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Anisotropic interactions of a single spin anddark-spin spectroscopy in diamond

R. J. EPSTEIN, F. M. MENDOZA, Y. K. KATO AND D. D. AWSCHALOM*Center for Spintronics and Quantum Computation, University of California, Santa Barbara, California 93106, USA

*e-mail: awsch@physics.ucsb.edu

Published online: 16 October 2005; doi:10.1038/nphys141

Experiments on single nitrogen–vacancy (N–V) centres indiamond, which include electron spin resonance1, Rabioscillations2, single-shot spin readout3 and two-qubit

operations with a nearby 13C nuclear spin4, show the potential ofthis spin system for solid-state quantum information processing.Moreover, N–V centre ensembles can have spin-coherence timesexceeding 50 μs at room temperature5. We have developedan angle-resolved magneto-photoluminescence microscopeapparatus to investigate the anisotropic electron-spin interactionsof single N–V centres at room temperature. We observenegative peaks in the photoluminescence as a function ofboth magnetic-field magnitude and angle that are explainedby coherent spin precession and anisotropic relaxation atspin-level anti-crossings. In addition, precise field alignmentunmasks the resonant coupling to neighbouring ‘dark’ nitrogenspins, otherwise undetected by photoluminescence. These resultsdemonstrate the capability of our spectroscopic technique formeasuring small numbers of dark spins by means of a singlebright spin under ambient conditions.

The N–V defect pair, with trigonal symmetry6, has ananisotropic electron-spin hamiltonian owing to spin–spin andspin–orbit interactions7. Consequently, the degrees of spin-levelmixing and coupling to nearby impurity spins are very sensitiveto the orientation of an applied magnetic field, which hasnot been controlled in experiments on single N–V centres.Figure 1a depicts the atomic structure and relevant energy levelsof the (negatively charged) N–V centre. The triplet (3A) groundstate8–10 has a zero-field splitting between the |mS = 0〉 and|mS = ±1〉 spin sublevels, where mS is the quantum number ofthe spin sublevel, quantized along the N–V symmetry axis, a 〈111〉crystal axis11. Zero-field spin splittings have also been measuredin the triplet (3E) excited state but there is no consensus on thearrangement of sublevels12–15. Linearly polarized optical excitationof the 3A → 3E transition preferentially pumps the spin system intothe |0〉 ground-state sublevel16. In addition, the average photon-emission rate is substantially smaller for transitions involving the|±1〉 levels than for the |0〉 level3, which enables the spin stateto be determined by the photoluminescence intensity IPL. Bothof the latter two effects have been attributed to spin-dependentintersystem crossing to the singlet (1A) level11,17.

The single-crystal samples investigated here are commerciallyavailable (Sumitomo Electric Industries) high-temperature high-pressure diamond with two polished parallel (100) surfaces andnominal dimensions of 1.4 mm×1.4 mm×1.0 mm. They containnitrogen impurities with densities of 1019−1020 cm−3, measuredby ultraviolet absorption18. N–V centres are naturally present withsubstantially lower densities ranging from 1010 to 1013 cm−3. Forensemble measurements, samples are irradiated with 1.7-MeVelectrons with a dose of 5×1017 cm−3 and subsequently annealed at900 ◦C for 2 h to increase the N–V centre concentration6.

The phonon-broadened 3E → 3A transition of the N–Vcentre is detected by means of non-resonant photoluminescencemicroscopy (see Methods). For example, Fig. 1b is a spatialimage of the spectrally integrated photoluminescence from adiamond sample with the laser focused roughly 1 μm below thesurface. Multiple resolution-limited features are observed in the20 μm×20 μm field. In order to determine that a given feature is

due to a single emitter, a histogram is plotted of the time τ betweenconsecutive photon detection events using a Hanbury Brown andTwiss detection geometry19, yielding the experimental intensitycorrelation function g(2)(τ). Figure 1c shows the data from a colourcentre labelled NV1. The value of g(2)(0) is below 0.5, proving thatNV1 is a single-colour centre20. In addition, the rise of g(2)(τ) aboveunity with increasing |τ| is indicative of intersystem crossing to the1A metastable state20,21.

These single-photon emitters are further characterized byoptically detected electron spin resonance (ESR; see Methods).Figure 1d contains data from NV1 with zero applied magneticfield. In this case, the |±1〉 ground-state levels are degenerate sothat only one resonance (mS = 0 → ±1) is observed at 2.87 GHz,the characteristic zero-field splitting of N–V centres11. The dataare fit with a lorentzian of 11 MHz full-width at half-maximum(solid line), which is comparable to reported values in similardiamond samples1.

Strain-dependent optical measurements on ensembles of N–Vcentres have indicated that electric dipole transitions are allowedfor dipoles in the plane perpendicular to the symmetry axis6.Figure 2a depicts an N–V centre with transition dipoles X ‖ [1̄1̄2]and Y ‖ [11̄0] in a (111) plane. The excitation is along [001] for allmeasurements, therefore IPL depends on the laser polarization angle

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2.80 2.85 2.900

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ount

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ντ

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) (τ)τ

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c

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Figure 1 Characterization of single N–V centres. a, The atomic structure and relevant energy levels. The green ‘bond’ depicts the N–V symmetry axis. b, The spatial imageof IPL on a linear colour scale, showing the emission from several N–V centres; NV1–NV4 (left to right) are marked. c, The intensity correlation function g (2) (τ ) versus τ forNV1, indicating single photon emission. d, Optically detected ESR for NV1. IPL versus microwave frequency νMW (circles) with a lorentzian fit (solid line). The laser power is1 mW for b and 370 μW for c and d.

ν

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YX

Figure 2 Polarization and magnetic-field anisotropies. a, Measurement geometry indicating transition dipoles X and Y. b, Normalized IPL (radial axis) versus the laserpolarization angle φ for NV1, NV2 and NV3. Polarization along [11̄0] corresponds to φ = 0◦ and data at φ and φ+180◦ are identical. c, Upper panel: calculatedground-state spin splitting ν as a function of B for θ = 6◦ (solid lines) and 54.7◦ (dashed lines). Middle panel: overlap |α|2 of each spin level with |0〉z at the same twoangles. Lower panel: IPL versus B for NV1, NV2 and NV3, with ∼1◦ angle between B and [111]. The laser power is 370 μW for b and 1 mW for c.

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– 4 – 2 0 2 4θ (°)

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Figure 3 Controlled level mixing by means of magnetic-field alignment. a, IPL versus B for NV1 at specified magnetic-field angles θ. b, Zoom of data in a (points) with fits(lines) to model described in the text. Data for θ = 0◦ are taken with smaller field steps and fit with an angle of 0.2◦ to account for residual spin mixing (see the text). c, IPL

versus B for NV4 (points) and fits (lines) at specified field angles. d, Normalized amplitudes A (points) of LAC and 500-G peaks versus θ with fits (lines). Laser power is 1 mWfor NV1 and 2.9 mW for NV4.

φ owing to unequal excitation of the two dipoles. The dependenceof IPL on φ is measured for 20 N–V centres and shows either verticalor horizontal lobes, as exemplified for three N–V centres in Fig. 2b.The measured anisotropies, defined as the ratio IPL(φ = 0◦)/IPL

(φ = 90◦), are roughly 2:1 and 1:2 on average; a simple anisotropycalculation gives 3:1, 3:1, 1:3 and 1:3 for the N–V symmetry axisalong [111], [1̄1̄1], [11̄1] and [1̄11], respectively (see Methods).The measured data are modified by the presence of polarizedbackground photoluminescence (subtracted from the data) and asmall dip, most visible for NV2 at φ = 0◦, which varies in depthfrom centre to centre. Nevertheless, comparison of the measuredand calculated anisotropies enables the number of possibleorientations of a given centre to be reduced from four to two.

The double degeneracy of the polarization anisotropy islifted by application of a magnetic field B. The upper panelof Fig. 2c shows the ground-state spin levels as a functionof B (the amplitude of B) calculated using the hamiltonian7

H = gμBB ·S+D(S2z −S(S+1)/3), where μB is the Bohr magneton,

g = 2.00 is the electron g-factor, S is the total electron spin withmagnitude S = 1 and D = 2.88 GHz is the ground-state spinsplitting. A level anti-crossing (LAC) near 1,000 G is predictedfor an N–V centre with symmetry axis at a small angle to B (6◦;solid lines), but not for a large angle (54.7◦; dashed lines). Themiddle panel shows |α|2, the overlap of |0〉z with each spin level,

|mS〉 = α|0〉z +β|−1〉z +γ|+1〉z, where |β|2 and |γ|2 are the otherrespective overlaps and the subscript z denotes the [111] basis; theevolution of |α|2 with B, calculated for both angles, illustrates themixing of spin states and will be relevant in modelling the data. Thelower panel is a plot of IPL as a function of B, with an angle of ∼1◦

between B and [111], for the same three N–V centres as in Fig. 2b.Whereas NV1 and NV2 have similar polarization dependences,their field dependences show that the symmetry axis of NV1 (NV2)is (non-)parallel to B. For NV1, the negative peak at ∼1,000 Gcoincides with the calculated LAC. In addition, NV1 shows a peakat ∼500 G, the origin of which is less clear.

In order to investigate these peaks further, IPL is measured asa function of B with B at a series of angles θ in the (11̄0) plane;a selection of such data from NV1 is shown in Fig. 3a. As Bapproaches the [111] direction (θ → 0◦), the LAC peak narrows,as expected from ensemble measurements22,23. At sufficiently smallangles, however, the LAC peak amplitude decreases for NV1(Fig. 3b) or even vanishes for some centres, such as NV4 (Fig. 3c).This is in contrast to the ensemble measurements22,23 that showeda maximum in the LAC peak amplitude at θ = 0◦. According tothe hamiltonian above, however, spin mixing should vanish atθ = 0◦. The presence of residual spin mixing at θ = 0◦ has beenattributed to strain and nuclear interactions24, which vary fromcentre to centre.

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Figure 4 Resonant coupling of a single spin to neighbouring spins. a, IPL versus B for an ensemble of N–V centres at two field angles. Inset: higher-resolution scansaround 500 G showing the nitrogen hyperfine structure. b, A single N–V centre (NV4) coupling to several nitrogen centres. IPL versus B at two indicated field angles with300 μW laser power. c, IPL versus B at two indicated laser powers for NV1, showing broadening of nitrogen peaks with increased power. For a (inset), b and c, a small linearbackground is subtracted from the data.

The LAC can be modelled for small values of θ by considering|0〉 and |−1〉 as pseudo-spin-1/2 states. With preferentialpopulation of |0〉z, the |+1〉 level is ignored because it has anegligible overlap with |0〉z (see Fig. 2c, middle panel). We thenhave an effective hamiltonian H = gμB(B − B0) · s, where B0

accounts for the zero-field spin splitting and s is the pseudo-spinoperator. The Bloch equations for B in the (11̄0) plane aretaken to be dsx

dt= −Ωzsy − sx

T2

,

dsy

dt=Ωzsx −Ωxsz − sy

T2

,

dsz

dt=Ωxsy − sz

T1

+Γ ,

(1)

where h̄� = gμB(B − B0), h̄ is the reduced Planck constant,� = (Ωx,Ωy,Ωz) is the Larmor precession vector, x ‖ [1̄1̄2],y‖[11̄0], B0 ‖z‖[111],Γ is the rate of optical spin orientation alongz, and T1 and T2 are effective spin relaxation times that depend onΓ (see Methods). In this model, the spin relaxation is anisotropicin that T1 and T2 are fixed relative to the crystal axes rather than themagnetic field. The steady-state solution for sz is

sz = T1Γ (1+Ω 2z T2

2 )

1+Ω 2x T1T2 +Ω 2

z T22

.

We then take IPL = an0 +bn−1 = a(1/2+ sz)+b(1/2− sz), where aand b (n0 and n−1) are the photoluminescence rates (occupation

probabilities) for the |0〉z and |−1〉z levels, respectively. This simplemodel describes the experimental data for a wide range of anglesand magnetic fields, where the same fit parameters are used for allangles (Fig. 3b,c lines). The fits yield T1 = 64 ns and T2 = 11 ns forNV4 using a laser power of 2.9 mW (Fig. 3c) and T1 = 130 ns andT2 = 23 ns for a power of 900 μW (not shown). The results indicatethat the laser introduces substantial anisotropic spin relaxation bymeans of excitation out of the ground-state manifold. This sourceof decoherence can be mitigated through pulsed excitation4.

The 500-G peak evolves similarly to the LAC peak but over abroader angular range. It has nearly the same amplitude and widthat a given field angle for all N–V centres investigated with suitableorientation. In addition, the peak has been observed in all foursamples measured. The evolution of the 500-G peak with θ andB can be reasonably accounted for in the model by postulating anLAC in the excited state, as is expected to occur at some field owingto the presence of zero-field spin splittings12–14. Figure 3d shows thenormalized amplitudes A of the 500-G and LAC (1,000-G) peaks asa function of θ. Fits of the model to this data (red lines) and to thefield scans (fits not shown) yield T1 = 36 ns and T2 = 1.8 ns for anexcited-state LAC at ∼500 G.

Similar data are taken on ensembles of N–V centres in Fig. 4a,where the 500-G peak is found to reduce in amplitude by ∼50%at θ = 0◦. In addition, higher-resolution field scans around 500 G(Fig. 4a, inset) show a quintuplet of peaks characteristic of thehyperfine structure of substitutional nitrogen (NS) centres25. Thesepeaks appear when the magnetic field tunes the electron spinsplitting of N–V centres into resonance with the many surrounding

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NS centres, resulting in enhanced cross-relaxation by means of themagnetic dipole interaction26–28. Notably, the NS peak amplitudesdiminish as |θ| increases, suggesting that the 500-G peak isassociated with a decrease in spin polarization, like the LAC peak.

The above results point to a regime (|θ| < 1◦) where thedepolarizing effects of the 500-G peak are mitigated, showing thecoupling of a single N–V centre to its neighbouring NS spins.Figure 4b shows two field scans of IPL for NV4 at θ = 0◦ and 1◦;the NS resonances become visible with a sufficiently small anglebetween B and [111]. Figure 4c shows similar data for NV1 atθ = 0◦ with powers of 300 and 900 μW; the NS peaks broaden anddiminish in relative magnitude at higher power, possibly resultingfrom ionization of the NS centres29. The depths of the NS peaks,differing for NV4 and NV1, are sensitive to the particular spatialdistribution of nearby nitrogen spins.

Finally, it is worth noting that the NS centres are ‘dark’ inthat they are not directly detected by photoluminescence. Bymeasuring a single N–V centre, the number of NS spins that canbe probed is decreased by orders of magnitude relative to theensemble measurements. Furthermore, this dark-spin spectroscopytechnique is in principle applicable to a variety of paramagneticdefects in diamond. With higher purity samples and single-ionimplantation30, these results could make possible the long-rangecoupling of two individually addressable N–V centres connectedby a chain of dark spins, enabling experimental tests of spin-latticetheories and quantum information processing schemes.

METHODSEXPERIMENTAL TECHNIQUES

The measurement apparatus is based on a confocal microscope with a HanburyBrown and Twiss detection scheme19. A diode-pumped solid-state laseremitting at 532 nm is linearly polarized and focused onto the sample with amicroscope objective of numerical aperture 0.73 and working distance 4.7 mm.The linear polarization is set to any desired angle by changing the retardance ofa variable wave plate (fast axis at 45◦ to the initially vertical polarization)followed by a quarter-wave plate (fast axis vertical). The laser spot is positionedon the sample in both lateral dimensions with a fast steering mirror. Thephotoluminescence from the sample is collected by the same microscopeobjective, passed through a dichroic mirror and a 640-nm long-pass filter, andsent through a 50/50 beam-splitter to two fibre-coupled silicon avalanchephotodiode modules.

For antibunching measurements, the outputs of the detectors areconnected to a time-correlated single-photon counting module. The data arenormalized by the detector count rates, time bin width and total integrationtime to yield g(2)(τ). The data are not corrected for backgroundphotoluminescence. For measurements of N–V centre ensembles,photoluminescence is detected with a photodiode and lock-in amplifier.In general, the photoluminescence is used as a feedback signal to compensatefor thermal drift, enabling a single N–V centre to be tracked for several days.The samples are at room temperature for all measurements discussed inthis letter.

The static magnetic field B is applied to the sample with a permanentmagnet mounted on a multiaxis stage that allows the distance between themagnet and the sample to be adjusted by a stepper motor, thereby setting B atthe sample. In addition, the polar and azimuthal angles of B are manuallyadjustable with micrometers while keeping B constant at the sample to betterthan 1%. For ESR measurements, a 25-μm-diameter gold wire is connected to amicrowave signal generator (with 16 dB m power output) and placed in closeproximity (∼50 μm) to the laser spot.

POLARIZATION ANISOTROPY CALCULATION

According to Fermi’s golden rule in the electric dipole approximation, theabsorption rate is proportional to |D ·E|2, where D is the dipole matrix elementand E is the excitation electric-field vector. The absorption anisotropy isestimated to be |Y ·V|2/|X ·H|2, where X and Y are the dipoles (see Fig. 2a) andV ‖ [11̄0] and H ‖ [110] are polarization vectors. A more accurate calculationwould account for the dipole radiation pattern, the large numerical aperture of

the microscope objective and refraction at the diamond–air boundary.However, the simple equation above is sufficient to explain both the anisotropyorientations and degeneracies that are measured.

BLOCH EQUATION SIMPLIFICATIONS

Equation (1) has been simplified by defining effective relaxation times T1 andT2 that depend on Γ . Explicitly, (T1)

−1 = (Tz)−1 +2Γ , where Tz is the intrinsic

relaxation time of sz . Likewise, T2 has a similar form. As Γ is proportional tothe laser power, the equation above explains why T1 and T2 decrease withincreasing power, as observed in the experiments.

Received 29 July 2005; accepted 6 September 2005; published 16 October 2005.

References1. Gruber, A. et al. Scanning confocal optical microscopy and magnetic resonance on single defect

centers. Science 276, 2012–2014 (1997).2. Jelezko, F., Gaebel, T., Popa, I., Gruber, A. & Wrachtrup, J. Observation of coherent oscillations in a

single electron spin. Phys. Rev. Lett. 92, 076401 (2004).3. Jelezko, F. et al. Single spin states in a defect center resolved by optical spectroscopy. Appl. Phys. Lett.

81, 2160–2162 (2002).4. Jelezko, F. et al. Observation of coherent oscillation of a single nuclear spin and realization of a

two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501 (2004).5. Kennedy, T. A., Colton, J. S., Butler, J. E., Linares, R. C. & Doering, P. J. Long coherence times at 300 K

for nitrogen-vacancy center spins in diamond grown by chemical vapor deposition. Appl. Phys. Lett.83, 4190–4192 (2003).

6. Davies, G. & Hamer, M. F. Optical studies of the 1.945 eV vibronic band in diamond. Proc. R. Soc. A348, 285–298 (1976).

7. Pryce, M. H. L. A modified perturbation procedure for a problem in paramagnetism. Proc. Phys. Soc.A 63, 25–29 (1950).

8. Reddy, N. R. S., Manson, N. B. & Krausz, E. R. Two-laser spectral hole burning in a colour centre indiamond. J. Lumin. 38, 46–47 (1987).

9. van Oort, E., Manson, N. B. & Glasbeek, M. Optically detected spin coherence of the diamond N-Vcentre in its triplet ground state. J. Phys. C 21, 4385–4391 (1988).

10. Redman, D. A., Brown, S., Sands, R. H. & Rand, S. C. Spin dynamics and electronic states of N-Vcenters in diamond by EPR and four-wave-mixing spectroscopy. Phys. Rev. Lett. 67,3420–3423 (1991).

11. Loubser, J. H. N. & van Wyk, J. A. Electron spin resonance in the study of diamond. Rep. Prog. Phys.41, 1201–1248 (1978).

12. Redman, D., Brown, S. & Rand, S. C. Origin of persistent hole burning of N-V centers in diamond.J. Opt. Soc. Am. B 9, 768–774 (1992).

13. Manson, N. B. & Wei, C. Transient hole-burning in N-V centre in diamond. J. Lumin. 58,158–160 (1994).

14. Lenef, A. et al. Electronic structure of the N-V center in diamond: experiments. Phys. Rev. B 53,13427–13440 (1996).

15. Martin, J. P. D. Fine structure of excited 3E state in nitrogen-vacancy centre of diamond. J. Lumin. 81,237–247 (1999).

16. Harrison, J., Sellars, M. J. & Manson, N. B. Optical spin polarization of the N-V centre in diamond.J. Lumin. 107, 245–248 (2004).

17. Nizovtsev, A. P. et al. NV centers in diamond: spin-selective photokinetics, optical ground state spinalignment and hole burning. Physica B 340–342, 106–110 (2003).

18. Kaiser, W. & Bond, W. L. Nitrogen, a major impurity in common type I diamond. Phys. Rev. 115,857–863 (1959).

19. Hanbury Brown, R. & Twiss, R. Q. Correlation between photons in two coherent beams of light.Nature 177, 27–29 (1956).

20. Kurtsiefer, C., Mayer, S., Zarda, P. & Weinfurter, H. Stable solid-state source of single photons. Phys.Rev. Lett. 85, 290–293 (2000).

21. Beveratos, A., Brouri, R., Poizat, J.-P. & Grangier, P. in Quantum Communication, Computing andMeasurement 3 (eds Tombesi, P. & Hirota, O.) 261–267 (Kluwer Academic/Plenum, New York, 2001).

22. van Oort, E. & Glasbeek, M. Fluorescence detected level-anticrossing and spin coherence of alocalized triplet state in diamond. Chem. Phys. 152, 365–373 (1991).

23. Martin, J. P. D. et al. Spectral hole burning and Raman heterodyne signals associated with an avoidedcrossing in the NV centre in diamond. J. Lumin. 86, 355–362 (2000).

24. He, X. -F., Manson, N. B. & Fisk, P. T. H. Paramagnetic resonance of photoexcited N-V defects indiamond. I. Level anticrossing in the 3A ground state. Phys. Rev. B 47, 8809–8815 (1993).

25. Smith, W. V., Sorokin, P. P., Gelles, I. L. & Lasher, G. J. Electron spin resonance of nitrogen donors indiamond. Phys. Rev. 115, 1546–1552 (1959).

26. Holliday, K., Manson, N. B., Glasbeek, M. & van Oort, E. Optical hole-bleaching by levelanti-crossing and cross relaxation in the N-V centre in diamond. J. Phys. C 1, 7093–7102 (1989).

27. van Oort, E. & Glasbeek, M. Cross-relaxation dynamics of optically excited N-V centers in diamond.Phys. Rev. B 40, 6509–6517 (1989).

28. van Oort, E., Stroomer, P. & Glasbeek, M. Low-field optically detected magnetic resonance of acoupled triplet-doublet defect pair in diamond. Phys. Rev. B 42, 8605–8608 (1990).

29. Farrer, R. G. On the substitutional nitrogen donor in diamond. Solid State Commun. 7,685–688 (1969).

30. Meijer, J. et al. Generation of single colour centers by focussed nitrogen implantation. Preprint athttp://arxiv.org/abs/cond-mat/0505063 (2005).

AcknowledgementsWe thank O. Gywat for valuable discussions and G. C. Farlow for high-energy electron irradiation ofseveral samples. This work was supported by AFOSR, DARPA/MARCO and ARO.Correspondence and requests for materials should be addressed to D.D.A.

Competing financial interestsThe authors declare that they have no competing financial interests.

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