Protecting a Diamond Quantum Memory by Charge State Control

Letter pubs.acs.org/NanoLett

Protecting a Diamond Quantum Memory by Charge State Control Matthias Pfender,† Nabeel Aslam,† Patrick Simon,‡ Denis Antonov,† Gergő Thiering,§,⊥ Sina Burk,† Felipe Fávaro de Oliveira,† Andrej Denisenko,† Helmut Fedder,†,¶ Jan Meijer,# Jose A. Garrido,‡,⌀,⬡ Adam Gali,§,⊥ Tokuyuki Teraji,∥ Junichi Isoya,□ Marcus William Doherty,▲ Audrius Alkauskas,▽ Alejandro Gallo,● Andreas Grüneis,● Philipp Neumann,*,† and Jörg Wrachtrup†,● †

Stuttgart Research Center of Photonic Engineering (SCoPE) and Center for Integrated Quantum Science and Technology (IQST), Third Institute of Physics, University of Stuttgart, 70569 Stuttgart, Germany ‡ Walter Schottky Institut, Physik-Department, Technische Universität München, Am Coulombwall 3, 85748 Garching, Germany § Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary ⊥ Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary ¶ Swabian Instruments GmbH, Frankenstr. 39, 71701 Schwieberdingen, Germany # Institute for Experimental Physics II, Universität Leipzig, Linnéstraße 5, 04103 Leipzig, Germany ∥ National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan □ Research Center for Knowledge Communities, University of Tsukuba, Tsukuba 305-8550, Japan ▲ Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Australian Capital Territory 2601, Australia ▽ Center for Physical Sciences and Technology, Vilnius LT-10257, Lithuania ● Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany ⌀ Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and the Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain ⬡ ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain S Supporting Information *

ABSTRACT: In recent years, solid-state spin systems have emerged as promising candidates for quantum information processing. Prominent examples are the nitrogen-vacancy (NV) center in diamond, phosphorus dopants in silicon (Si:P), rare-earth ions in solids, and VSi-centers in silicon-carbide. The Si:P system has demonstrated that its nuclear spins can yield exceedingly long spin coherence times by eliminating the electron spin of the dopant. For NV centers, however, a proper charge state for storage of nuclear spin qubit coherence has not been identified yet. Here, we identify and characterize the positively charged NV center as an electronspin-less and optically inactive state by utilizing the nuclear spin qubit as a probe. We control the electronic charge and spin utilizing nanometer scale gate electrodes. We achieve a lengthening of the nuclear spin coherence times by a factor of 4. Surprisingly, the new charge state allows switching of the optical response of single nodes facilitating full individual addressability. KEYWORDS: Diamond, nitrogen-vacancy center, charge state control, spin qubit, quantum memory

S

magnitude different spin relaxation times. As an example, NV electron spins typically relax on a time scale of ms under ambient conditions,7 while nuclear spins do have at least minutes-long spin relaxation times.8 However, the hyperfine coupling of nuclear spins to the fast relaxing electron spins in

pin defects are excellent quantum systems. Particularly, defects that possess an electron spin together with a set of well-defined nuclear spins make up outstanding, small quantum registers.1−3 They have been used for demonstrations in quantum information processing,3,4 long distance entanglement,5 and sensing.6 In such systems, the electron spin is used for efficient readout (sensing or interaction with photons), whereas the nuclear spins are used as local quantum bits. Owing to their different magnetic and orbital angular momentum, electron and nuclear spins exhibit orders of © XXXX American Chemical Society

Received: April 28, 2017 Revised: September 1, 2017 Published: September 5, 2017 A

DOI: 10.1021/acs.nanolett.7b01796 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. NV center in diamond and its charge states. (a) Sketch of the NV center in diamond containing the nitrogen nuclear spin (purple arrow), the electron spin (blue arrow), and the electronic wave function (green). The right side shows the electronic occupation of the orbitals ex, ey, and a1 within the diamond bandgap15 for three different charge states (“+”, “0”, “−”). Only the unpaired electrons in the ex,y orbitals contribute to the electron spin. The corresponding electron and nuclear spin energy levels are sketched above for the case of 14N. For the 15N case, the mI = 0 level and hence the quadrupole splitting is obsolete, mI = ± 1 becomes ±1/2, and the hyperfine and Zeeman terms change. (b) Principle of gate voltage induced charge state switching. The voltage difference between the two hydrogen terminated (hence conductive) stripes of the diamond surface (blue + , red − ) affects the Fermi level at the location of the NV center under one H-terminated stripe and close to an oxygen-terminated (nonconductive) diamond stripe (pale blue). If the Fermi level crosses the charge transition level, a change in the dominant charge state is observed.16 (c) Confocal microscopy scan of the diamond surface revealing the gate structure. Overlayed schematics illustrate parts of the two hydrogen terminated electrodes in form of an interdigitated capacitor. (d) Wire diagram of the general measurement scheme. The main workhorse is the charge and spin state selective quantum gate U on the nitrogen nuclear spin (see Supporting Information). (e) Corresponding physical implementation utilizing a sequence of laser, microwave (MW), and radiofrequency (RF) fields and the applied voltage.

under ambient conditions.28 Hence, the Fermi level with respect to the valence band edge is drastically lowered (in some locations even within the valence band) compared to intrinsic diamond.29 Recently, it was shown that this transparent surfaceconductive layer completely quenches the photoluminescence of NV centers in its close proximity. As the charge state transition level from NV0 to NV+ was expected to be around 1 eV above the valence band edge,29 the absence of fluorescence in H-terminated regions was tentatively attributed to NV centers residing in their positive charge state16 (see Figure 1a). However, also fluorescence quenching due to close proximity to a conductive layer might explain the lack of fluorescence. We emphasize that NV centers under illumination are far from any equilibrium charge state,17,30,31 and therefore, one can only guess that a positive charge state might be involved. In subsequent dark periods after illumination, the charge state might settle into NV+ or change further into other charge states.30,31 Proper bias applied to lateral gate electrodes on Hterminated surface depletes the charge carrier (holes) density around the gate contact area. At full depletion, the Fermi level at the surface is shifted away from the valence band edge. This eventually leads to switching of the charge state (potentially NV+ → NV0 → NV−) of such NV centers. Here we show that such nanoscale gate structures can be used to stabilize a third charge state with an S = 0 ground state under dark conditions, which we attribute to NV+ (see Figure 1b,c). To this end, we apply the intrinsic nitrogen nuclear spin qubit of the NV center as a probe to reveal information about the charge and spin state of the NV center17 (see Figure 1d,e). We utilize this NV+ charge state to prolong the nuclear spin T2 lifetime. Furthermore, the absence of fluorescence allows tailoring the optical response from multiple NV centers within a confocal spot and therefore increases individual addressability. To switch the charge state of NV centers, we prepare Hterminated, conductive gate electrodes onto an otherwise oxygen-terminated (O) and therefore nonconductive diamond surface.16 NV centers have been created approximately 10 nm below the described surface (see Figure 1b and Supporting Information). As H-terminated diamond surfaces quench the

most cases significantly deteriorates the nuclear spin coherence, and eventually its relaxation time, down to time scales similar to the electron spin. For NV centers at room-temperature, this limits coherence times to around 8 ms.6,8,9 Recently, this limitation could be overcome for weakly coupled 13C spins (i.e., ∼3 kHz coupling as compared to 3 MHz as for the host 15N nuclear spin). To this end, the NV center was either illuminated far beyond saturation,10 its charge state was intermediately switched to neutral, or it was illuminated far below saturation.8 However, none of these techniques worked out for the nitrogen nuclear spin; even worse, decoherence was increased under these conditions.8 For other hybrid spin systems, for example, for Si:P, this strict limit was overcome by ionizing the electron spin donors and thereby removing the electron spin. The resulting T2 times were up to the order of minutes for the host 31 P spin in Si:P ensembles11,12 and less than a second for single 31 P spins when addressing single Si:P centers.13,14 It is known that the NV center in diamond exists in various charge states.15 Besides the widely employed negative charge state (NV−), it is known to have stable NV017 and eventually NV+ configurations. NV− has an electron spin triplet ground state with total spin S = 1. Calculations as well as spectroscopic data suggest that the NV0 ground state is S = 1/2,17−19 while the NV+ ground state is likely S = 0 (for transition from NV− to NV+ consider removing electrons from molecular orbitals, highest energies first;15 see also DFT results below), that is, nonmagnetic and suitable for protection of the nuclear spin memory. Several experiments have demonstrated the optical ionization from NV− to the neutral NV0 charge-state17,20−24 and electroluminescence from single NV0 centers.25 These experiments characterize the NV− and NV0 charge states via their photophysics and different fluorescence spectral fingerprints (see Figure 1a). Apart from optical ionization, deterministic electronic charge state control is feasible, for example, using a hydrogenterminated (H) diamond surface with in-plane or electrolyte gates for Fermi-level manipulation16,22,26,27 (see Figure 1b and Supporting Information). Hydrogen termination of diamond creates a two-dimensional profile of free holes on the surface B


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Figure 2. Characterizing the positively charged NV center. (a) Confocal microscopy image of single NV centers. The left image (light blue background) was recorded at the voltage corresponding to the NV− charge state. In the right image (light red background), the NV’s fluorescence is quenched by reversing the gate voltage. Blue, gray, and pink denote NV−, NV0, and NV+ throughout the figure. (b) I−V characteristic of the surface gate structure. (c) Two spectra on the left show one of the 15N nuclear spin transitions for the NV± and the NV0 charge state, respectively. Their normalized amplitudes yield the charge state probabilities W± and W0 (see Supporting Information). W± would increase for any charge state exhibiting an electron spin state mS = 0, as is expected for NV+ (S = 0, mS = 0). The graph on the right shows the charge state probabilities for varying voltages (error bars are projection noise, see Supporting Information). The reappearance of the W± signal at high voltages suggests the presence of NV+. (d) 15N nuclear spins Rabi oscillations between spin state mI = ± 1/2 for the NV− (mS = 0) and the tentative NV+ charge state, respectively. The right curve shows the maxima of the NV+ Rabi oscillation for varying duration TU of initial NV+ voltage application. We deduce an NV+ settling time of 0.54 ± 0.08 ms. For the NV− charge state, hyperfine interaction increases the Rabi frequency (see text and Supporting Information). (e) 14N quadrupole splittings for the three known charge states (resonances of experimental spectra → circles; theory → squares). Any magnetic hyperfine and nuclear Zeeman terms are subtracted.

we set a gate voltage and perform an RF π-pulse in resonance with the mentioned transition to flip the nuclear spin. As a control experiment, we also track the amplitude of the |S = 1/2, mI = ↓⟩ ↔ |1/2, ↑⟩ 15N spin transition in the NV0 state.17 Both nuclear spin transitions are displayed on the left side of Figure 2c. From the amplitudes of the latter transitions, we deduce the probability of being in the corresponding charge state W± and W0 (see Supporting Information).17 The line width of the NV0 15N resonance is significantly broader because higher RF power is required to saturate the homogeneously broadened transition and infer the probability.17 We do not discriminate between W+ and W− at this point. We start out in the NV− state at a gate voltage of −8 V. W± and W0 reveal a switch from NV− to NV0 at around −2 V for the NV center investigated (see Figure 2c). The latter state is stable until around +8 V, where W0 decreases and W± increases again. Two reasons for the latter change are conceivable. Either NV− reappears at higher voltages, or we detect the presence of NV+ with an electron spin state mS = 0, which is more likely and will turn out to be indeed the case. The small value of witness W± at +8 V as compared to −8 V will turn out to be due to nonideal NV+ witness conditions (see Supporting Information). Next, we compare nuclear spin Rabi oscillations in the NV− and the NV+ case (see Figure 2d). The smaller Rabi frequency for the NV+ case at the same radiofrequency and the same RF amplitude is explained by the absence of an electron spin (i.e., S = 0) and the corresponding impact on the nuclear spin states. Ω − The Rabi frequency ratio ΩNV+ > 1 can be explained by

fluorescence of NV centers, the gate electrode structure can be seen in the confocal microscopy image (see Figures 1c and 2a). In Figure 2a and b, the electrical current and the NV fluorescence response to a varying gate voltage are shown. For up to ±10 V, the resistance of the capacitor is on the order of 100 MΩ. For properly located NV centers, the voltage change results in a fluorescence response (see Figure 2a). The fluorescence of those NV centers located in the center of the H- or O-terminated regions is expected to be stable under voltage changes, whereas NV centers in the border regions are likely to switch charge states because the Fermi-level change is most pronounced in these regions16 (see Figure 1b). Next, we concentrate on NV centers that change into a nonfluorescing state upon a suitable voltage change. For different charge states, the quadrupole splitting Cq as well as the hyperfine coupling A of the nitrogen nuclear spin to the NV electron spin varies significantly (see Supporting Information for the spin Hamiltonian).17 Hence, we can perform charge and electron spin selective control gates on our nuclear spin qubit. To this end, we initialize the nuclear spin into its mI = +1 state (|1n⟩ in Figure 1d,e) utilizing single shot readout while being negatively charged.3 Then we set a certain gate voltage resulting in a related charge state. In this charge state, we seek to perform radiofrequency (RF) pulse sequences in resonance with an NMR transition of the nitrogen nuclear spin. Finally, NV− is reset by the proper gate voltage to read out the 15N spin state and thus check for a successful RF sequence (see Supporting Information). For identification of NV+, we start out with 15NV centers because they possess a nuclear spin I = 1/2 and therefore lack quadrupole splitting. We probe the existence of an mS = 0 electron spin state in all accessible NV charge states by identifying the corresponding 15N nuclear spin transition |mS = 0, mI = ↓⟩ ↔ |0, ↑⟩. For this purpose, the nuclear spin is initialized into mI = ↑ (denoted by |1n⟩ in Figure 2c), and then

NV

dressing of nuclear spin states with the electron spin character via hyperfine interaction and a related increase of Rabi frequency for the NV− case and no dressing due to the absence of an electron spin in the NV+ case. The corresponding perturbation ansatz yields

Ω NV− Ω NV+

=1+

γẽ 2A⊥D γñ γẽ 2Bz 2 − D2

= 1.832

with the electron and nitrogen nuclear spins’ reduced C


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studies suggest the NV center in the negative, neutral, and positive charge state to be in the 3A2 (electron spin triplet), 2E (doublet), and 1A 1 (singlet) many-body ground state, respectively, exhibiting C3v symmetry. However, the 2E ground state is a so-called correlated many-body state that cannot be accurately described by the applied Kohn−Sham DFT method. We refine the 2E ground state applying a DFT based configuration interaction method. The results reveal a depletion of the charge density on the nitrogen atom (see Supporting Information). Hence, the 14N quadrupole splitting is further reduced compared to DFT ground state calculations and thus breaks the linear trend. At room temperature, the NV electron spin longitudinal relaxation limits the nitrogen nuclear spin coherence time to about T2 ≈ 8 ms in contrast to the nuclear spin’s longitudinal relaxation time T1 of several minutes.8,17 In a spinless environment like diamond, the T1 and T2 values are supposed to increase dramatically by removing the central electron spin. Hence, the absence of an electron spin in the NV+ center suggests T1 as being the ultimate limit for T2. The analogous strategy was successfully implemented for 31P spins associated with Si:P, however, under cryogenic conditions.12 We characterize the nuclear spin lifetimes in NV+ by preparing the 14N spin in mI = 1 (|1n⟩) and subsequently setting the appropriate gate voltage (see Figure 3b). The 14N

Table 1. Experimental (exp.) and ab Initio Calculated (calc.) Values (MHz) for Nuclear Spin Quadrupole Splittings Cq of 14 N for Various NV Charge Statesa calc. exp.

NV−

NV0

NV+

−5.02 ± 0.19 −4.945

−4.92 ± 0.19 −4.655

−4.82 ± 0.19 −4.619

a

QN scatters between 0.0193 and 0.0208 barn in the literature.32 This uncertainty is reflected in the calculated values.

Figure 3. Protected nuclear spin quantum memory. (a) Increased nuclear spin lifetimes in the NV+ charge state. The spin−echo coherence time (squares) is 25 ± 10 ms, and the longitudinal relaxation time (diamonds) is 0.3 ± 1.4 s. We expect both values to be limited by paramagnetic noise originating from the surface and subsurface impurities. The Rabi oscillation (circles) has a decay constant of 22 ± 12 ms. (b, c) Wire diagram for the spin−echo and the T1 measurement, respectively.

states, associated with the carbon dangling bonds, since they are highest in energy (see Figure 1a). In turn, the carbon-danglingbond fraction of the a1 state increases at the cost of nitrogendangling-bond contribution. Hence, the remaining electrons occupying the altered a1 state tend to increase their distance to the nitrogen nucleus, and the electric field gradient Vzz reduces. Therefore, the quadrupole splitting Cq is expected to decrease. Quantitative results for the quadrupole splitting Cq of the 14NV center in different charge states are obtained utilizing ab initio simulations. The electric field gradient Vzz is calculated within Kohn−Sham density functional theory (DFT). The results support experimentally obtained values (Figure 2e) and theoretical statements made above. The quadrupole splitting reduces when electrons are removed from the system; the theoretical calculations predict a linear decrease (see Table 1 and Supporting Information). However, the experimentally obtained value for NV0 is closer to the result of NV+ than to NV−. Only the experimental results for NV− and NV+ are within the uncertainty range of the DFT estimates. Theoretical

coherence time is deduced from a spin echo measurement in NV+ shown in Figure 3a. In addition, a long Rabi oscillation and measurement of the longitudinal relaxation are depicted. The coherence lifetime is clearly increased. However, the increase is less than anticipated. This can be attributed to two effects. First, the utilized NV centers were created by nitrogen implantation close to the diamond surface for the band bending effect of the gate structure to play a significant role. Nearsurface NV centers commonly suffer from short coherence times on the order of ∼10 μs due to electron spins on the surface and paramagnetic defects created during implantation33−36 (see Supporting Information). Only recently, novel methods have experimentally demonstrated how to overcome D


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Figure 4. Proposal for a scalable NV diamond quantum processor. (a) Schematic of individual NV nodes addressable via nanoscopic gate electrodes (gray, insulator; gold, electrode; purple, leads). NV centers under H-terminated surface are in their NV+ state and therefore do not couple to other nodes because of the lack of an electron spin, their nuclear spin state remains undisturbed, and they do not contribute to fluorescence response when illuminated. Individual electrodes with a positive voltage deplete the hole conducting layer locally and shift the Fermi level into the NV−-stable region. Therefore, such NV centers can be coupled to their NV− neighbors via magnetic dipole interaction and they are optically accessible. Unsuitable NV nodes are not supplied with an electrode and remain in NV+. (b) Sketch of quantum register operation modes using red and blue boxes to highlight charge states, purple and blue arrows for nuclear and electron spin, green lightnings for laser, and red stars for fluorescence. Initialization: (1−2) Laser initializes all electron spins, (3) swap to nuclear spins, and (4) switch to NV+ for storage. Operation: (1) Swap two nuclear spins to electron spins in NV−, (2) entangle electron spins, (3) swap back to nuclei, and (4) switch all NV centers to NV+. Readout/init: (1) switch one NV to NV− with initialized electron spin, (2) correlate electron spin with nuclear spin, (3) readout one electron spin and project nuclear spins (2−3, single shot readout), (4) switch back to NV+.

In our study, we have investigated many NV centers, most of which did not show NV+ switching as anticipated due to improper location within the O-terminated regions of the sample.16 In total, we investigated around five NV centers that showed NV+ switching. These results pave the way for a fascinating and feasible implementation of the Kane proposal for a scalable, solid-state, spin-based quantum processor.42,43 As sketched in Figure 4a, an H-terminated and transparent diamond surface would mute all NV based electron spins below as already discussed above (see Figure 1). By adding insulated, nanoscopic top gates selected NV centers might be switched back into NV− upon request. The average distance of two magnetically interacting NV centers would need to be around 30 nm or less to allow for coherent interaction.4 It is interesting to note that further increase of the gate potential VG would lead to a lateral depletion of the surface conductive channel. The scale of the lateral depletion effect can be expressed as rl ∝ VGa/nsb,44 where ns is the areal charge density in the surface channel, and the exponents a and b are roughly in the range of 0.5−1. For H-terminated diamond, the ns value is typically in the 1012−1013 cm−2 range.45 This allows a precise control of the depletion edge rl of about few nanometers per Volt of the gate bias44 and hence individual addressing of closely located NV centers. Furthermore, experiments revealed switching speeds of diamond based electronic devices of up to 120 GHz.46 Several such NV centers might then coherently interact (see Figure 4b), for example, via magnetic dipole−dipole interaction,47 and the resulting quantum state can then be stored unharmed on the nuclear storage qubits as for example 14N, 15N, or 13C nuclear spins with hyperfine interaction strengths down to a few kHz.6,8,10 For readout of quantum information, individual NV centers are switched into NV−, their nuclear spin states are transferred to the electron spin and finally readout optically without touching other nuclear spin qubits of NV centers, which reside in NV+. The fast potential charge state switching rate compared to the hyperfine coupling strength and available dynamical decoupling methods as demonstrated for example in refs 8 and 10 and shortly introduced in the beginning are

these effects (e.g., via plasma treatment of the surface, p-type sacrificial layers or nanoscale nitrogen doped layers close to the surface).36−41 If the decoherence is caused by paramagnetic defects on or near the surface,35 the same effect limits the coherence time of the nuclear spin, weakened by the small gfactor of the nuclear spin, to the order of ∼100 ms for a basic spin echo. Another decoherence effect is indicated by the comparably short nuclear spin T1 time of 0.3 s. If the charge state is not stable but fluctuates (e.g., transitions to NV0 occur), the nuclear spin would dephase (T2) on a time scale of some ten microseconds after the first charge state change, whereas the nuclear spin population difference would decay (T1) on the order of some 0.1 s.17 Hence, a charge state fluctuation with a rate of about 10 Hz is a possible explanation of the observed T1 and T2 times of the nuclear spin in NV+. We have observed delayed response of charge states to voltage changes on the millisecond time scale as depicted in the right graph of Figure 2d. In addition, however, we observed also slow and inert response on the order of seconds, following rather time-average sequence characteristics such as voltage or illumination. We attribute this behavior to the large capacitance and possible slow dynamics of deep traps of the diamond device. Further experiments with much smaller capacitors will shed light on this behavior. To summarize, we have identified and characterized the positive charge state of NV centers in diamond. We demonstrated deterministic and reversible electric switching of single NV centers into the newly detected charge state. It was found that nuclear spin energy eigenstates are resilient under this switching operation and thus serve as probe for NV+. They confirmed the absence of an electronic spin, which enabled electron-spin-unlimited nuclear spin coherence storage in NV+, even for strongly coupled nuclear spins as the one of the host nitrogen. Furthermore, the NV+ state does not fluoresce under 532 nm illumination that is commonly used for NV− excitation. At the current stage, we can not exclude quenching as a reason for absent fluorescence. A potential quenching mechanism would roughly coincide with the NV center being in its positive charge state. Hence, NV+ does not contribute to photon shot noise when other proximal NV centers within the same confocal spot are optically interrogated. E


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sufficient to protect quantum coherence on nuclear spin memories for up to 105 charge state transitions. Note that for the current millimeter-size, hence slow device and the utilized 14N spin, even a single charge state transition would destroy quantum coherence on the nuclear spin memory. Apart from the potential realization of a scalable quantum processor, the storage of quantum information has proven to be a vital resource for nanoscale quantum metrology. In ref 6, a quantum memory enhanced the performance of the NV electron spin sensor. This enables, on the one hand, coherent interactions of the sensor qubit to spectrally highly selective 13C spin qubits. On the other hand, high spectral resolution correlation spectroscopy was demonstrated. In both cases, spectral resolution is inversely proportional to the storage time of the quantum memory. Our results would yield an increase of spectral resolution by a factor of 5. Furthermore, muting the electron spin sensor also increases the coherence lifetime of sample spins and therefore allows for high-resolution spectroscopy in the first place.8 All these achievements could further improve recent NV-diamond applications in NMR spectroscopy of external sample spins.48

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b01796. Description of experimental setup; measurement scenarios; details about diamond sample fabrication; details about in-plane gate electrodes; complete spin Hamiltonian; DFT-based calculations (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Matthias Pfender: 0000-0003-3934-8306 Adam Gali: 0000-0002-3339-5470 Marcus William Doherty: 0000-0002-5473-6481 Audrius Alkauskas: 0000-0002-4228-6612 Philipp Neumann: 0000-0003-2146-0412 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Roman Kolesov, Kangwei Xia, Ali Momenzadeh, Prithvi Reddy, and Jerome Jackson for fruitful discussions and technical advice. We acknowledge financial support by the German Science Foundation (SFB-TR 21, SFB 716, SPP1601), the Volkswagen Stiftung, the JST and JSPS KAKENHI (No. 26246001 and No. 15H03980), and EU grant DIADEMS (Grant No. 611143). F.F.O. acknowledges the financial support by CNPq Project No. 204246/2013-0, and M.W.D. acknowledges financial support by the Australian Research Council (DE170100169).

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REFERENCES

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Protecting a Diamond Quantum Memory by Charge State Control

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