RAPID COMMUNICATIONSPHYSICAL REVIEW B 90, 081117(R) (2014)

Isotopic identification of engineered nitrogen-vacancy spin qubits in ultrapure diamond
T. Yamamoto,1,2,* S. Onoda,2 T. Ohshima,2 T. Teraji,1 K. Watanabe,1 S. Koizumi,1 T. Umeda,3 L. P. McGuinness,4 C. Müller,4B. Naydenov,4 F. Dolde,5 H. Fedder,5 J. Honert,5 M. L. Markham,6 D. J. Twitchen,6 J. Wrachtrup,5 F. Jelezko,4 and J. Isoya7
1

National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
2
Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan
3
Institute of Applied Physics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
4
Institute for Quantum Optics, University of Ulm, D-89081, Ulm, Germany
5
3rd Physics Institute and Research Center SCoPE, University of Stuttgart, D-70174, Stuttgart, Germany
6
Element Six Limited, King’s Ride Park, Ascot, Berkshire, SL5 8BP, United Kingdom
7
Research Center for Knowledge Communities, University of Tsukuba, 1-2 Kasuga, Tsukuba, Ibaraki 305-8550, Japan(Received 26 June 2014; revised manuscript received 19 August 2014; published 29 August 2014)
Nitrogen impurities help to stabilize the negatively-charged-state of NV− in diamond, whereas magnetic
fluctuations from nitrogen spins lead to decoherence of NV− qubits. It is not known what donor concentration
optimizes these conflicting requirements. Here we used 10-MeV 15 N3+ ion implantation to create NV− inultrapure diamond. Optically detected magnetic resonance of single centers revealed a high creation yield of
40 ± 3% from 15 N3+ ions and an additional yield of 56 ± 3% from 14 N impurities. High-temperature anneal wasused to reduce residual defects, and charge stable NV− , even in a dilute 14 N impurity concentration of 0.06 ppb
were created with long coherence times.
DOI: 10.1103/PhysRevB.90.081117

PACS number(s): 76.30.Mi, 61.80.−x, 76.70.Hb

The realization of quantum registers, which are comprisedof several quantum bits (qubits), is currently a central issue
in quantum information and computation science [1]. Among
many competing quantum systems, photoactive defect spinsof negatively charged nitrogen vacancy (NV− ) centers indiamond are unique solid-state qubits, due in part to ambientpressure and temperature operation [2–4]. The NV− center
is a single-photon emitter with zero-phonon-line (ZPL) at
637 nm [5], where both of 3A2 electronic ground and 3E excitedstates locate inside the diamond band-gap. The spin sublevels,|ms = 0 and |ms = ±1, of the triplet (S = 1) ground state
are separated by ∼2.87 GHz due to spin-spin interaction[6]. Arbitrary states including superpositions of spin levels
may be created by resonant microwave pulses after optical
initialization, and then readout by measuring fluorescenceintensity [3]. Experimental proofs of strongly-coupled NV−
spins, [7–9] magnetic coupling between a NV− spin andanother electron spin [9,10] or nuclear spins, [11–15], in
addition to coupling to photons [16,17] or optical cavities[18–20], exemplify the robust yet mutable nature of the NV
scheme as well as the beginnings of scalability.
The NV quantum coherence decays in time due to magnetic
fluctuations from substitutional nitrogen (N0s ) electron spins
and 13 C nuclear spins, and spin-lattice relaxation [21–23].
Thus the use of high purity ([N0s ] ∼ ppb) type IIa diamondswith reduced 13 C content, and position controlled N ion
implantation to create NV− centers, is a promising avenue
towards a high quality multiqubit system [8]. Nevertheless,substitutional nitrogen impurities, which donate electrons to
NV centers, are actually essential for stabilizing the NV−
charge state [24]. The negative NV charge state is predominantat thermal equilibrium if [Ns ] = [N0s + N+s ] > [NV], and thisis generally true for isolated NV centers in type Ib diamond([N0s ] ∼ 20–200 ppm) [25–27]. With decreasing N0s donor*

yamamoto.takashi@nims.go.jp

1098-0121/2014/90(8)/081117(6)concentration, microscopic distributions of donors surrounding each NV center are significant for the charge state, rather
than the Fermi position relative to the ground state of NV− . As
a result locally inhomogenous distributions of either NV0 or
NV− are expected [28]. This may explain the relatively large
reduction in NV− population observed by photoluminescence
spectroscopy in type IIa diamonds ([N0s ] ∼ 30–300 ppb) [26].
The presence of the neutral NV0 charge state (S = 1/2) isundesirable as its applications are hindered by rapid dephasingin the ground state. Therefore the understanding of a minimum
concentration threshold of N0s impurities in order to form stable
NV− spin qubits is of concern for reliable engineering andscalability.
In this study, we isotopically distinguish engineered 15 NV−
spin qubits due to 15 N implantation from 14 NV− due topreexisting 14 N impurities in ultrapure diamond, both ofwhich can be created by 15 N3+ (10 MeV) implantation. Usinga combination of confocal microscopy and spin resonance,
we observe an implantation creation yield of ∼100%, ofwhich 14 NV− centers comprise more than half this value. The
nitrogen concentration of less than 0.1 ppb is low enough toattain long coherence times (∼2 ms) and sufficient to stabilize
the charge state of NV− qubits, under reduced concentrationsof residual defects by high-temperature anneal.
In experiments, a high-purity, 99.99% 12 C-enriched(0.01%-13 C) homoepitaxial diamond (Element Six Ltd.)grown by chemical vapor deposition was used. The concentration of N impurities was expected to be less than 0.1 ppb
from the crystal growth condition [29,30], which is far below
the detection limit of secondary ion mass spectroscopy orelectron spin resonance for the film thickness here. 15 N3+ ionswith an incident energy of 10 MeV per ion were implanted
into the (100) crystal surface. By scanning a microbeam offull-width at half-maximum (FWHM) size ∼1.5 μm, a squaregrid of implantation sites separated by ∼8 μm was created[Fig. 1(a)]. The average number of implanted ions was 2.8
per implantation site by measuring the beam flux before and081117-1©2014 American Physical Society

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PHYSICAL REVIEW B 90, 081117(R) (2014)

(a)
100

5 μm

15

NV-

14

Photons (kcps)

S12
S8

NV-

14

S13

S14

S9

S10

S15
S11

S4

S5

S6

S7

S0

S1

S2

S3

Photons (kcps)

0
(b)
36
35

data

Ab Ab

2900

2905

2910
2915
2920
Microwave frequency (MHz)Photons (a.u.)

(c)
2x103

Number(d)Aa

A a = 3.1 MHz
A b = 2.2 MHz

2925

2930

850

900

638 nm ZPL

1
0
550
8
6
4
2
0

600

650

700
750
Wavelength (nm)

800
15

NV-

NV− centers, rather, all pairs were formed by one eachof 15 N and 14 N. This agrees with a numerically estimatedformation probability of ∼1% for 15 NV− pairs locating withina ∼0.3 μm laser spot, when given our microbeam size (FWHM
of 1.5 μm).
Room-temperature photoluminescence (PL) spectra werealso measured for individual centers with 0.5 mW of 532-nm
excitation (into the objective) and an accumulation time of 30 s.
Recent studies have shown that dynamical charge conversion
between NV− and NV0 occurs under illumination, and thecontrollable dynamics has been discussed [34–38]. Both NV−
and NV0 may be observed even for a single NV center, with
time-averaged PL spectroscopy, if significant photoconversion
appears during optical pumping (for example, see Ref. [39]).
However, we observed characteristic spectrum of the negative
charge state from all 14 NV− and 15 NV− centers: [40] a weakzero-phonon-line (ZPL) at 638 nm accompanied with broad
vibronic sidebands [Fig. 1(c)]. No distinct signals of NV0
charge states (575-nm ZPL) were found, at least within theaccumulation time of 30 s. Two centers that did not show an
ODMR signal, indicated by black arrows in Fig. 1(a), were
unknown centers since their PL spectra were different fromeither NV− or NV0 .
Additional spins belonging to paramagnetic residual defects, resulting from the implantation and anneal process, may
dominate the decoherence of implanted NV− spins [41,42].
Also, residual point defects such as divacancies may act as
accepters [43] to ionize NV− to NV0 . To overcome theseobstacles, high-temperature anneal has been shown to beeffective in reducing the concentration of residual paramagnetic defects at 1000 ◦ C [41,44,45], with a concomitant
increased population of NVs with long coherence times[42] and improved spectral stability [46] when compared to800 ◦ C anneal. Previous studies have also investigated NV
charge instability due to residual defects after ion implantation[10,33,39,47–52], neutron [24] or electron irradiation [27],and anneal temperatures of 600–900 ◦ C, while effects fromthe surface are additionally involved in shallow implantation
studies [53–57]. In the present work, both high temperatureanneal and high energy implantation were performed toprovide a clean environment with minimal degradation of theNV− properties.
Figure 1(d) shows the number of 14 NV− and 15 NV−
centers at each implantation site in Fig. 1(a), labeled by Sj(j = 0,1,2, . . . ,15). In total, eighteen 15 NV− and 25 14 NV−
were created from 45 implanted 15 N ions (2.8 × 16) in thesixteen implantation sites. Dividing the number of created
NV− centers by the number of implanted 15 N ions gives acreation yield of Y = 40 ± 3% for 15 NV− and 56 ± 3% for14
NV− , where the NV− centers indicated by the white arrows
in Fig. 1(a) were excluded for the counting since these centers
are far from an implantation site and might be owing to a
misshit. As reported in Ref. [41], the spin coherence times (T2 )in this implantation area were ∼2 ms at room temperature,
which are the longest among implanted NV− qubits, andcomparable to the longest recorded for naturally-formed NV−
centers during crystal growth [30,58,59]. In addition to a total
yield of 96%, we also obtained ∼100% yield for implanted
NV− centers with T2 times up to 1.6 ms in another highpurity 12 C − 99.99% enriched diamond (Element Six Ltd.)15

NV-+15NV-

14

NV-

S0 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15
Implantation site

FIG. 1. (Color online) (a) Confocal microscope image of lateral(xy plane) distribution of NV− centers with 532-nm excitation
at a depth of ∼3.8 μm (left). The white dashed lines indicate acalculated square grid of implantation sites (2.8 ions/site) [40]. The
fluorescent spots indicated by black arrows were unknown centers(see text). The map of NV− centers identified by ODMR (right):
15
NV− (solid circle), 14 NV− (open circle), and 14 NV− −15 NV− pairs(cross). (b) ODMR spectrum of an NV− pair comprised of 14 NV−(hyperfine splitting of A = 2.2 MHz) and 15 NV− (A = 3.1 MHz) in
the transition of |ms = 0 ⇔ |ms = +1. (c) PL spectrum of an 15 NV−
center with 532-nm excitation. (d) The number of 15 NV− (black bar)and 14 NV− (white bar) in each implantation site.

after implantation [31,32]. To form NV centers, the sample
was annealed at 1000 ◦ C for 2 h in a vacuum of ∼10−6 Torr.
Observation of hyperfine structure of either 15 N (with anuclear spin of I = 1/2, natural abundance 0.37%) or 14 N
(I = 1, 99.63%) by optically detected magnetic resonance(ODMR) spectroscopy allowed determination of whether theinvestigated NV− centers were due to 15 N implants or 14 N
impurities already present in the epitaxial layer [Fig. 1(a)] [33].
The ODMR spectra were measured at room temperature, undera static magnetic field of ∼2 mT in order to separate the twotransitions: |ms = 0⇔|ms = +1 and |ms = 0⇔|ms = −1.
ODMR was able to resolve NV− pairs with different axis orientations when their separation is below the confocal resolution[Fig. 1(b)]: the triplet and doublet hyperfine structures show
14
NV− with hyperfine constant A = 2.2 MHz and 15 NV−with A = 3.1 MHz, respectively. No pairs consisted of two

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Atoms/μm/ion

Vacancies/μm/ion

A 15
B 14

4

B

A

2
B

0

A
A
BP
15

B

B

P
B

A

B

A

4
2
0

B
AA

4.0

3.2

e

2.8

3.0

h(

t
Dep

3.8

B

3.2 3.6

B
14

4.2

B
B

NV-+15NV-

A

P

B
P

B

NV-

NV-

P 14

3.4

S0
S1 2
S
S3 4
S
S5
S67
S 8
S 9
S
S 1011S 2
S1 3
S 1 14
S 15
S

P
A
A
BAA

B

sit

m)

0

where Nq /Ni is the ratio of the number of implanted 15 N
ions (Ni ) to the number of 15 NV− created by implantation(Nq ). The product Ni Pr gives the number of substitutional

6

ion

(1)

15

tat

Nq (cv )Ni Pr=
Pt (cv ),
Ni
Ni

1200
1000
800
600
400
200
0

ms
N ato es
nci
Vaca

10
8

lan

Y (cv ) =

2.8

0

4.2

)
.0
.8 4
h (μm
Dept
.6 3
3
3.4
3.2
3.0

p
Im

by similar implantation and annealing process (data notshown).
Low-energy (10–30 keV) nitrogen ion implantation has
provided creation yields of 20%–21% [9,49], which is justbelow the maximum expected value of 25% [60]. Comparedto this, high-energy (18 MeV) implantation has exhibited
45% yield, which was interpreted due to the increased
number of vacancies generated by increasing the implantationenergy [50]. However, NV centers comprised of preexisting
N impurities may also be counted in the yield, and thus thecreation efficiency should change with the concentration of[N0s ] in each sample.
To investigate further the creation of 14 NV− and 15 NV−
centers, we measured the spatial distributions of each centerby confocal microscopy. A diffraction-limited fluorescencespot from a single center has a lateral diameter (xy plane) of∼0.3 μm and a diameter of ∼0.7 μm along the optical axis
(z axis). To measure the coordinates, (x,y,z), of individualNV− centers with high precision, we used a Gaussian fit tofind the position of maximal intensity of the fluorescenceprofile, giving an accuracy of <0.1 μm in all axis directions.
NV− pairs were inseparable by fitting and thus measured
as at the same position [40]. We compared the observed
spatial distribution of NV− centers, to the computed statistical
distributions of implanted 15 N atoms and vacancies using
stopping and range of ions in matter (SRIM) Monte Carlo [61](a displacement energy of 37.5 eV [62], a diamond densityof 3.52 g/cm3 , and 8 × 104 of incident 15 N ions were used).
By using the vacancy distribution computed by SRIM, wethen simulated a statistical vacancy distribution
after diffusion√
with an isotropic diffusion length of 2Dt ≈ 0.08 μm, where
D = D0 exp[−Ea /(kB T )], with diffusion coefficient D0 =3.7 × 10−6 cm2 /s (Ref. [63]), Boltzmann’s constant kB =1.4 × 10−23 T/K, activation energy Ea = 2.3 eV (Ref. [64]),temperature T = 1273 K, and time t = 7200 s. [40]Experiments showed no obvious difference in the lateral(xy-plane) distributions between 15 NV− and 14 NV− centers[40]. On the other hand, we observed differences in depth(z-axis) distributions between the two nitrogen sources: themean depth of 3.5 ± 0.3 μm for 14 NV− was shallower thanthat of 3.8 ± 0.2 μm for 15 NV− . The depth distributionof 15 NV− centers shows no evidence of channeling [40],and the mean depth agrees well with the computed depth
range of implanted 15 N atoms by SRIM (3.82 ± 0.04 μm).
Interestingly, all 14 NV− centers were located at the same orshallower depths than those of 15 NV− centers (Fig. 2), which is
expected to result from the vacancy profile which trails towards
surface (open circle in Fig. 2), as compared to the sharp Bragg
peak of implanted 15 N atoms (solid circle). No 14 NV− centerswere observed at depths shallower than 2.8 μm due to the low
concentration of vacancies.
Now we discuss the creation efficiency for implanted
15
NV− centers. The creation yield, Y (cv ), is written as

NumberISOTOPIC IDENTIFICATION OF ENGINEERED . . .

FIG. 2. (Color online) (b) Depth (z-axis) distributions of observed NV− centers at each implantation site as histogram: 15 NV−(black), 14 NV− (gray), and 14 NV− −15 NV− pairs (blue). The graphin the back side shows the simulated depth distributions for implanted
15
N atoms (solid circle) and vacancies with isotropic diffusion lengthof ∼0.08 μm (open circle).
15

N atoms among the implanted 15 N ions, dependent on thereplacement probability Pr at a carbon lattice site, and Pt (cv )is the probability of trapping a vacancy at a neighboring siteof substitutional 15 N atom, which is proportional to concentrations of vacancies, cv [50]. For Pt (cv ) ≈ 1, the obtained
yield of 40% gives a replacement probability of Pr ≈ 0.4,
which agrees well with recent molecular dynamics simulations
showing that 37% of implanted ions are substituted to latticesites after implantation [60]. This suggests that our 10-MeV
implantation and annealing process provides enough vacancies
to form 15 NV− with a high trapping probability of Pt (cv ) ≈ 1,
and the creation efficiency is limited by those 15 N implants
which remain as interstitial nitrogen after implantation (∼60%of implanted ions).
Next we consider 14 NV− formation. Preexisting 14 N impurities near an implanted 15 N can be converted to 14 NV− centers,
as observed from the pairs of 14 NV− and 15 NV− . In addition tothis, shallower 14 N impurities near vacancy cascades generated
by 15 N ion implantation, can be also transformed into 14 NV
centers, and the creation probability depends on concentrationsof substitional 14 N impurities ([N0s ]) and vacancies (cv ). Hence,
Eq. (1) can be modified as 0 
 0   
Ns Vv PrcY Ns ,cv =Pt (cv ) v ,
(2)
Ni
cv

where Vv is an effective volume containing enough vacancies
to form 14 NV− centers, and the replacement probability into
carbon sites is given as Pr = 1 since 14 N impurities aresubstitutional atoms. The probability of trapping a vacancy,c
Pt (cv ) ≈ 1 in Eq. (1), is replaced by Pt (cv ) cvv , where the factorcof cvv results from a smaller vacancy concentration, cv , for 14 N
impurities than cv for implanted 15 N atoms. Figures 3(a) and

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PHYSICAL REVIEW B 90, 081117(R) (2014)
4x103
3

20
220

0.0

420

620

2
1
0

-0.5
2.5

3.0

3.5
Depth z ( m)4.0(b) 0.5

40
0.1

20

2

10

N atoms/μm2/ion

0.0

30

15

Lateral distance x (μm)

Vacancies/μm2/ion

Lateral distance x (μm)(a) 0.5

0

-0.5
2.5

3.0

3.5
Depth z ( m)

4.0

FIG. 3. (Color online) Simulated xz-plane distributions of (a)vacancies with an isotropic diffusion length of ∼0.08 μm and (b)implanted 15 N atoms with an incident energy of 10 MeV, where z-axis
is the implantation direction. The area-density isolines of vacancies
and 15 N atoms are shown as white lines in (a) and (b), respectively.

3(b) show the simulated statistical distributions of vacancies(after diffusion) and 15 N atoms, respectively, where z axis
is the ion implantation direction and the white solid lines
indicate isolines of area density in each xz-plane projection.
Calculating a volume of revolution (Vv ) by rotating thearea of more than 420 vacancies/μm2 /ion around x = 0
axis in Fig. 3(a), and counting the number of vacancies(nv ) inside this volume, yields an average concentration ofn
cv = Vv = 28 ppb, where the selected depth range correspondsv
to the experimental range of 2.8  z  3.9 for 14 NV− centers(Fig. 2). Similarly, calculating the volume Vv containing morethan 2 atoms/μm2 /ion from Fig. 3(b), and counting thenumber of vacancies inside Vv from Fig. 3(a), gives the average
concentration of cv = Vnvv = 42 ppb. Here, Vv is the volume
in which implanted 15 N atom is found with the probabilityof 90%. Assigning those values and the observed yield of[1] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe,
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Y = 0.56 into Eq. (2), we obtain a concentration of 14 N
impurities as 0.06 ppb, which agrees with the expected value(<0.1 ppb) from the growth condition [29,30].
Photoconversion between NV− and NV0 , observed in PL
spectra has been reported for shallow NV− centers (<200 nm
depths), in spite of a similar (∼ppb) or higher (∼ppm)
concentrations of N donors as described here [39,53,57].
Ionization of shallow NV− to the NV0 charge state has
been attributed to surface effects such as electron depletiondue to an acceptor layer [53,54] or hole accumulation due
to upward band bending at the hydrogen-terminated surface[56]. The observation of the stable negatively charged state in
the present study implies that surface effects are negligiblefor deep NV centers at 3–4-μm depths. On the other hand,
low energy implantation (<5 keV) [57] through nanohole
apertures [51,65] is a promising route to fabrication of arraysof NV centers with high positional precision, however, short
T2 times due to surface spins are problematic for building
quantum registers. One solution is to overgrow an additional
diamond layer onto the surface, which has succeeded in
prolonging T2 times [66]. Our results show that NV− spin
qubits at the depth 2.8 μm exhibit reliable properties of longcoherence times and stable charge states.
In summary, engineered NV− spins qubits by 15 N3+ ion
implantation into high-purity, 13 C-depleted diamond werestudied in a reduced background concentration of residual
defects after high-temperature anneal. We observed a creation
yield of 15 NV− (40 ± 3%), which is likely to be limited by
the population of implants having an interstitial configuration(∼60%) [67]. Even with a N impurity concentration estimatedas 0.06 ppb, a considerable fraction of created NV− centersconsisted of preexisting N impurities. The low concentrationof nitrogen impurities, which allow for long coherence
times (∼2 ms), still play a significant role for NV− charge
stabilization. A provisional mechanism for charge stabilization
will be required when fabricating NV− from only implanted
ions by further lowering the N donor concentration.
This study was carried out as “Strategic Japanese-German
Joint Research Project” supported by JST and DFG (FOR1482,
FOR1493, and SFB716), ERC, DARPA, and the Alexandervon Humboldt- and Volkswagen-Foundation. We thank Denis
Antonov, Yoshiyuki Miyamoto, Brett C. Johnson, and Alexander P. Nizovtsev for valuable discussions, and Kay D. Jahnke,
Pascal Heller, Alexander Gerstmayr, and Andreas Häußler forassistance with the experiments.

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