. The raw data are fit using equation (6), from which we empirically determine $\braket{\tilde{S}_{i}}$ and $\braket{\epsilon}$. Figure 3(d) depicts the results of this measurement for both readout protocols, with the SNR calculated using equation (7) for both the data (symbols) and fits (curves).

Interestingly, the spin SNR following RTI for both SCC and PL readout, when controlling for NV- fidelity, is $\sim 7\%$ higher than for SSI. This is attributed to improved optical spin polarization in the real-time protocol, since the red laser induces negligible recombination; this is consistent with previous observations [35]. The initial spin purity, estimated from measurements of the excited-state lifetime, is approximately 91% and 94% for the steady state and real-time protocols, respectively [33].

By combining the RTI model with the spin SNR as a function of $F_{\mathrm{NV}^{-}}$, we can optimize the signal acquisition for a given experiment. To achieve this, we define the readout efficiency,

[TABLE]

where $\tau_{I}$ is the initialization time, $\tau_{O}$ is the spin operation time, and $\tau_{R}$ is the spin readout time. This figure of merit is related to the sensitivity, and encompasses the single-shot SNR, the spin operation duration, and the associated initialization and readout overheads [7]. The total SNR after multiple measurement cycles with a total integration time, $T$, is simply given by $\braket{\mathrm{SNR}}=\xi\sqrt{T}$. We assume the operation time is fixed by the desired sensing or computation protocol. We have previously considered the optimization of the readout duration, power, and threshold for SCC, and we include those procedures when necessary [36, 7].

Real-time control allows for additional design flexibility in an experiment, as longer time spent initializing results in a higher spin readout SNR yet fewer total averages. Equation (8) quantitatively captures the trade-off between these two quantities. The initialization time is given by

[TABLE]

where $\tau_{\mathrm{pump}}=$0.5\text{,}\mathrm{\SIUnitSymbolMicro s} is the duration of the $532\text{\,}\mathrm{nm}$ charge reset pump and $\tau_{\mathrm{overhead}}=$1.5\text{\,}\mathrm{\SIUnitSymbolMicro s} is the overhead in the initialization sequence omprised of the green AOM delay, singlet decay time, and $\tau_{\mathrm{delay}}$. Note that $\tau_{I}$ is an average quantity since equation (8) is assumed to be an ensemble average over many trials.

With a model describing the readout efficiency, we can numerically optimize equation (8) to determine the protocol parameters that maximize the readout efficiency for a given operation time. To assess the results in context of typical NV-center experiments, we compute and measure the baseline readout efficiency, $\xi_{\mathrm{baseline}}$, corresponding to steady state initialization and traditional PL readout for different operation times. We then define the speedup as the reduction in integration time required to achieve a fixed SNR when comparing a new technique to the baseline,

[TABLE]

A speedup of unity defines the break-even time; the operation time at which it is equally efficient to use the enhanced technique over the baseline protocol.

Figure 4 presents the results of this optimization for four different scenarios: SSI with PL readout, RTI with PL readout, SSI with SCC readout, and RTI with SCC readout. The predicted and measured speedup curves for PL and SCC readout are shown in Figs. 4(a) and (b), respectively. For PL readout, we observe a break-even time for using the RTI of $\sim$70\text{,}\mathrm{\SIUnitSymbolMicro s}, and a maximum speedup of 1.74$\pm 0.09$ for an operation time of $1\text{\,}\mathrm{ms}$. Interestingly, we find that our full model always results in a choice of measurement parameters that make SCC more efficient than PL readout. RTI offers a further boost for operation times over $30\text{\,}\mathrm{\SIUnitSymbolMicro s}$, with a maximum observed speedup of 20.8$\pm 1.2$ for $\tau_{O}=$1\text{\,}\mathrm{ms}. The measurements slightly out-perform the model at long operation times; this can likely be explained by uncertainty in the calibration measurements that underlie the model curves.

Figure 4(c) shows the total SNR as a function of integration bandwidths for each of the four techniques. Here, we have fixed the operation time to be $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$. In each case, the total SNR scales with the inverse square root of bandwidth as expected. Of note is the integration bandwidth for which each technique achieves $\braket{\text{SNR}}=1$, which represents the maximum frequency of environmental dynamics that can be resolved above the noise. The RTI protocol coupled with SCC readout offers the best performance for this operation time. In addition, Fig. 4(c) confirms that the optical pulse sequences required for RTI and SCC do not introduce any appreciable noise in the bandwidth we consider.

NV-center quantum sensors stand to gain significant sensitivity improvements from using RTI protocols of the charge state. The largest speedup is realized for long operation times that approach $1\text{\,}\mathrm{ms}$, which coincide with the typical requirements for spin relaxometry [37, 14] as well as dynamical decoupling sequences [38, 39]. The single NV center studied here exhibits a Hahn-echo $T_{2}=$800\text{,}\mathrm{\SIUnitSymbolMicro s}$$. Explicitly accounting for the RTI and SCC overhead, our observed $\xi$ corresponds to an ac magnetic sensitivity of $1.3\text{\,}\mathrm{n}\mathrm{T}\mathrm{/}\mathrm{Hz}^{1/2}$ [33]. Other readout techniques used in quantum sensors, such as the nuclear-assisted method [40, 10], would also see similar signal-acquisition improvements due to RTI. In many situations, the gains are likely to be even larger than we have demonstrated, since NV centers located in nanodiamonds or close to surfaces typically exhibit lower steady-state charge populations than those in bulk diamond [36, 20]. For example, using our model and assuming a 25% NV- steady-state population, RTI would enable a factor-of-6 speedup for PL readout and a factor-of-75 speedup for SCC readout with an operation time of $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$.

While we have focused on applications that require strict consideration of the overhead from initialization and readout, the techniques are directly applicable to situations in which initialization fidelity is prioritized over total measurement time. For example, the initialization error can be reduced by a further factor of 2 by increasing the threshold to 2 photons, and the delay error can be reduced by decreasing $P_{\mathrm{probe}}$, which leads to $F_{\mathrm{NV^{-}}}=99.4\pm 0.1\%$ with $\tau_{I}=$7\text{,}\mathrm{ms}$$ [33]. Such control over the charge state could facilitate precise measurements of the local electrostatic environment [41, 20], aid in the quantification of photon collection efficiency for photonic devices [42], and improve the single-shot SNR for infrequent SCC measurements [43]. In addition, the fidelity associated with initializing, controlling, and measuring coupled nuclear spins [21, 30, 17] is intricately tied to the NV center’s charge and spin purity and thus could be improved with RTI.

In conclusion, we demonstrated an efficient method for initializing the charge state of an NV center in real-time and assessed how this can be used to improve the efficiency of spin readout. Real-time control could be applied to other aspects of the NV center, such as projective initialization of nuclear spins [44] and increasing the spin state initialization fidelity through time-gating. In addition, this advanced control can be applied to other emerging solid-state spin defects, especially those which may have a high fidelity readout mechanism but a less-than-ideal spin or charge pumping transition.

Acknowledgements

This work was supported by the National Science Foundation under awards ECCS-1553511 (DAH, JDL, and LCB) and ECCS-1842655 (TYH and LCB). The authors thank H. S. Knowles and Z. Zhang for useful discussions and D. Bluvstein, S. A. Breitweiser, and R. J. Patel for valuable comments on the manuscript.