Paramagnetic color centers in semiconductors are presently capturing widespread interest as versatile qubits for nanoscale sensing and quantum information processing [1,2]. In particular, optical access to individual color centers coupled to single-electron spin control and millisecondlong coherence spin lifetimes have led to stunning demonstrations of entanglement and quantum logic in diamond and other wide-band-gap materials [3,4]. Although the prevalent approach in much of this work focuses on the relationship between the defect spin state and the photons it emits or absorbs, recent efforts have been expanded to explore the virtual atom's "valence" charge carriers as a means for transporting quantum information [5], creating local environments protected against spin decoherence [6], or enabling more convenient forms of defect spin readout [7]. For example, the use of spin-tocharge conversion schemes has led to demonstrations of electrical spin qubit detection in diamond [8][9][10] or as a route for spin-polarized carrier injection [5].
Here we combine magnetic resonance and multicolor confocal microscopy to alter the charge state of a small ensemble of negatively charged nitrogen-vacancy (NV -) centers in diamond conditional on their spin state. Successive cycles of ionization and recombination of the "qubit" NVs respectively produce free electrons and holes, which we subsequently capture via an ensemble of neighboring carrier-type-selective traps. Adapting this ancillaaided integrated detection (AID) strategy to time-resolved measurements, we demonstrate basic building blocks of NV -spin control for different trap types. Although under the present conditions standard photoluminescence readout still proves more sensitive, we expose through experiment and modeling a broad parameter space that could be potentially exploited not only to boost sensitivity beyond existing techniques, but also, more generally, as a platform for applications where the charge carrier itself serves as a flying qubit.
The cartoon in Fig. 1(a) summarizes our starting working geometry, comprising small ensembles of NV centers surrounded by a larger set of charge traps [11]. The latter take the form of point defects whose fluorescence changes (e.g., from dark to bright or vice versa) upon capture of a carrier. For the present studies, we first use silicon-vacancy (SiV) centers, whose charge state can be controlled with light pulses of suitable wavelength [12,13]. Though surface effects [14][15][16][17] and/or carrier tunneling [18] can render the charge state of defects unstable, SiV centers at moderate concentrations (∼0.1 ppm in the present sample) are known to feature long-lived charge states and, hence, serve as classical memories with virtually unlimited storage time in the dark [19].
The mechanism underlying spin-conditional ionization of the NV-a spin S ¼ 1 defect featuring triplet ground and excited states [20]-can be understood with the help of the energy diagram in Fig. 1(b). Optical excitation induces a spin-preserving transition within the triplet manifold, followed by radiative decay. Intersystem crossing to a manifold of intermediate singlet states (where S ¼ 0) is more likely when the initial NV triplet state is jm S ¼ AE1i, thus leading to spin-selective shelving (the basis for NV spin optical readout [21]). At sufficiently high laser powers, photon absorption during the excited triplet lifetime (∼10 ns) propels the NV -excess electron into the conduction band, hence changing the charge state of the NV into neutral [22]. When the illumination interval is comparable with the shelving time (∼100 ns), the above twostep photon process is more probable for the jm S ¼ 0i state-relatively immune to intersystem crossing-thus leading to spin-selective electron injection into the conduction band. This spin-to-charge conversion (SCC) process [7,[23][24][25] underlies recent demonstrations of electrical spin readout [8,9], down to individual NVs [10].
In our experiments, we first study a [100]-type 1b diamond crystal simultaneously hosting NVs, SiVs, and nitrogen impurities with approximate concentrations of 10 -2 , 10 -1 , and 1 ppm, respectively. Figures 1(c)-1(e) lay out the fundamentals of our spin storage protocol: We use multiple red (632 nm) laser scans to charge initialize NVs and SiVs within a 40 × 40 μm 2 area into a nonfluorescent state [26]. We then cycle the NVs at the center point of this region between their neutral and negative charge states via simultaneous green (520 nm) and red laser pulses (of duration t SCC ¼ 100 ns). The latter are separated by (optional) microwave (MW) pulses, whose length (t MW ¼ 100 ns) and frequency (2.87 GHz) are adjusted so as to invert the populations of the jm S ¼ 0i and jm S ¼ AE1i states of the ground triplet [Fig. 1(c)]. Each event of NV ionization (i.e., NV -→ NV 0 ) and recombination (i.e., NV 0 → NV -), respectively, results in the generation of a free electron and a hole, which subsequently diffuse away from the illumination point to be ultimately captured by a neighboring trap. Under these conditions, SiVs exhibit a one-way transformation into the negatively charged, bright state [26], thus leading to the formation of a fluorescent disk centered around the point of optical excitation [Fig. 1(d)]. Note that identical numbers of electrons and holes are injected during multiple repetitions of the qubit control protocol, hence allowing one to store the qubit spin state via the capture of one carrier type or the other, provided the traps are predominantly sensitive to one type only, the case for SiV [26].
For n ≫ 1 cycles of ionization-recombination, the integrated number of carriers-and, correspondingly, the average radius of the SiV -disk in the ensuing confocal image-is larger when the MW field is off (because the NV -spin state is jm S ¼ 0i, where ionization is more likely). We expose this spin-dependent contrast in Fig. 1(e), where we subtract the SiV fluorescence patterns obtained with and without resonant MW acting on the NV crystal-field transition after an "integration" time
where t e is the wait time between successive cycles. This trap-encoded spin signal (SiV-AID) takes the form of a concentric dark ring, absent when the MW is detuned off resonance [left and right panels in Fig. 1
To quantify the effect at arbitrary MW frequencies ν, we first calculate the integrated SiV -fluorescence hF iðr i ; νÞ ¼ P j F ðφ j ; r i ; νÞ over all angles φ j along concentric, 1-μm-wide rings of increasing radii r i . We subsequently use this radial distribution to determine the contrast C ðSiVÞ AID ðνÞ ¼ 2½I on ðνÞ -I off =½I on ðν 0 Þ þI off , where IðνÞ ¼ P i hF iðr i ; νÞ is the integrated fluorescence, here restricted to a ring of width w ≈ 7 μm around r ≈ 14 μm for optimal SNR [see Fig. 1(f)]. In the above expression, ν 0 is the NV -spin resonance frequency, and the label indicates on or off MW. Using these definitions, Fig. 1(g) shows the SiV-AID magnetic resonance spectrum of NV -. We find it to be in good agreement with that obtained from collecting the NV -spin-dependent photoluminescence, the most common readout protocol here referred to as standard optical sensing (SOS).
Given the unlimited lifetime of trapped charge states at these defect concentrations [19,27], signal integration can be carried out over a broad time interval, here ranging from 50 ms to 10 s. Figures 2(a) and 2(b), respectively, show some snapshots of the evolving SiV charge distribution within this temporal span, alongside the integrated spin signal at each of these times. Furthermore, the present approach can be easily adapted to time-resolved measurements of the spin qubit. A first demonstration is presented in Fig. 2(c), where we use the sequence in Fig. 1(c) with a variable MW pulse duration to measure the NV -spin Rabi response. A more involved scheme is shown in Fig. 2(d), this time adapted to measure the NV -spin echo signal [Fig. 2(e)].
While SiVs serve as convenient traps for the present application, they are certainly not the only type of defects one can resort to. One immediate possibility are NV centers, effectively trapping holes when negatively charged but displaying a poor electron capture cross section in the neutral state [26]. Extending the results above, we implement NV-encoded spin storage using ancilla NVs sufficiently removed from the point of laser illumination. Figure 3(a) shows the experimental protocol: Unlike in Fig. 1(c), this time we use a green laser scan to charge initialize the area around the point of optical excitation into a majority of negatively charged NVs. For these experiments, we use a SiV-free diamond crystal with nitrogen and NV concentrations of 1 and 10 -2 ppm, respectively. Though convenient to enhance sensitivity, this modified diamond composition is not mandatory, as the SiV - fluorescence can be selectively filtered out from the recorded emission spectrum [26]. To reveal the spin state of the qubit NVs (i.e., the NVs directly exposed to the green or red beams), we subtract the fluorescence patterns G on=off -this time produced by the ancilla NVs-with and without MW. We find a nonzero difference only when the microwave is resonant with the NV -crystal field transition [left image in Fig. 3(c)], thus yielding an NV-encoded integrated spin signal (NV-AID). Contrary to Fig. 1(e), the fluorescence change δG ≡ G on -G off is positive, corresponding to fewer ancilla NVs transitioning to neutral when the MW is on; the latter, in turn, agrees with the notion of less frequent NV - ionization-recombination cycles due to MW-induced NV --state shelving in the singlet manifold. Interestingly, the maximum fluorescence difference is found near the point of illumination, indicative of a spin-dependent NV - concentration under optical excitation. Note, however, that this contribution has a negligible impact on the radial fluorescence distribution hδGi-vanishing near the origin, Fig. 3(d)-and, thus, on the integrated NV-AID signal δJðνÞ ¼ P i hδGiðr i ; νÞ. As a matter of fact, we measure a time growth [Fig. 3(e)] comparable to that observed above for silicon vacancies [Fig. 2(b)]. Likewise, we attain good agreement between the NV-AID and SOS spectra [Fig. 3(f)].
To better understand the range of conditions where the use of AID can be advantageous, we model spin-to-charge conversion via the stochastic variables q j , j ¼ 0; 1, respectively, associated with the probabilities of generating a charge carrier when the initial NV -state has spin projection jm S j ¼ j. Using hi and δ 2 to, respectively, denote mean values and variances, we find that the detection sensitivity after n repeats is given by [11]
where hλi is the fraction of carriers captured by the ensemble of useful ancilla traps (i.e., those that can be subsequently read out), hk a i is the average number of photons collected during charge readout of an ancilla, and v j ≡ pq j þ w is a stochastic variable describing ancilla trap activation. In the latter expression, w denotes contributions from background carriers (i.e., produced by the ionization of defects other than the qubit NV [11]), and p is a Boolean stochastic variable associated with the probability of finding the qubit NV in the negatively charged state prior to SCC. Finally,
Þ=n is the average time per repeat during AID, calculated as the sum of contributions from the SCC light pulse duration t SCC , the spin evolution time t e during the chosen protocol, and the ancilla traps charge initialization and readout times, t 0 ia and t 0 ra , respectively. Depending on the fidelity of the SCC process and the ancilla brightness, we identify different, complementary regimes: For example, assuming, for simplicity, hλi ∼ hpi ∼ 1 and in the limit where hk a i 2 P j δ 2 v j ≫ hk a i P j hv j i 2 (typically corresponding to hk a i ≫ 1), we obtain
dependent only on the qubit spin-to-charge conversion probabilities. Conversely, when hk a i 2 P j δ 2 v j ≪ hk a i P j hv j i 2 , the sensitivity can be written as
improving inversely with the SCC contrast and the square root of the number of photons collected during ancilla charge readout. Both limits are formally identical to those found in standard SCC-based detection, implying that AID shares the benefits of charge readout [24,25]. Importantly, however, the integrated nature of the AID detection removes the characteristic SCC time overhead so long as the ensemble initialization and readout times are sufficiently short. Furthermore, in the regime of Eq. ( 3), additional gain over SCC can be attained by choosing ancilla traps featuring photon emission rates exceeding that of the qubit, and/or with longer ionization-recombination times [11]. For an NV center acting as the spin qubit, this latter limit can be attained at low temperatures where optical transitions are spin selective [28] (thus facilitating efficient spin-conditional charge initialization and ionization, i.e., δ 2 v j ∼ 0). Our present experimental conditions are far from this ideal regime, partly because the time intervals required for point-by-point charge initialization and readout as implemented herein are intrinsically long. More importantly, background traps coexisting with the ancillas (such as nitrogen impurities as well as other types of variable-charge defects abundant in chemical-vapor-deposition diamond [29]) can trap spin-encoded carriers. Indeed, dynamic conversion from and to a starting charge state effectively reduces the number of signal-carrying charges able to activate additional ancilla defects, hence leading to a nonlinear, slower signal growth [as observed in Figs. 2(b) and 3(e)] and, thus, to a reduced SNR [11,[30][31][32]. Note that optical excitation of background defects at the point of illumination can also produce informationless, background carriers whose capture by the ancilla traps negatively impacts the AID SNR. In the limit dominated by poor ancilla activation efficiency (i.e., hλi ≪ 1) and multiple background carriers (i.e., hwi ≫ hpihq j i, j ¼ 0; 1), Eq. (1) yields
where the advantages of integrated charge readout vanish (the case in this work).
PHYSICAL REVIEW LETTERS 125, 236601 (2020)
Despite the present unfavorable conditions, there is much room for improvement as the location, concentration, and type of ancilla defects-here simply defined by the intrinsic conditions of our samples during crystal growthcan instead be separately optimized using existing defect engineering protocols. Future work can benefit from defect engineering and charge guiding, e.g., to suppress background carriers produced either during NV charge initialization or from ionization of other coexisting defects near the qubit site. By the same token, arrays of electrodes could be exploited to prevent unintended carrier trapping away from the target ancillas or to physically separate electrons and holes so as to double the integrated signal. Along the same lines, we note that, because photogenerated carriers diffuse in three dimensions (3D), the two-dimensional (2D) plots observed here contain only a fraction of the total spin signal.
Interestingly, AID and SOS are not mutually exclusive, as the latter can easily be made part of the former by recording the NV fluorescence during (a fraction of) the SCC pulse. By the same token, since the nuclear spin state of the host nitrogen is robust to NV -ionization [19], repetitive nuclear spin readout schemes [33,34] can be adapted so as to enhance the number of carriers produced during each repeat via multiple runs of the SCC pulse in each repeat. Reading the spin state of the qubit defect through the fluorescence of an ancilla emitter separates spin qubit manipulation and readout into two independent processes that can be individually adjusted. The latter provides an intriguing route to more efficiently probe spin qubits with photon emission at inconvenient wavelengths (such as the SiV 0 in diamond), with a low quantum yield (such as rare earth ions), or with undesired phonon-shifted fluorescence (such as the NV).
Although qubit readout is the most obvious application, many of the ingredients that make the present results possible could also serve as a general platform to tackle problems of fundamental and applied interest. One intriguing possibility is the use of spin-selective defect ionization as a route for spin-polarized carrier injection, of interest for spintronics applications in systems such as diamond where the use of ferromagnetic electrodes is impractical [5]. Preliminary experiments in our labs suggest these ideas can be extended from ensembles to pairs of defects, one serving as the carrier source and the other as the target. Among other options, such sets could be exploited to measure capture cross sections at the level of individual spin qubits, to implement alternative forms of sensing, or to track carrier transport under the action of external forces.