6. Coupling of two single NV centers — Scaling up thecenters — Scaling up the
6.2. Creation of NV center pairs
a b
depth in
side diamond z (µm) 4.3
5.2 4.86
lateral posi tion (µm -0.45 )
0.45
depth in side di
amond z (µm) 4.3
5.2 4.86
lateral posi tion (µm -0.45 )
0.45
implanted 14N ions created vacancies
Figure 6.2.: Simulation of ion implantation by SRIM/TRIM ®. a, Probability distribution of an implanted 14N ion in diamond. Depth and lateral distributions are shown. b, Probability distribution of the vacancies created by an implanted 14N ion. One ion creates on average 2576 vacancies of which a considerable part is located in the area of the stopped ions where on average every nm of depth one vacancy is created per ion.
like three distinct NV electron spin levels without interchange. In future experiments the nuclear spins should be used to store the correlations created by the interaction of the electron spins.
The effect of the magnetic dipolar interaction on the energy levels and eigenstates is minor compared to the other contributions in eq. (6.2). In all experiments in this chapter energy level splittings will be much larger than 50 kHz. Thus a secular approximation is valid, i.e. energy level changes due to the interaction occur but changes of the eigenstates due to off-diagonal terms in ˆHdip can be neglected.
6.2. Creation of NV center pairs
ion implantation The present experiments are conducted in isotopically purified CVD diamond with a 12C concentration of 99.99% and a (001) surface.1 The nitro-gen content in this sample is less than 1 ppb and it is therefore very unlikely to find a native NV center.2 Thus the NV center pairs are created artificially, namely by ion implantation and subsequent annealing of the sample (see section 2.2.2).
The low13C content leads to long decoherence times and allows to study NV pair in-teraction in a clean environment. In addition the long coherence lifetimes allow smaller coupling strengths and thus larger distances between the NV centers within a pair. The low nitrogen content assures that the created NV centers are indeed formed out of the implanted nitrogen ions and not from residual nitrogen atoms in the lattice that capture
1The actual isotopically purified diamond is a several µm thick layer that was deposited on a synthetic diamond substrate by microwave plasma assisted CVD growth using purified methane.
2The approximate intrinsic NV density is∼108cm−3.
6. Coupling of two single NV centers — Scaling up the quantum processor
a produced vacancy.
As mentioned above NV distances on the order of a few 10 nm or less are necessary to achieve a coupled pair. This puts a high demand on the positioning accuracy of the implanted ions which has not been demonstrated so far. Actually many aspects affect the successful creation of a suitable pair of negatively charged NV centers:
• surface distance: Recently it has been shown that surface properties have a high in-fluence on the NV center (e.g. charge state [112], spin environment [145]). Indeed, shallow implanted NV centers show inferior coherence properties and sometimes tend to change their charge state.
• conversion efficiency: To generate an NV center we need a substitutional nitrogen atom in the diamond lattice and proximal vacancies one of which should eventually bind to the nitrogen forming the color center. The probability to produce vacancies rises with implantation energy (see figure6.2b). Indeed, low energy implants show low conversion efficiency to NV centers (≈1 % [29]).
• implantation energy: A higher energy leads to a higher implantation depth. Before an implanted nitrogen ion comes to rest in the diamond lattice it straggles in lateral and axial direction (see figure 6.2a). The amount of straggle is increasing with increasing implantation energy. The freely available software SRIM ® [193]
is used to simulate implantation events of ions into matter.
• ion beam focus: The high energy ion implantation facility used here has a focus of ≈200 nm.3
The last aspect, namely the beam spot size is the bottleneck when creating NV pairs for this experiment. On the other hand we can afford higher implantation energy such that the lateral straggle is roughly the beam size. This increases conversion efficiency and increases the distance to the surface thus decreasing deleterious surface effects.
Eventually the implantation energy used is 13 MeV per nitrogen ion which results in an implantation depth of ≈ 5 µm and straggle radius of ≈ 90 nm (i.e. the square-root of the variance of the radius, see figure 6.2a). With these settings multiple arrays of implantation sites were created where each site has a certain amount of implanted ions and this amount varies from one array to another (nominal number of ions per spot are in the range from 5 to 100, see figure6.3a). Finally, the NV pair we use throughout this chapter was found in the array where each site nominally contains 6 implanted nitrogen ions (see figure 6.3b). From the average number of NV centers found in this array we deduce a conversion efficiency (from ion implantation to NV center formation) of 21 %.
optical characterization The technique of NV pair generation explained above has a very low success rate. Therefore, it is necessary to characterize the implantation sites
3The nitrogen ions were implanted by Jan Meijer at Rubion at University of Bochum.
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6.2. Creation of NV center pairs
c
20 µm 500 nm
IPL (arb. units)
0 1
τ (ns)
0 100
0 1
g2 (τ)
a b
2 NV centers
1 NV center
Figure 6.3.: Confocal scans of implantation area including NV pair. a, Implantation area with 10 N atoms per impact site. The colorbar indicates the fluorescence intensityIPL. b,Zoom of implantation area with 6 N ions per site. Three ions have been converted; two as an NV pair and a separated one. c, Fluorescence autocorrelation function of the NV pair. Apparently, two single emitters are within the confocal volume.
of each array in order to find those sites that are likely to obtain a coupled NV pair.
The following characterization steps are performed to narrow down the number of NV pair candidates:
1. Take a confocal scan image of an implantation array and find single fluorescent spots that contain more than one NV center. The fluorescence rate gives a rough estimate of the number of NV centers, later a fluorescence autocorrelation mea-surement can be done to verify the former finding (figure 6.3c).
2. Take a close-up of the former fluorescent spot (see figure 6.3b). Any visible de-viation from the circular shape4 originates from a lateral separation that is easily more than 10 nm. These spots can be rejected. (It is possible to check also the axial PSF shape; however, because of the lower resolution in this direction the implantation distribution should always fall well into the axial PSF.)
3. Take a super-resolution image of the remaining candidates using stimulated emis-sion depletion (STED) [44] or ground state depletion (GSD) microscopy [63]. Res-olutions of down to ≈ 5 nm have been demonstrated [44] which is sufficient to rule out any candidates that are too far apart in lateral and axial direction. We have only used lateral GSD scans on candidate pairs (see figure6.4a and appendix B.1.2). Here a doughnut shaped illumination profile is used exhibiting a steep intensity gradient close to the center.
4. An alternative approach to resolve two NV centers with sub-wavelength separation is fluorescence lifetime imaging (FLIM) [194]. The basic idea of this method is to
4The actual shape might differ from a circle. The 2d PSF in the focal plane of a single emitter has to be taken to verify the shape.
6. Coupling of two single NV centers — Scaling up the quantum processor
3.18 3.26
10nm
100nm
(arb. units)
0 1
IPL
a b
Figure 6.4.: Super-resolution images of the NV pair. a, GSD imaging mechanism (left, see text). A large area is illuminated except a very confined central region. Thus, even close NV centers can be separately excited. GSD scan (right) cannot resolve the NV pair. Obviously their separation is below the resolution limit of≈20nm. The colorbar indicates the fluorescence intensity IPL. b, Illustration of FLIM imaging (left, see text). Cross-correlation image of the two FLIM sub-images (see appendixB.1.1). The separation of the two centers is≈10nm.
exploit different fluorescence lifetimes of the fluorescent objects under study to acquire a separate image for each fluorescent object (see appendix B.1.1). In the present case the fluorescence lifetimes of the two NV centers are made different by applying an appropriate magnetic field (see below).
Those NV pairs that pass all these tests will be investigated by means of EPR to gather information about their relative distance and orientation.
For the present diamond sample and the coupled NV pair under investigation the con-focal images, the fluorescence autocorrelation measurement and the GSD are displayed in figures 6.3b,c and 6.4a. Next we go more into detail about the FLIM measurements.
For this technique it is necessary for the two NV centers to have different fluorescence lifetimes. As it turns out the NV centers of the coupled pair have a different crystal-lographic orientation. Thus, by applying a sufficiently strong magnetic field (≈70 mT) along the symmetry axis of one center this one will be in its mS = 0 state of the ground state after green laser illumination whereas the other center will be in a mixture of mS = 0,±1 (see section2.2.4). Because of the different fluorescence lifetimes formS = 0 and mS = ±1 the light emitted from the two NV centers is now distinguishable (see section 2.2.3).5 Once this is assured 2 images (one for each NV, see figure B.1) are ac-quired where the pixel values of each image are the amplitudes the of the corresponding exponentially decaying fluorescence intensity. Finally both images can be accumulated long enough such that the uncertainty of the corresponding NV position is less than the distance between both centers. Here, we perform a cross-correlation of the two images to obtain the most likely lateral displacement of the two NV centers (see figure 6.4b).
As it turns out the lateral separation is about 10 nm which might very well be sufficient
5If both centers have the same orientation an inhomogeneous (on the 10 nm scale) magnetic field could be applied. In addition this can be used to address two equally aligned NVs individually by mw radiation and for magnetic resonance imaging [65].
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