SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION doi: /nnano Quantum measurement and orientation tracking of fluorescent nanodiamonds inside living cells L. P. McGuinness, Y. Yan, A. Stacey, D. A. Simpson, L. T. Hall, D. Maclaurin, S. Prawer, P. Mulvaney, J. Wrachtrup, F. Caruso, R. E. Scholten and L. C. L. Hollenberg Nanodiamond preparation Type 1b high pressure high temperature non-detonation diamond nano-crystals (NaBond) with an average size of 45 nm, were dispersed in a water solution (10 µg/ml) prior to suspension in cell media. The zeta potential from the suspension was measured to be -55mV in a PH of 7 indicating a stable solution of nanoparticles. Dynamic light scattering (DLS) measurements of the nanodiamond:h 2 O suspension show an average particle size of 140 nm (see Figure 1), indicating a small amount of aggregation in the solution Mean Number (%) Particle Size (nm) Supplementary Figure 1: Dynamic light scattering measurement on the nanodiamond suspension. nature nanotechnology 1

2 Faklaris et al. 1 have shown the extent of the nanodiamond aggregation is exacerbated by the cell medium DMEM. This effect can be mitigated with the addition of 10% FCS (Fetal calf serum) to the cell medium. In the present work, a small volume of the nanodiamond:h 2 O solution was diluted into the cell media with 10% FCS prior to the 3 hour incubation to avoid unwanted agglomeration. We note that even in the presence of aggregated nanodiamond we are still able to routinely identify nanodiamonds hosting single NV centres. Functionalisation of the nanodiamond surface may alleviate the issue of agglomeration and combined with ion implantation techniques could allow for commercial quantities of uniform and stable nanodiamond suspension to be formed. HeLa cell viability under room temperature conditions To characterise the time scales of cell death more precisely a cell viability study was conducted on a separate HeLa cell culture prepared under the same conditions described in the methods, and over similar timescale to the quantum measurements outlined in Study 2. Cell viability was measured by Propidium Iodide (PI) nucleic acid stain using flow cytometry. PI is membrane impermeant and excluded from viable cells, which is commonly used for identifying dead cells. After the treatments at specific intervals, HeLa cells were washed with PBS, trypsinized, collected by centrifugation and resuspended in PBS containing 3 µm PI at room temperature for 15 minutes. Positive control was counterstained with 3 µm PI and 0.1% Triton X-100 in PBS at room temperature for 5 minutes. After the staining, FL2 fluorescence intensity of cells were analysed by flow cytometery in the presence of the dye.

3 Supplementary Figure 2: Cell viability of HeLa cells incubated with nanodiamonds and kept at room temperature in PBS, as per the quantum measurement conditions. a) Representative fluorescence intensity histograms of cells. b) Percentage of viable cells quantified by flow cytometry analysis. Data are the mean ± standard deviation of the duplicates, each measured 20,000 cells. (*) p < 0.01 (t-test). As shown in Supplementary Figure 2, untreated cells had viability of ~ 95%. In contrast, positive control was all stained with PI after permeabilised with 0.1% Triton X-100. Cell viability at 5 h, 10 h, and 12 h intervals had no significant changes compared to untreated cells, while cell viability decreased to ~84% at time point of 22 h. Taken together, it suggests that the conditions used to perform the quantum measurements in this study have negligible effect on cell viability up to 12 h. These results are consistent with previous reports on biocompatibility of nanodiamonds 2. Quantum measurements The energy level scheme of the C3v-symmetric NV system (see Figure 1c and 1d) consists of ground (3A), excited (3E) and meta-stable (1A) states. The ground state manifold has spin sublevels (m s = 0, ±1), which in zero field are split by 2.87 GHz. The difference in the fluorescence rate from the NV centre between the m s = 0 and ±1 states (~30%) gives rise to the optically detected

4 magnetic resonance (ODMR) signal. By applying resonant microwave excitation the population of the spin states can be coherently driven between the m s = 0 and +1 ( 1) states. The control sequences used to characterise the Rabi oscillations and spin echo profiles of the NV centres are illustrated in Supplementary Figure nm excitation RF pulse generation Spin readout Rabi /2 /2 spin-echo e measurement time Supplementary Figure 3. Quantum control sequences for Rabi and spin-echo measurements. Analysis of ODMR spectrum variability The distribution of various ODMR spectra for the 45nm nanodiamonds investigated (see Supplementary Figure 4 for a representative sample) can be characterised by two independent parameters; the splitting between the ODMR peaks (E) and the midpoint of the ODMR peaks (D). Measurements on 25 nanodiamonds give a standard deviation of 11 MHz, for the distribution of D and E (Supplementary Figure 5). Summing up the unique combinations of D and E within one standard deviation (with a resolution of 1MHz) gives almost 500 unique combinations. We also observe a small percentage of NV centres displaying coupling to nearby 13 C nuclei. By enriching the abundance of 13 C to 5% one may obtain on average two 13 C nuclei in the first three shells surrounding each NV centre 3. These paramagnetic nuclei produce additional peaks in the hyperfine spectrum, which can be used as further markers to identify individual NV centres. The first three shells have five groups of equivalent carbons, giving 15 unique combinations that

5 containing two 13 C nuclei, not including interactions between 13 C nuclei. When interactions are included, the number of possible combinations increases from 7x10 3 to well over Supplementary Figure 4. Representative ODMR spectra for 45nm nanodiamonds containing single NV centres. The distributions of crystal field splitting D and peak splitting E from the representative set of single NV centres is shown in Supplementary Figure 5 (a) and (b). (a) (b) Supplementary Figure 5. (a) Distribution of crystal field splitting D from the measured set of 25 single NV centres. (b) Distribution of energy splitting E for the same set of centres.

6 Precision Tracking We analyse the contribution to the uncertainty in our quantum probe tracking from three different sources. Photon shot noise, and background fluorescence noise For a vibration free system and fixed probe, the uncertainty in peak location for a line scan along an axis (x) depends solely upon the uncertainty in the diffraction limited spot (x) (i.e. the pointspread function), the detected signal S, the number of samples N in distance Г, and the background and shot noise, b and s respectively. Supplementary Figure 6 shows line scans through x, y and z for NV-2. In our case, where the signal dominates the background, the noise is determined by Poissonian statistics and the position uncertainty 4 at the 1σ level is given by x 1.2 / SN. For the parameters shown in Supplementary Figure 6 this gives an uncertainty in position along each direction of ( x, y, z) (0.6nm, 0.6nm, 1.1nm). Differences in the peak position between the Gaussian fit and the data (seen in Supplementary Figure 6) are thought to be due to asymmetries in optics, refractive index mismatch and additional localised background fluorescence. It is assumed that these effects will only contribute to the accuracy of the peak location, not the precision. It can be seen from this result that using NV centres for tracking can give remarkably high precision, limited only by the time needed to collect photons.

7 Intensity (x10 3 cps) a) R b) R c) X axis ( m) Intensity (x10 3 cps) Y axis ( m) Intensity (x10 3 cps) R Z axis ( m) Supplementary Figure 6. Scans through x, y and z for a nanocrystal inside a living HeLa cell. Vibration/drift of nanopositioner and stage During each line scan along x, y and z, movement of the microscope system will lead to additional position errors not accounted for in the above statistical analysis. In order to calibrate the drift of the set-up, an immobilised nanodiamond attached to the glass coverslip was tracked over a period of 2 hours. The position displacement between consecutive measurements (7 second intervals) was used to determine the repeatability of each peak location and give an estimate for the precision (Supplementary Figure 7). The standard deviation of the displacements calculated in this way are (6nm, 7nm, 11nm) for the (x, y, z) coordinates respectively. It should be noted that this method overestimates the position uncertainty as each line scan was performed in approximately one tenth of the interval time, and the uncertainty is of the same order as the nanopositioner s ability to return to the same position for each scan (<10nm repeatability). The quoted precision given here is therefore expected to be conservative.

8 Supplementary Figure 7. Calibration measurements of positional drift for an immobilised nanodiamond attached to the coverslip over 2 hours. Diffusion of the nanodiamond probe in a living cell Motion of the probe during signal collection will lead to increased position uncertainty in the same way as stage movement. For a freely diffusing nanoparticle of 45nm in size, this movement is expected to be considerable, but we observe that internalised nanodiamonds undergo confined motion, allowing confocal localisation at one second timescales. By plotting the displacement of a single nanodiamond inside HeLa-2 between consecutive tracking intervals (30 s), the motion during a line scan (1 s in x and y directions and 1.5 s in the z direction) can be estimated. This gives the positional uncertainty at the 1σ level of 9 nm in the x and y directions and 22 nm in the z direction. We note that this technique can also be used in conjunction with stimulated emission depletion (STED) microscopy 5 to further improve tracking precision and resolution.

9 Rabi frequency of a slowly rotating nanodiamond The Rabi results are analysed by considering the NV spin in an applied microwave field at an angle to the NV axis within the nanodiamond crystal structure (Figure 4a). The NV Hamiltonian in the presence of an oscillating microwave (MW) field with amplitude B is given by: MW H NV S sin S cos B ( t) S, 2 D S B cos( t) z NV MW 0 x z NV FC where the quantisation axis (z direction) is defined by the NV axis itself, B ( t) FC is the net field due to fluctuations internal (lattice P 1 defects, lattice 13 C nuclei at 1.1% natural abundance and surface spins) and external (intracellular environment) to the nanodiamond, and the driving frequency 0 is determined by ODMR (Figure 2). Changes in fluctuation rates and RMS amplitude within B FC( t) during the cell lifetime directly affect the decoherence time measured in spin-echo 6 (Figure 3). The Rabi frequency is determined by the S x term alone (the S y term can be ignored by symmetry) and is thus governed by the orientation of the quantisation axis with respect to the driving field 7 by ( ) 0 sin (at resonance), where 0 corresponds to the NV axis aligned perpendicular to the MW field. Rotation of the nanodiamond causes the NV axis to rotate in the MW field changing the observed Rabi frequency.

10 Precision and temporal resolution of orientation tracking using ODMR In order to precisely measure the orientation of the NV axis relative to the background field, we must accurately locate the centroid of the Lorentzian shaped spectrum. This is achieved via an iterative process in which the deviation from the true centroid scales as 2 -n Γ after n levels of iteration (where Γ is the linewidth). To distinguish the height of the spectrum at n+1 iterations, S n+1, from that at n iterations, we require the difference ΔS = S n+1 -S n to be less than the noise amplitude in the signal, δs. Since the noise is dictated by shot noise statistics, we expect the noise amplitude to scale with the number of measurements as δs ~ (C N) -1, where C is the spectral contrast. At each level of iteration, we must take sufficient N to ensure δs < ΔS. The number of measurements required at the nth level of iteration is critically dependent on the effective shot count rate R. To determine R, we note that for our setup, a 1000 pt ODMR sweep takes 7s. After 32 sweeps (Supplementary Figure 8), we find the normalised standard deviation of the data to be Since the assumption of shot noise holds, the effective shot count rate is R = ( s) -1 = 868 Hz. For operating conditions of B 0 = 60 G, Γ = 16 MHz and contrast between m s = 0 and m s = 1 states of 30%, the time t required to determine the orientation to precision is: t 4 s, showing that approximately 3 ms of acquisition is required to measure the orientation to within an accuracy of 1 o (δθ = ).

11 Supplementary Figure 8. Shot noise of the ODMR data as a function of the number of sweeps used to determine the ODMR rotation measurement sensitivity. Supplementary References 1. Faklaris, O. et al. Photoluminescent diamond nanoparticles for cell labeling: study of the uptake mechanism in mammalian cells. ACS Nano 3, 3955, (2009). 2. Liu, K. K., Cheng, C. L., Chang, C. C. & Chao, J. I. Biocompatible and detectable carboxylated nanodiamond on human cell. Nanotech. 18, , (2007). 3. Mizuochi, N. et al. Coherence of single spins coupled to a nuclear spin bath of varying density. Phys. Rev. B 80, 4, (2009).

12 4. Bobroff, N. Position measurement with a resolution and noise-limited instrument. Rev. Sci. Instrum. 57, 1152 (1986). 5. Rittweger, E., Han, K. Y., Irvine, S. E., Eggeling, C. & Hell, S. W. STED microscopy reveals crystal colour centres with nanometric resolution. Nat. Photon. 3, (2009). 6. Hall, L. T., Cole, J. H., Hill, C. D. & Hollenberg, L. C. L. Sensing of Fluctuating Nanoscale Magnetic Fields Using Nitrogen-Vacancy Centers in Diamond. Phys. Rev. Lett. 103, (2009). 7. 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).