SUPPLEMENTARY INFORMATION

Transcription

1 doi: /nature10401 SUPPLEMENTARY METHODS We perform our experiments using a home-built cryogenic scanning confocal microscope. The critical components of this system include one 532 nm laser and two 637 nm lasers, a flow cryostat with optical access, cryogenic piezoelectric stages for fine position control, high efficiency, low background optical collection for fluorescence detection, and integrated optical and electronic components fabricated onto our diamond sample. Device fabrication We work with a type IIa chemical vapor deposition grown diamond (Element 6) and study naturally occurring NV centers located 5-15 µm below the surface. In order to deterministically etch a solid immersion lens (SIL) around a specific NV-center we first define a 200 nm thick gold coordinate system onto the surface via electron beam lithography. This coordinate system is visible in our confocal setup, in which we determine the relative positions of the NV-centers, as well as in the focused ion beam system (FEI Strata DB 235), which is used to etch the SILs at these positions. We use a 30 kv gallium ion beam to mill the lenses. The desired lens profile is approximated by etching concentric rings of varying diameters 1. After writing the lenses we clean the sample for 30 min in a boiling mixture of equal parts of perchloric, sulfuric and nitric acid. As a final step we define a 200 nm thick gold microwave strip line and electronic gates around the lenses via electron beam lithography. Experimental apparatus Our device is thermally anchored to the cold finger of a Janis ST-500 flow cryostat at a temperature of T = 8.6 K, and mounted on an XYZ stepper/scanner piezo stack (Attocube). The device is mounted at the focus of a 0.9 NA, 1 mm working distance microscope objective (Olympus) within the vacuum shroud of the cryostat. Microwave coaxial lines are thermally anchored to the radiation shield of the cryostat before connection to the device, and the DC lines are disconnected in the experiments described in this paper. At low temperatures, NV centres exhibit sharp zero phonon lines (ZPL) around 637 nm which we address with two resonant lasers (New Focus Velocity tunable external cavity diode laser and Sirah Matisse DS dye laser with DCM dye). Each laser is locked to a wavemeter to ensure long-term frequency stability. In addition, we use off-resonant green excitation (532 nm Millenia Pro, Spectra Physics) to initialize the NV centre in the negative charge state. Under green or red excitation, we detect photons exclusively in the NV phonon sideband ( nm), which can be readily separated from the excitation lasers with dichroic filters (Semrock). Photons are detected with avalanche photodiodes (Perkin-Elmer SPCM) and time-tagged by a time correlated single photon counting system (Picoharp 300). From comparison of observed count rates to the NV excited state lifetime, we estimate our total collection efficiency to be in the range of 2-3%, consistent with measurements of transmission of our optical system and specified efficiencies of our detectors. Three sources drive microwave (MW) and radio-frequency (RF) control of the NV centre and proximal nuclear spins. Two signal generators (Rohde & Schwarz SMB100A, R&S SMBV100A) are gated by internal pulse modulation and IQ modulation or an external mixer (Marki Microwave); their outputs are combined before amplification (Amplifier Research 25S1G4A). Radio-frequency signals are directly synthesized by an arbitrary wave generator (Tektronix AWG5014) and amplified (Amplifier Research 30W1000B) before combination (custom diplexer, K&L Microwave) with microwave signals. The arbitrary wave generator also controls the timing of the experiments. It generates pulse sequences for laser and MW/RF excitation, and sends synchronization triggers to the photon counting system. 1

2 Resonant excitation - ensuring correct charge state and frequency resonance Our experiments require that the NV centre we study is in the correct negative charge state and that its E x and A 1 transitions are on resonance with the two 637 nm lasers. However, under continuous red excitation the NV centre ionizes to its neutral state 2, and green excitation (which can restore the negative charge state) induces spectral diffusion. We employ two methods to ensure charge and frequency stability for the NV centre: The first technique begins each pulse sequence with green excitation, and simply checks at the end of every experimental run whether the NV centre still responds to simultaneous excitation with the two red lasers (see Fig. 1a). We then keep only data sets where sufficiently many counts are observed that the NV centre must be negatively charged and on resonance (we typically use a threshold that corresponds to roughly 500 kcounts/second with one saturation intensity of red excitation). Under these conditions, we typically keep 2 5% of our data. a 532 nm Ex A1 Experimental pulse sequence charge/resonance check b Ex A 1 Experimental pulse sequence charge and resonance check N ~ nm Ex A 1 charge and resonance check N ~ 50 FIG. 1: (a) First technique for ensuring negative charge state and transition frequencies resonant with excitation lasers. (b) Second technique. After each experimental sequence (left) we check whether the NV centre responds to simultaneous excitation by the two 637 nm lasers; if it fails to produce sufficient fluorescence, the resonance-finding sequence (right) is triggered, which continues until negative charge and resonant frequencies are re-established. A faster and more flexible technique does not apply green excitation unless the NV centre s charge or resonance condition changes. We still require observation of sufficient counts during combined E x and A 1 excitation following each experimental run (eliminating all data that does not meet this condition), but we only apply green excitation when the NV centre fails to meet this threshold. Then the system alternates between green excitation (to initialize charge and shift resonant frequency) and E x + A 1 excitation (to check if charge and resonant frequency are correct) until the NV centre again meets the threshold fluorescence level for charge and resonance conditions. The second technique provides much faster data acquisition rates when the experimental pulse sequence is long, or when we condition further on measurement outcomes within the experimental pulse sequence. In particular, we use this second method for all data acquisition involving conditional preparation of nuclear spin states (Figs. 3 and 4 of the main text). Under these conditions, we observe that roughly 50 attempts with green excitation are required to re-establish resonance with both lasers, while roughly 10 experimental sequences can be completed before we must again apply green light (see Fig. 1b). These numbers depend strongly on spatial alignment, the frequency and power of the two lasers, and the precise value of the threshold for establishing resonance, so we quote only order-of-magnitude estimates. 2

3 s doi: /nature10401 SUPPLEMENTARY ANALYSIS Excited state structure Single-shot readout via resonant excitation and fluorescence detection requires both high collection efficiency and a long-lived cycling transition. While we can enhance collection efficiency by nanofabrication of the diamond crystal, the degree of cycling of the optical transitions is set by the spin projections of the excited states, which in turn strongly depend on strain 3 5. For strain in the range of δ 0 10 GHz, E x has sufficiently low m s = ±1 contribution to allow for single-shot readout (Fig. 2a). However, at δ 3 GHz, the spin splitting in the ground state equals the E x A 1 splitting, causing a spectral overlap of transitions coupling to m s = 0 and m s = ±1 and thus rendering optical pumping and resonant spin readout impossible. These restrictions limit the range of strain for which single-shot spin readout can be achieved. Furthermore, at temperatures above around 10 K, phonon scattering in the excited state leads to a significant redistribution of population between E x and E y 6. Because the E y state exhibits a level anticrossing with the other (m s = ±1) E states around 7 GHz strain, phonon mixing into E y can dramatically shorten the spin flip time under optical excitation of E x. Except for extremely low-strain NVs, low temperatures are thus critical to achieve high single-shot readout fidelity. a NV A NV B E x E y Percentage m = Transverse strain (GHz) b kcouts/second NV B E y A Laser detuning (GHz) E X FIG. 2: (a) m s = 0 projection of E x and E y excited states as function of transverse strain (following analysis in 4 ). Values for the discussed NV centres are indicated. (b) Photoluminescence excitation spectrum for NV B. Transitions to E x and A 1 used in pulsed experiments are shown, along with the strain-split E y transition 12.3 GHz below the E x transition. Laser frequency is given as a detuning from THz. Comparison of NV A and NV B The main text presents single-shot readout data for two NV centres, NV A and NV B. The approximate transverse strain for NV A and NV B is indicated in Fig. 2, and is found from half the splitting between the E x and E y transitions (see Fig. 1c in the main text and Fig. 2b) in the PLE spectra. While the E x state itself exhibits a similar degree of spin-mixing at both strain values, phonon-induced transitions into E y lead to increased spin-flip rates for NV B, for which E y is significantly mixed with other spin states. We can directly observe the different behavior of NV A and NV B under resonant excitation by examining the spin flip rate as a function of laser power. While higher peak count rates and lower saturation powers indicate a better SIL placement for NV B, strain leads to faster spin flip rates (see Fig. 3). Under resonant E x excitation we thus do not detect very many photons from NV B (2.6 on average) before a spin flip occurs, leading to a less accurate single-shot readout than observed for NV A 3

4 b Peak count rate (kcps) a 532 nm Ex A I s= 7±2 nw I s= 5.9±0.4 nw NV A E laser power (nw) x optical pumping spin readout charge readout Spin flip rate (khz) c Peak count rate (kcps) I s = 2.5±0.6 nw I s = 1.9±0.2 nw NV B E x laser power (nw) FIG. 3: (a) Pulse sequence. Data shown in (b) and (c) is extracted from phonon sideband fluorescence during the spin readout pulse on the E x transition. Data is conditioned on high count rates during the charge readout section to ensure that the NV centre transitions are close to resonance (i.e. using the first technique described in the text). (b) Saturation curves for NV A. Each data point shows the maximum count rate obtained at the start of the fluorescence time trace (red) or spin relaxation rate obtained by fitting the fluorescence time trace to a single exponential (blue). Peak count rate and spin flip rate saturate as the laser power is increased, with similar saturation powers of 7 ± 4 nw and 5.9 ± 0.8 nw respectively. (c) Saturation curves for NV B. Saturation powers from fit are 2.5±1.2 nw and 1.9 ± 0.4 nw for peak count rate and spin flip rate respectively. Spin flip rate (khz) (see Fig. 4). For both NV A and NV B, the average readout fidelity is primarily limited by the error in reading out m s = 0. Figure 4 shows the fidelity for m s = 0 and m s = ±1 readout individually as a function of the readout duration. The m s = 0 fidelity grows with readout duration as we are more likely to detect a photon the longer we integrate; conversely, the m s = ±1 fidelity decreases with readout duration owing to increased likelihood of background counts or off-resonantly induced spin flips (see discussion below of photon statistics). The optimal readout duration (maximizing average fidelity) represents the tradeoff between the two; its precise value depends sensitively on the power used to excite the readout transition, with shorter durations better at higher powers. Owing to increased background at higher powers, the best readout fidelities are achieved for readout laser intensity well below a saturation power. Electronic spin preparation To estimate the optical pumping efficiency for NV A, we examine the time dependence of the fluorescence during optical pumping. In particular, following nominal preparation into m s = 0 (m s = ±1), we fit the fluorescence time trace under E x (A 1 ) excitation to a single exponential with an offset, Ae t/t1 +B (see Fig. 1e of the main text); this yields information about the preparation fidelity into m s = ±1 (m s = 0). Owing to possibly imperfect preparation, the amplitude A of the exponential is less than or equal to the fluorescence rate that would result from a perfectly-prepared m s = 0 (m s = ±1) state. Because of background counts from ambient light and detector dark counts, the offset B is greater than or equal to the fluorescence rate from remaining undesired population in m s = 0 (m s = ±1) following optical pumping. The ratio B/(A + B) is thus greater than or equal to the fraction of optically active population remaining in the m s = 0 (m s = ±1) state in other words, an overestimate of error in optical pumping. The precise value of the preparation error depends on the laser intensity, but typical values (from e.g. 4

5 Fraction of occurrences a b Fidelity NV A Readout duration (µs) m = 0 preparation s NV B 1.0 NV B 2.6 cts/shot 0.1 cts/shot Photon number Max 93.2±0.5% Fraction of occurrences m = ±1 preparation s Fidelity m s = ±1 avg. m s = Max 85±3% NV B Readout duration (µs) Photon number m = ±1 s avg. m = 0 s FIG. 4: (a) Fidelity as a function of readout duration for NV A, analysis of data shown in Fig. 2b of the main text. The m s = ±1 (m s = 0) fidelity is calculated as the probability to identify the system as m s = ±1 (m s = 0) following optical pumping on transitions to the E x (A 1 ) state. (b) Photon count histograms (recorded during a 50 µs readout with 0.5 nw E x excitation power) for NV B following optical pumping into the m s = 0 (left) and m s = ±1 (right) states. Inset shows fidelity as a function of readout duration. Shaded areas indicate the error margins. data presented in Fig. 1e in the main text) are in the range of 0.35 ± 0.06% for m s = 0 preparation and 0.8 ± 0.1% for m s = ±1 preparation after subtraction of detector dark counts at 50 counts/second. The above analysis neglects population of the singlet levels, which contributes a small bi-exponential character to the fluorescence decay 7. Specifically, there is an initial fast decay as the singlet state is populated (leading to a steady state fraction of optically active population in the singlet states) followed by a slow decay as the spin relaxation occurs. Under the assumption that the fraction of optically active population in the singlet states remains constant after the initial fast decay, the relevant amplitude for estimating optical pumping efficiency is the amplitude of the slower decay. In the case of m s = ±1 preparation the two exponentials can be fit, and yield an optical pumping error estimate of 0.7 ± 0.1% equal, within uncertainty, to the simpler estimate above. The intersystem crossing to the singlets also explains the low count rates observed from excitation of the A1 transition. Current understanding suggests that the A1 excited state relaxes into the singlet states at a rate comparable to the radiative decay rate. 8,9 This decay rate is too fast to observe in our data, but it has an impact on the maximum 5

6 count rates. Since decay out of the singlets is more than an order of magnitude slower than the radiative decay rate 8,10,11, the (non-fluorescing) equilibrium population in the singlets is significant, leading to the observed low fluorescence from A1 excitation. We use these estimates of optical pumping efficiency to quantify spin polarization with green (532 nm) excitation. By comparing fluorescence statistics during readout after green initialization with those after A 1 initialization, we extract the fraction of m s = 0 after green initialization to be 89 ± 3%. Resonant optical pumping thus decreases the error in spin preparation by more than a factor of 30. Photon statistics during readout The probability distribution of photon counts from electronic spin readout of the bright (m s = 0) state is essentially set by three contributions: a) the spin flip rate γ 0, limiting the total number of scattered photons, which in the limit of long integration time (t int γ0 1 ) yields a geometric distribution of emitted photons, b) the photon detection efficiency, which selects emitted photons according to a binomial distribution, and c) low background counts following a Poissonian distribution. Given the fewpercent collection efficiencies present in our setup, the expected distribution is very close to a geometric distribution, in agreement with our data. While we can calibrate background counts (approximately 100 counts/second) from ambient light and detector dark counts, we observe a significantly higher fluorescence rate during readout after preparation into m s = ±1 than would be expected solely from background. This fluorescence depends on the readout power and exhibits a geometric photon distribution; the autocorrelation of the background decays at the characteristic spin-flip rate. Since the averaged time trace of the background is flat, we attribute this fluorescence to laser-induced spin flips from m s = ±1 to the bright m s = 0 state during the readout. Such a process could occur, for example, through off-resonant excitation of the m s = ±1 A 1 transition followed by spin mixing in the excited states or coupling to the singlets. This effect represents the dominant readout error of m s = ±1, resulting in a decrease in average readout fidelity for increasing integration times (Fig. 4). Moreover, the same process limits the spin preparation fidelity for both spin states. As a consequence, we observe the highest optical pumping efficiencies and readout fidelities for excitation intensity well below saturation power. Quantum jumps Continuous resonant excitation of the m s = 0 E x transition pumps the system into the dark m s = ±1 state. To excite the spin out of this state, in Fig. 2e of the main text we apply weak MW repumping at GHz, resonant with the hyperfine transitions corresponding to four out of twelve nuclear spin configurations in NV A (see next section). Provided the nuclear spins are in one of those four configurations, the MW excitation drives the system back into the bright m s = 0 state, enabling the observation of quantum jumps. We verify the effect of the MW by dividing a fluorescence time trace of 8 s duration into bins of 3.3 µs, and plotting average durations of bright and dark periods as function of MW power (Fig. 5). To reduce the bias towards long dark periods due to non-driven nuclear spin states, we only include dark periods shorter than 100 µs in this analysis (without this filter, we observe dark periods of up to 12 ms). We find that the duration of dark periods scales with the MW power, as expected for the rate of MW induced spin-flips m s = ±1 m s = 0. The optical pumping rate from m s = 0 m s = ±1 however is larger than the MW induced spin-flip rate, explaining the bright periods of 4.9 µs average duration, independent of MW power. Although we do not provide a full quantitative model to this data, the dependence of dark period duration on MW power confirms that the observed intensity fluctuations can be attributed to a discrete evolution of the spin state. 6

7 FIG. 5: Average duration of bright (m s = 0) and dark (m s = ±1) periods in an 8 s fluorescence time trace of E x excitation as function of power of MW excitation driving the spin transition (bin size 3.3 µs). Projective readout and measurement based state preparation An ideal quantum measurement would project an initial superposition state onto a spin eigenstate, reveal which projection occurs, and leave the system in the same eigenstate. In our system, projection of the spin happens either when the NV centre emits the first photon or, in the case of m s = ±1, as failure to emit a photon exponentially reduces the probability amplitude for occupation of the fluorescent state. While projection occurs on the timescale of a few optical cycles, the time required to detect a signal is considerably longer. As a result, there is a tradeoff between the fidelity with which we measure the projected spin state and the probability to leave it undisturbed, so that our readout only partially fulfills the requirements of ideal quantum measurement. Nevertheless, a probabilistic preparation protocol that detects only m s = 0 spin projections can be used to obtain both a high correlation between the projected and detected states and a low probability to flip the spin during measurement. Detection of a photon during a short readout pulse is very strongly correlated with an initial m s = 0 spin projection (the error is given by 1-F ±1 in Fig. 4), and this correlation improves as the readout duration decreases. Similarly, the probability to flip the spin during measurement vanishes in the limit of decreasing readout time. To demonstrate high fidelity projective state preparation, we prepare a set of spin superpositions using microwaves (including all data from Fig. 2d of the main text), and perform two successive readouts. The first readout ((1), variable duration) projects the spin state, which we then detect during a second readout ((2), fixed duration 8.3µs). In Fig. 6 we show the conditional probability P (0 (2) 0 (1) ) to measure m s = 0 during the readout (2) conditioned on obtaining the outcome m s = 0 in readout (1). As the first readout duration decreases, the conditional probability to measure m s = 0 increases, approaching the bare m s = 0 readout fidelity following optical pumping (87% for our best data sets, 82% for data taken under the same conditions as Fig. 2d Main). For short readout durations our measurement-based preparation is, within statistical uncertainties, indistinguishable from optical pumping into m s = 0. Ultimately, in the limit of short readout duration the fidelity for preparation by measurement is constrained only by spin-mixing in the excited E x state, which for low strain is less than 0.5%. Hyperfine structure The electronic spin associated with the nitrogen-vacancy centre in diamond couples to a variety of spins in its environment. While interactions with the bulk electronic 12 or nuclear 13 spin bath lead to dephasing and decoherence, the NV centre can interact coherently with sufficiently proximal nuclear spins 14. In 7

8 Conditional m s = 0 probability Projective readout duration (µs) FIG. 6: Combining data for all microwave pulse durations shown in Fig. 2d of the main text, we show the probability to measure m s = 0 during readout segment (2) after conditioning on detection of m s = 0 during readout segment (1). The duration of the projective readout (1) is varied, while the duration of readout (2) is kept constant at 8.3 µs. The dashed line indicates the readout duration used in the projective state preparation for Fig. 2d of the main text (blue data points) and nuclear spin preparation. particular, the I = 1 14 N (or I = N) nuclear spin of the host nitrogen atom always couples to the NV centre spin, leading to a characteristic three- (or two-) line electron spin resonance (ESR) spectra with MHz (3.03 MHz) 15,16 splittings. Additionally, NV centres in natural isotopic concentration diamond can also interact strongly with I = C nuclear spins located on nearby lattice sites; the resulting hyperfine structure depends critically on the locations of the nearest 13 C isotopic impurities. In this paper, we consider two NV centres with very different isotopic environments. NV B does not couple strongly to any 13 C nuclei, though detailed electron spin resonance (ESR) scans do reveal weak (0.46 MHz) interactions with an isolated two-level system, likely also a 13 C nuclear spin. Because changes in the state of this weakly-coupled 13 C spin only slightly perturb NV B, we can address the electronic and 14 N nuclear spin states regardless of the other spin state. Indeed, the ESR spectra presented in the main text show no evidence of this spin because we use sufficient microwave power to drive ESR transitions unconditional on the 13 C spin state. Nevertheless, the presence of this extra spin limits the fidelity with which selective π pulses can drive a single 14 N hyperfine line. In contrast, NV A exhibits significant hyperfine interactions with two 13 C isotopic impurities. Combined with hyperfine structure from the host 14 N nuclear spin, these interactions lead to a complex ESR spectrum where each line corresponds to one or more of the twelve nuclear spin states. We identify the spins as 13 C nuclear spins by comparison of measured hyperfine splittings to known 13 C interaction strengths 17 and verification of expected coherent dynamics in electron spin echo envelope modulation measurements 14. Because of the small electronic Zeeman splitting in Earth s magnetic field, there is some redundancy in the ESR spectrum, and all of the nuclear spin states are contained in half of the spectrum. We indicate in detail which nuclear spin configurations contribute to the observed lines in the lower half of the spectrum (shown in Fig. 3b of the main text), using positive values for the hyperfine interaction for the 13 C nuclear spins 17 and a negative value for the 14 N nuclear spin 16. To demonstrate nuclear spin preparation it thus suffices to examine half of the lines, and show that a line corresponding to a single 3-nuclear-spin configuration (here labelled transition 1) is enhanced at the expense of the others. 8

9 a Fluorescence intensity m = +1 s m = -1 s 98 NV B Microwave frequency (GHz) Hyperfine splittings from fit 14 N: 2.169(7) MHz 13 C: 0.46(1) MHz b Fluorescence intensity m = -1 s m = +1 s 94 NV A Microwave frequency (GHz) Hyperfine splittings from fit 14 N: 2.18(3) MHz 13 C: 2.53(4) MHz 13 C: 12.78(1) MHz Transition N: C: ½ -½ ½ -½ ½ -½ ½ -½ -½ ½ -½ ½ 13 C: ½ ½ ½ -½ ½ ½ -½ -½ -½ -½ ½ -½ FIG. 7: (a) ESR for NV B in ambient magnetic field. ESR data are recorded without nuclear preparation and using standard green excitation for the spin detection, for which the fluorescence intensity is a proxy for the polarization of the electronic spin into m s = 0. Microwaves are applied in a 5 µs pulse with a Rabi frequency of approximately 100 khz prior to fluorescence detection of the electronic spin. Upper traces illustrate the contributions from transitions to the m s = +1 and m s = 1 branches as determined by a fit to 12 Gaussian components constrained to have the same amplitude, with positions determined by two two-fold (Zeeman and 13 C) splittings and one three-fold ( 14 N) splitting. Hyperfine parameters extracted from the fit are listed at right; numbers in parentheses are one standard deviation uncertainty in the fit in the last digit. (b) ESR for NV A in ambient magnetic field. Separate contributions from m s = ±1 transitions are illustrated above using components of the fit to 24 Gaussian lines constrained to have the same amplitude, with three two-fold (Zeeman and two 13 C) splittings and one threefold ( 14 N) splitting. Hyperfine parameters extracted from the fit are listed at right. Transitions 1-5 marked on the plot correspond to nuclear spin configurations tabulated in columns below. Numbers 1, 0, 1 indicate the projection of the 14 N nuclear spin on the NV axis, while ± 1 2 indicates the projections of the 13 C nuclear spins on their respective principal hyperfine axes. 9

10 Nuclear spin preparation Projective measurement of the electronic spin enables measurement-based preparation of the states of other spins with which it interacts. By entangling the desired state of a nuclear spin with the electronic spin state m s = 0 and subsequently measuring the electronic spin, we can project the nuclear spin state onto a value determined by the outcome of our measurement. The entangling operation that we use is a CNOT gate whereby the state of the nuclear spin controls whether or not a microwave pulse flips the electronic spin. Each line in the hyperfine spectrum corresponds to a nuclear spin controlled rotation of the electronic spin. We work with the lowest frequency hyperfine line; for NV B, this corresponds to the 14 N state m I = 1; for NV A, this corresponds to the 14 N, 13 C, 13 C state m I = 1, 1 2, 1 2. To ascertain the degree of nuclear spin polarization we can anticipate in our experiments, we performed simulations of the nuclear controlled electron rotation taking into account the measured hyperfine structure and spin dephasing rate. In Fig. 8, we show results of these simulations for a hypothetical NV centre with hyperfine and coherence properties similar to NV B. In the case of perfect optical pumping, the nuclear spin preparation fidelity depends only on the relative probability to drive the desired m I = 1 transitions compared to the undesired m I = {0, +1} transitions. The presence of the additional 13 C and dephasing processes makes it impossible to obtain a perfectly selective π pulse. However, by appropriately choosing a microwave Rabi frequency (1.2 MHz in the simulations) and pulse duration, we can very nearly drive a π pulse on the m I = 1 transitions while very nearly rotating the m I = 0 transition by 2π. The resulting characteristic bump observed in the total signal near 400 ns (see Fig. 8b, brown dashed curve) appears in our experimental data and allows us to select a nearly optimal microwave pulse duration. More sophisticated composite pulse sequences or pulse shaping will likely enable improvements in the fidelity of the nuclear controlled electron rotation. Imperfect optical pumping further reduces the effectiveness of nuclear spin preparation because it creates additional population in the m s = 0 state we use to select the desired nuclear spin state. Even if the nuclear controlled rotations were perfect, the nuclear spin preparation for NV B would be three times worse than the electron spin preparation (because the nuclear spin is only in the desired state 1 out of 3 times). Including both sources of error, we see that for optical pumping efficiencies in the range of % the nuclear spin can be prepared in one of the m I = 1 states with a probability between 0.86 and Spin relaxation data discussed earlier suggests that our optical pumping efficiency can be above 99%. The finite fidelity of the electron spin readout does not have a significant impact on the nuclear spin preparation. We design the pulse sequences so that the desired nuclear spin state is entangled with m s = 0, and condition subsequent measurements on detection of a photon within a very short pulse window (400 ns). From the observed counts per shot during m s = ±1 readout (see Fig. 4), the chance to misidentify the electronic spin state is less than 1 in Higher fidelity nuclear spin preparation is possible by repeating the sequence and conditioning on multiple successful outcomes. In essence, the first nuclear spin preparation introduces a nuclear spin population imbalance, reducing the detrimental effects of imperfect optical pumping and imperfect selective π pulses. In principle, repetitive preparation should saturate in fidelity when the nuclear spin state purity is limited by the chance for nuclear spin flips during the conditioning electron spin readout. In practice, data rates become prohibitively slow for more than two repetitions because of the low probability to observe a photon during the short 400 ns readout pulse. We cannot precisely measure the degree of nuclear spin polarization we obtain, but we can make an estimate under reasonable assumptions and derive a rigorous lower bound. Following nuclear spin preparation, the measured ESR hyperfine spectrum shows enhanced amplitude for transitions corresponding to the prepared nuclear spin state. We extract information about the nuclear spin preparation from the depth of these transitions by two methods: (1) We compare the amplitude of transitions corresponding to the prepared state to transitions that correspond to other nuclear spin states; (2) We examine the absolute depth of the prepared state transition. To determine the relative amplitudes of different transitions, we fit the data to a set of Gaussian lines. 10

11 a MW frequency b Probability total signal m = -1 I F prep 100% 99% 98% m = I -1 0,1 0.2 m I = 0, MW pulse duration (µs) FIG. 8: (a) The hyperfine structure used in the simulations mimics that of NV B, including both the 14 N and 13 C interactions and a 2µs Gaussian dephasing process. For simplicity, we show here only transitions to m s = 1, but our simulations include the full 3-level system m s = ±1. (b) Dashed lines show the probability to drive the m I = 1 transition (blue) or m I = {0, +1} transitions (purple) assuming an initially unpolarized nuclear spin system. The brown dashed line illustrates the total probability to leave the electron spin unaffected, mimicking the expected fluorescence signal in experimental Rabi nutations. Solid lines show predicted nuclear spin preparation probability into m I = 1. Simulations are shown where the optical pumping into m s = ±1 has a 0%, 1%, or 2% chance to leave the system in m s = 0, spanning the range of expected values in our experiments. We constrain the fit to have the same hyperfine and Zeeman splittings extracted from unpolarized data (these splittings are given in Fig. 7), and we assume that the amplitudes for the undesired nuclear spin states are identical and the widths for all transitions are the same; without these constraints, it is not possible to obtain reasonable fits to the data. We allow for minor variations in detuning, and extract the relative amplitude of the desired and undesired transitions. We then estimate the state preparation fidelity as the ratio of the amplitude of the prepared nuclear spin state transition to the sum of the amplitudes for all transitions. In the case of NV B, the fit shown in Fig. 3 of the main text includes only the 14 N hyperfine interactions (neglecting the weakly-coupled 13 C) and assumes equal amplitudes of m I = 0 and m I = +1, but we see no difference when including the additional 13 C coupling or allowing for different amplitudes of m I = 0 and m I = +1; in either case we obtain an amplitude ratio of 96 ± 4% (though the error is higher with additional parameters). In the case of NV A, we calculate 88 ± 10% for the constrained fit. These values agree within error with the higher end of fidelity estimates in our simulations, as would be expected with high optical pumping efficiencies. Because we do not repump the electronic spin following the conditional readout (at least for singlyprepared data p = 1), the ESR spectra in main text, Fig. 3a,b do not exhibit the full expected contrast. Moreover, we make several assumptions to obtain reasonable fits to our data. Consequently one might object that the above estimate is not rigorous as the electronic spin is not fully polarized. We can place a rigorous lower bound on the nuclear spin polarization by examining the absolute amplitude of the hyperfine transition corresponding to the prepared state. In the case of NV B, with single preparation p = 1, the amplitude is only 42 ± 1% owing in large part to imperfect electron spin preparation and readout. For comparison, during the 400 ns pulse we anticipate that there is about a 6% probability to induce an electron spin flip (the spin flip decay constant is approximately 6 µs for the readout conditions used); moreover the expected visibility for NV B electronic spin readout is only 70 ± 3%. For NV A, the absolute amplitude for the desired transition is 60±4% with one preparation step p = 1. With two preparation steps (which also repumps the electron spin), data acquisition rates are slow, and 11

12 we only take a few data points. The depth of the desired transition relative to the mean of the other data points (see Fig. 3 in main text) is 71 ± 3% as compared to the 87 ± 1% visibility expected from the electron spin readout for NV A. This indicates we have at least 82 ± 4% fidelity nuclear spin preparation. The success probability for nuclear spin preparation depends on the duration and intensity of the projective resonant readout pulse as well as the initial distribution of nuclear spin population. In Fig.3a (main text), for NV B, preparation into m I = -1 succeeds 2.3% of the time; preparation into m I = {0, 1} succeeds with 9.1% probability. For NV A, the success rate for a single-step preparation into m I = 1, 1 2, 1 2 is 1.5%, while the second step succeeds 12% of the time. Because each preparation attempt only requires roughly 10 microseconds, our success rates are not prohibitively slow. The preparation success probabilities are not equal to nuclear state occupation probability because our projective readout pulse is shorter than the typical timescale on which we detect a photon from m s = 0. The data for NV B was taken with a readout duration of 400 ns at an intensity for which the maximum count rate was 376 kcps and the spin-flip time was 6 µs under optical excitation; under these conditions, we expect to obtain a photon during the 400 ns pulse with 15% probability. Data for NV A was nominally acquired under conditions where expected photon detection probability was 10%. However, spatial drift can cause the intensity of the excitation at the location of the NV center to change. Nevertheless, the observed success probability for nuclear spin preparation agrees reasonably well with the probability that the nuclear spin state is occupied times the probability to detect a photon during the projective readout pulse. Clearly, scaling to larger numbers of nuclear spins will reduce the success probability with the size of the nuclear state space. However, lower strain, lower temperatures, and improved collection efficiency can enhance the photon detection probability during the projective readout, so that khz success rates could potentially be attained with up to six nuclear spins. Alternately, measurement-based preparation could be combined with a lower-fidelity deterministic preparation technique such as coherent population trapping or dynamic nuclear polarization to obtain high preparation fidelity with faster success rates. Nuclear spin repetitive readout When a nuclear spin state is not significantly affected by electron spin readout, it can be repeatedly mapped onto the electron spin state and measured. These ideas have been explored using room temperature detection 15,18 to enable single shot readout of a nuclear spin even with low-fidelity non-resonant electron spin readout. In these experiments, the key idea was reducing the nuclear spin flip rate under non-resonant excitation so that many successive measurements could be recorded. This spin flip rate reduction was accomplished by applying large ( 1 Tesla) magnetic fields to reduce the rate of electronnuclear spin flip-flops in the NV excited state. In our experiments, we do not apply large magnetic fields, so the nuclear spin has a significant chance to undergo a spin flip during each readout. Nevertheless, because single-shot electron spin readout is possible in our device, a few readouts suffice to reach high fidelity nuclear spin readout. We perform nuclear spin readout as shown in Fig. 9. After preparing a desired nuclear spin state, we optically pump the NV centre into m s = 0 and then apply a CNOT gate that rotates the electronic spin by very nearly π when the nuclear spin is in a specific state (m I = 1 for NV B, m I = 1, 1 2, 1 2 for NV A). We then read out the electronic spin, measuring low count rates for the specified nuclear spin configuration and high count rates otherwise. Each 10 µs electronic spin readout can induce nuclear spin flips because the hyperfine interactions are significantly stronger for the 14 N nuclear spin in the optically excited states 15,19. An exponentially decaying fit indicates a 1/e decay at 17.8 ± 0.3 readout steps (each 10 µs); for these experimental conditions the nuclear spin has a 6% chance to flip during each readout cycle if it is in the state that undergoes optical excitation. The fidelity observed in straightforward nuclear spin repetitive readout is comparable to the fidelity for electronic spin readout. However, the method by which we calculate fidelity includes both preparation and measurement errors. If our preparation of state 1 succeeds with probability p 1 and state 2 succeeds 12

13 a Prepare in m I= 0 or 1 A 1 sp MW ϖ E x Condition on >0 Prepare in m I = -1 ϖ MW sp E x Condition on >0 Readout sp ϖ ro N b Probability NV B p = 1 Counts per shot m = -1 preparation I m I = 0,1 preparation Repetitive readout index Counts in 20 repetitions FIG. 9: (a) Pulse sequences used for nuclear spin preparation and readout. (b) Representative data for NV B with a single preparation step and 20 readout repetitions (80% fidelity). Optimal fidelity (84% in this case) is achieved with 4 to 6 repetitions. Further repetitions reduce the fidelity because the nuclear spin flips. Inset shows the nuclear spin decay under repeated 10 µs electronic spin readouts. with p 2, while the probability to correctly identify each is f 1 and f 2 respectively, the fidelity we measure is reduced by preparation error to F = 1 2 (p 1 f 1 + (1 p 1 ) (1 f 2 ) + p 2 f 2 + (1 p 2 ) (1 f 1 )). (1) By repeating the conditional preparation step, we improve the observed fidelity to 92% for NV B, indicating that a single preparation step is inadequate to obtain high nuclear spin polarization. We can also use the readout itself to prepare initial nuclear spin states (see Fig. 3 of main text). By setting a low threshold for identification of the specific nuclear spin state (m I = 1 for NV B, m I = 1, 1 2, 1 2 for NV A) and a high one for other states, we can increase the contrast between subsequent readout events to as high as 96%. The readout fidelities observed for electronic and nuclear spins are individually at or above the threshold for observation of Bell s inequality violations (92%). Moreover, we anticipate that straightforward improvements to our experimental apparatus and sample will allow a significant improvement in readout fidelity. Reduced temperatures, improved collection efficiency optics, and optimal location and orientation of the NV in the SIL can reasonably reduce readout errors by a factor of two to three. 13

14 Measurement crosstalk In Figure 4 of the main text, we present data where we manipulate and read out the electronic and nuclear spin associated with NV B. To investigate the degree to which the two single-shot readout results are truly independent, we examine the influence of one measurement outcome on the statistical distribution of the other. Each data point in the two-dimensional plot contains 1000 experiments, each with two measurement outcomes, one for the electronic and the nuclear spin. For each data point, we calculate the conditional probabilities p(m s = 0 m I ) and p(m I = 1 m s ) for the two possible measurement outcomes of the electronic spin m s and nuclear spin m I. We then separately examine the influence of the electronic outcome on the nuclear measurement and vice versa. To understand the measurement crosstalk from the electronic to the nuclear spin, in Figure 4c of the main text we plot p(m I = 1 m s ) as a function of the RF duration (averaged over the MW pulse duration; error bars give the two sigma statistical uncertainty in the mean in this averaging process), and examine how the electronic spin measurement outcome influences our observation of the nuclear Rabi nutations. The nuclear Rabi nutations have a non-sinusoidal form because the nuclear spin in the m s = 0 manifold has a Λ structure from the 14 N quadrupole splitting 5 MHz. We fit the data to the expected form for a degenerate Λ system, and find that the electronic spin measurement indeed has an impact on the visibility of the nuclear spin oscillations. In particular, we observe a 17 ± 6% reduction in contrast when the electronic spin is measured to be in m s = 0. This measurement crosstalk arises because of the finite probability for flipping the nuclear spin each time the NV centre is optically excited. Under similar circumstances, we observed a 6% probability for nuclear spin flips during electron spin readout, which should induce a 12% loss of contrast. The observed contrast reduction agrees within error with such an estimate. To elucidate crosstalk from the nuclear spin to the electronic spin, we perform a similar analysis. In Figure 4b of the main text we show p(m s = 0 m I ) as a function of MW duration (now averaged over the RF pulse duration; again, error bars show two statistical uncertainty in the mean), and observe a significant discrepancy between the data sets with m I = 1 and m I = 0, 1. Since the electronic spin is in a V configuration, we fit the data to the expected form for Rabi nutations in a V system with variable splitting between the m s = ±1 states. The only significant difference between the fits is the splitting, as expected. We find that the two Rabi frequencies for the fit Ω 1 = 26.7±0.2 MHz, Ω 0,+1 = 27.0±0.2 MHz are essentially the same, but 0,+1 = 3.1 ± 0.6 MHz and 1 = 5.9 ± 0.4 MHz differ significantly, coming close to the measured hyperfine splittings of 6.4 MHz (for m I = 1) and 2.1 MHz (for m I = {0, 1}). The difference between the conditional probabilities therefore arises from insufficient microwave power, which prevents us from nonselectively driving all hyperfine transitions - it is not a measurement crosstalk. [1] Hadden, J.P. et. al. Strongly enhanced photon collection from diamond defect centers under microfabricated integrated solid immersion lenses. Appl. Phys. Lett. 97, (2010). [2] Robledo, L., Bernien, H., van Weperen, I. & Hanson, R. Control and Coherence of the Optical Transition of Single Nitrogen Vacancy Centers in Diamond. Phys. Rev. Lett. 105, (2010). [3] Tamarat, P. et. al. Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond. New J. Phys. 10, (2008). [4] Doherty, M.W., Manson, N.B., Delaney, P. & Hollenberg, L.C.L. The negatively charged nitrogen-vacancy centre in diamond: the electronic solution. New J. Phys. 13, (2011). [5] Maze, J.R. et. al. Properties of nitrogen-vacancy centers in diamond: the group theoretic approach. New J. Phys. 13, (2011). [6] Fu, K.-M.C. et. al. Observation of the Dynamic Jahn-Teller Effect in the Excited States of Nitrogen-Vacancy Centers in Diamond. Phys. Rev. Lett. 103, (2009). [7] Togan, E. et. al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, (2010). 14

15 [8] Manson, N.B., Harrison, J.P. & Sellars, M.J. Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics. Phys. Rev. B 74, (2006). [9] Batalov, A. et. al. Temporal Coherence of Photons Emitted by Single Nitrogen-Vacancy Defect Centers in Diamond Using Optical Rabi-Oscillations. Phys. Rev. Lett. 100, (2008). [10] Acosta, V.M., Jarmola, A., Bauch, E. & Budker, D. Optical properties of the nitrogen-vacancy singlet levels in diamond. Phys. Rev. B 82, (R) (2010). [11] Robledo, L., Bernien, H., van der Sar, T. & Hanson, R. Spin dynamics in the optical cycle of single nitrogenvacancy centres in diamond. New J. Phys. 13, (2011). [12] Hanson, R., Dobrovitski, V.V., Feiguin, A.E., Gywat, O. & Awschalom, D.D. Coherent Dynamics of a Single Spin Interacting with an Adjustable Spin Bath. Science 320, 352 (2008). [13] Maze, J.R., Taylor, J.M. & Lukin, M.D. Electron spin decoherence of single nitrogen-vacancy defects in diamond. Phys. Rev. B 78, (2008). [14] Childress, L. et. al. Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond. Science 314, (2006). [15] Steiner, M. et. al. Universal enhancement of the optical readout fidelity of single electron spins at nitrogenvacancy centers in diamond. Phys. Rev. B 81, (2010). [16] Felton, S. et. al. Hyperfine interaction in the ground state of the negatively charged nitrogen vacancy center in diamond. Phys. Rev. B 79, (2009). [17] Smeltzer, B., Childress, L. & Gali, A. 13 C hyperfine interactions in the nitrogen-vacancy centre in diamond. New J. Phys. 13, (2011). [18] Jiang, L. et. al. Repetitive Readout of a Single Electronic Spin via Quantum Logic with Nuclear Spin Ancillae. Science 326, (2009). [19] Fuchs, G.D. et. al. Excited-State Spectroscopy Using Single Spin Manipulation in Diamond. Phys. Rev. Lett. 101, (2008). 15