NV- - N+ pair centre in 1b diamond

The study establishes that the degree of optically induced spin polarization that can be achieved for NV$^- $in 1b diamond is limited by the concentration of single substitutional nitrogen, N$^0$ . The polarization of the individual NV centres in the diamond is dependent on the separation of the NV$^-$ and the nitrogen donor. When the NV$^-$ - N$^+$ pair separation is large the properties of the pair will be as for single sites and a high degree of spin polarization attainable. When the separation decreases the emission is reduced, the lifetime shortened and the spin polarization downgraded. The deterioration occurs as a consequence of electron tunneling in the excited state from NV$^-$ to N$^+$ and results in an optical cycle that includes NV$^0$. The tunneling process is linear in optical excitation and more prevalent the closer the N$^+$ is to the NV$^-$ centre. However, the separation between the NV$^-$ and its donor N$^+$ can be effected by light through the excitation of NV$^-$ and/or ionization of N$^0$. The optical excitation that creates the spin polarization can also modify the sample properties and during excitation creates charge dynamics. The consequence is that the magnitude of spin polarization, the spin relaxation and coherence times T$_1$ and T$_2$ have a dependence on the nitrogen concentration and on the excitation wavelength. The adjacent N$^+$ gives an electric field that Stark shifts the NV$^-$ transitions and for an ensemble results in line broadening. It is observation of changes of these Stark induced effects that allow the variation in NV$^-$ - N$^+$ separation to be monitored. Spectroscopic measurements including that of the varying line widths are central to the study. They are made at low temperatures and include extensive measurements of the NV$^-$ optical transition at 637 nm, the infrared transition at 1042 nm and ODMR at 2.87 GHz.


Introduction
A vacancy adjacent to a substitutional nitrogen (NV) in diamond can be detected at the single site level. The negatively (NV-) charged centre has a spin (S=1) ground state that can be optically pumped into one spin projection with near 100 per cent efficiency and the spin projection read optically, all under ambient conditions. These capabilities have lead to a phenomenal array of single NV − applications in life sciences, magnetic sensing, quantum information processing and nano-detection. (see reviews: [1] [2][3] [4]). There are also applications that utilize ensembles of NV − centres. This includes detection of magnetic fields with the possibility over wide areas [5] [7] [6] [8] and often for materials with biological [9] [10] or geological interest [11] [12] . In the case of these latter ensemble applications it is desirable that the centres maintain the properties of the single centres. However when ensembles are used these novel properties are degraded but to what extent has not been quantified or explained. The aim of this paper is to investigate the optical properties of nitrogen vacancy centres in diamond and focus on how and to what extent the properties of NV − centre are corrupted in comparison to single sites.
The negative charge state, NV − , requires an electron from a donor in the diamond lattice, usually from a substitutional nitrogen to form an NV − -N + pair. The donor is essential but if well separated from the NV − it has little influence on the properties of the NV − centre and this is the preferred situation for using a single NV − centre for applications. With NV − in 1b diamond there is a density of substitutional nitrogen atoms and for a given NV centre any one of the substitutional nitrogen atoms can provide the electron to form the NV − -N + pair. In this work it is shown that the properties of the NV − -N + centres vary with separation of the pair and it is the average properties that are observed, measured and utilized in any application. Optical excitation that is used to measure the centre can also change the NV − -N + separation and in the process modify the properties. The focus of this paper is to explain how this occurs and give details of the dependence on nitrogen concentration and excitation wavelength. The investigation relies on low temperature optical spectroscopy and an overview of optical characteristics and spectra of the NV system is included by way of an introduction.

Properties of NV Centre
The nitrogen-vacancy centre in diamond is formed with irradiation that create vacancies (here 2 MeV electrons at 1 x 10 17 to 1 x 10 18 /cm 2 ) followed by annealing. The annealing at temperatures > 700 0 C causes the vacancies to become mobile and be trapped at nitrogen sites to form the nitrogen-vacancy pair. The pair are aligned along a <111> direction to give a centre with trigonal symmetry (C 3V ). The centre can occur in the neutral NV 0 or negative NV − charge state and the centres have prominent optical transitions with zero-phonon lines at 575 nm (2.156 ev) and at 637nm (1.945 eV) respectively. The centres have been studied extensively and the electronic structures are well established [1]. To assist discussion a simplified schematic of the structures are given in Figure 1. .  Figure 1: The electronic structure of NV centres. Solid arrows indicate transitions between electronic states and the transitions can be accompanied by vibrations. Dashed arrows are nonradiative decay, possible tunneling and inter-system crossing. Values given for the inter-system crossing of NV − are normalized to the radiative value of 1/13ns and approximate values are used to make discussion easier to follow. Readers are referred to [1] [13] [14] for more formal treatment of energy scheme and to [15], [16] [17] for inter-system crossing values.
NV 0 centre The neutral centre, NV 0 has the zero-phonon line at 575nm and the optical transition has been shown to be between a 2 E ground state and 2 A 2 excited state [18]. An electron spin resonance signal has also been detected and attributed to an intermediate 4 A 2 state [20]. Modeling of the vacancy centres in diamond is described by molecular orbitals formed from the dangling bonds of the carbon atoms associated with the vacancy in addition to orbits of any adjacent impurities. In the case of the nitrogen-vacancy pair there is a non-degenerate a 1 orbit in the valence band that is generally ignored. In the gap between valence and conduction bands there is a non-degenerate a 1 and degenerate e state (of A 1 and E symmetry, respectively in C 3V ) and it is the occupation of these states that give the electronic levels. For NV 0 there are three (neglecting the one in the valence band) electrons giving the 2 E(a 2 1 e) ground state, the 2 A 2 (a 1 e 2 ) excited state and the intermediate 4 A 2 (a 1 e 2 ) states. The optical transition has a Huang-Rys factor of S = 3.3 [19] giving 3.7% (e −S = 0.037)of strength in the vibronic band and the 2 E -2 A 2 absorption stretch from 575 nm to 400 nm and emission from 575 nm to 700 nm. The emission is shown in Figure 2 . Figure 2: NV 0 2 A 2 -2 E emission from room temperature to 5K. A very small contribution from NV-is noted with zero-phonon line at 637nm. The absorption at 725nm is due to an alternative defect [19].
NV − centre In the case of the negatively charged NV − centre the transition at 637nm involves a transition between an orbital A 2 ground state and excited E orbital doublet [21] . Both states involve four electrons and are spin triplets, 3 A 2 (a 2 1 e 2 ) and 3 E(a 1 e 3 ) as shown in Figure 1. The optical transitions involves transitions between like-spins and the three spin projections for m s = 0, m s =+1 and m s =-1 have equal strength. The transition has a Huang-Rys factor of S = 3.65 [21] which implies the zero-phonon line involves only 2.6 % (e −S = 0.026 ) of the overall transition strength and most of the signal is associated with the accompanying vibrational sidebands. The bands in absorption and emission bands are shown in Figure 3 and Figure 4, respectfully. As shown in the electronic structure in Figure 1 there is inter-system crossing from the excited 3 E state to singlets and decay within the singlets result in weak 1 A 1 -1 E infra-red emission [22] as shown in Figure 5.
Experimental details A diamond crystal can contain NV 0 and NV − centres and then excitation will give emission of both centres. The intensity of each depends on their concentration but also on the excitation wavelength within their respective absorption band. An example is shown in Figure 6. For this measurement and throughout the study the lasers available were a 5 Watt Ar + ion laser with wavelengths 514 nm, 501 nm, 496 nm, 488 nm, 476 nm and 458 nm, a tunable dye lasers with wavelengths fixed or swept within the range 670 nm to 570 nm and intensities from 10 mW to 500 mW depending on wavelength, and fixed frequency lasers at 532 nm (to 5 W) and 445 nm (to 400 mW). The samples had dimensions of several mm and the beams were not Figure 3: The 3 A 2 -3 E absorption of NV − for various temperatures between 275K and 5K. The dashed line is the variation of absorption of singly-substitutional nitrogen. Other impurities give the features at 595nm and 494nm [19]. Figure 4: Emission of the 3 A 2 -3 E transition of the NV − from room temperature to 5 K. At lower temperatures the relative strength of the zero-phonon compared to the sideband is incorrect as a strongly absorbing sample was used and there is re-absorption of the zero-phonon line.
in general focused preferring to average over a significant area as the samples exhibited macroscopic inhomogeneities. When more than one laser was involved the beams were overlapped on the sample. Emission was dispersed by a monochromator. In the visible detection involved a GaAsphotomultiplier with response from 400 nm to 900 nm and in the infra red by a liquid-N 2 -cooled Ge detector with response from 800 nm to 2 microns. The same monochromator and detectors were used for transmission measurements of a white light from a current stabilized tungsten source. Figure 5: Emission of the 1 A 1 -1 E transition as function of temperature. The slope is the extreme long wavelength limit of the visible emission. The numbers to the left of ZPL give the peak intensities as off scale. The infra-red is weak compared to the visible and spectra corrected for instrument response is given in figure 7. The vibrational sideband has peak at 40 meV (322cm −1 ), weak feature at 66 meV (532 cm −1 ) and drop-off at 90 meV (725 cm −1 ). The first peak moves to lower energy with temperature and at room temperature is 33 meV (266 cm −1 ) and very broad 30 meV (242 cm −1 ) at 375 K. The band also losses intensity with increasing temperature.
Samples were within a cryostat and temperature could be controlled within the range 300 K to 4 K.
NV − Infrared emission With excitation in the visible the NV − centre is excited from the 3 A 2 ground state to the 3 E excited state. The part of the decay from 3 E is visible emission and part decays via the singlets. The decay path via the singlets including the infrared emission gives rise to spin polarization. Variation in the strength of the infrared emission indicates the polarization is not constant and it is accounting for the variation in spin polarization that is one of the main aims of this work. The inter-system crossing from the 3 E to upper singlet level 1 A 1 is small for the m s = 0 spin state and large for m s = ± 1 ( values of 0.1 and 1, respectively, are adopted in Figure 1). With these inter-system crossing rates optical cycling causes population to be transfered to the m s = 0 spin state and as decay from this state is almost entirely radiative the emission is high. A magnetic field can be used to quench this spin polarization and reduce emission. For example, a field along <001> makes an equal angle with the axis of all four orientations of the NV centre and when the field is high the eigenstates have equal contribution of m s = 0 and 33.3 % population is obtained in all the three spin states of each of the four NV − orientations. The quenching of spin polarization that can be obtained with such a magnetic field is greater than can be obtained with ground state microwaves as both ground and excited states are effected. A magnetic field of 500 gauss is sufficient to the quench the spin polarization to 4 % of that in the absence of field [23] [16]. The emission is decreased with the application of the magnetic field and the percentage drop is termed as the optical contrast C . Such a measurement for a single centre has obtained contrast of C = 40%. As there is little inter system crossing from the m s = 0 state when the spin polarization is high and only 1% decay via the singlets. Consequently any emission associated with the 1 A 1 -1 E transition in the case of single sites will be weak and infrared emission for single sites has not been detected.
Contrary to the single-site situation, with NV − ensembles the 1 A 1 -1 E infrared emission is readily detectable [22]. The infrared emission can be further increased by applying the magnetic field as above that quenches the spin polarization. Part of the population from 3 E is transfered from decaying via the triplets giving the visible emission to decaying via the singlets that includes the infrared emission. The situation is illustrated in Figures 7a, 7b where the signals have been Figure 6: Emission of a sample at 10K containing both NV − and NV 0 with excitation at wavelengths adopted within the following studies (approximately 40 ppm nitrogen). The excitation wavelengths are marked by letter L. The emission is only from NV − when the excitation is in the red > 575nm progressing to predominantly from NV 0 for excitation in the blue. The noise on the 637nm trace is due to instability from hole burning when exciting resonantly within the ZPL. The dashed trace indicates the wavelength dependence of absorption (arbitrary scale) of single-subsitutional nitrogen, N 0 .  Figure 7: 7a The low temperature visible and infrared emission corrected for spectral response shown with and without a magnetic field applied. The field decreases the visible emission and the difference is shown as a negative response. 7b The field increases the infrared but for clarity the change is also shown as a negative response. The relative areas of the change in signal strength between visible (7a) and infrared (7b) is 10 3 .
corrected for system response and the changes of the emission introduced by the magnetic field are shown as a negative signal in black. The fraction lost in the visible decay has to be gained by the singlet decay. (There is negligible change to NV 0 emission). It can be seen that the gain of infrared emission is small (10 −3 ) compared to the loss of visible emission. It is concluded that the infrared decay is largely (by the factor of 10 3 ) non-radiative. The presence of non-radiative decay was know previously [22] but the determination of the fraction is new. The measurements in Figure 7a also indicate that for this sample, ≈ 23% of decay from the excited 3 E state is via the singlets. This fraction is large compared to the 1% predicted above for single centres. The increase in the percentage decay via the singlets for the present sample compared to single sites is due to vastly different spin polarization. The difference in the degree of spin-polarization between ensembles and single-sites has been recognized previously. For single centres population in the mid to high 90% has been reported to be in the m s = 0 state [24] [25] [26] [27] whereas much lower values are reported for ensembles. Harrison et.al. [28] has measured a value of 78%. Felton et.al. [29] have suggested lower polarization and Drake et.al. [30] has given values as low as 36 % for ensembles. The intention in what follows is to identify the process that could account for such significant reduction and variation of spin polarization.

Tunneling
Samples 1b diamond have nitrogen substitues for carbon at lattice sites. Such single substitutional nitrogen can act as an electron donor and is essential for the creation of negatively charged NV centres. 1b is the normal diamond type for synthetic diamond when prepared using high temperature and high pressure (HTHP) and nitrogen concentrations are frequently reported to be of order of 100's parts per million (ppm). Such crystals are available commercially, for example, from Element-6 or Sumitomo. This study focuses on three such samples available from previous studies. From the strength of the infrared absorption at 1130 cm −1 [34] the samples were found to have 212 ppm, 115 ppm and 40 ppm single-substitutional nitrogen ( Figure 8). A fourth sample was also investigated but was not strictly 1b as it contained 192 ppm nitrogen incorporated as nitrogen pairs (A-centre) in addition to some substitutional nitrogen (1a diamonds has A-centres only.). Brief details of other samples are given later. The samples studied were 1 to 2mm thick and from visible absorption [35] concluded to have concentrations of order of 1-5ppm NV, significantly less than the nitrogen concentrations.  [34] as well as substitutional nitrogen. Traces are normalized to two photon absorption as given in reference [36].
NV 0 -N 0 ↔ NV − -N + tunneling The 1b diamonds will have a random distribution of single substitutional nitrogen. After radiation and annealing they will provide the environment for individual NV centres as in the upper schematic in Figure 9. The concentration of NV centres can be determined from absorption measurements but what is more significant here is the relative Figure 9: Diagram illustrates situation of a 1b diamond with several interstitial nitrogen atoms occur at random locations about a central NV − . With blue illumination the N 0 nitrogen atoms are ionized and after relaxation one remains as N + at a random location. Subsequent radiation this will repeat but N + not necessarily in the same location. When the NV − is excited an electron can tunnel in the excited state to the N + (fast if close, slow if more distant) leaving the NV in the neutral NV 0 charge state. However, when NV 0 is in ground state an electron can tunnel from a nitrogen to the NV 0 . The tunneling rate will prefer adjacent nitrogen donors. The result of the red illumination is a NV − with close N + concentration of NV − and NV 0 centre and this can be determined from the emission spectrum with laser excitation. Using low intensity excitation measurements of the 115 ppm sample gives 99% of the NV centres in the negative charge state NV − and 1% in the neutral charge state NV 0 ( Figure 10). As pointed out by Collins [31], the charge state depends on proximity of nitrogen donors. For the 115 ppm sample the median distance to the nearest nitrogen impurity will be of the order of 10 atomic spaces (1.82nm). The 99:1 NV-/NV0 ratio indicates that any NV center with an N 0 closer than 3 nm (15 atom spacings) will form an NV − -N + pair. Hence, it is clear from this that tunneling in 1b diamonds from nitrogen donors N 0 to NV 0 can be over a few nm's. The specific distances will vary as will the time scales.
With low light levels (<1mW /cm 2 ) as used in the above measurements, the fraction of NV 0 is not changed and with the 115 ppm case only 1% of the NV centres are in the NV 0 charge state. However, if the optical power is increased the proportion of NV 0 is also increased as shown in Figure 10a. The increase arises from tunneling in the NV − excited state. The tunneling in the excited state is in the reverse sense to the ground state, now from NV − to N + to give NV 0 and N 0 . The increase of NV 0 via this process with red light is linear in excitation intensity as shown in Figure 10b. This is measured by exciting with a red laser at 620 nm and monitoring the increase in NV 0 by detecting its emission at 600 nm using a weak (< 1mW /cm 2 ) probe at 532 nm. Should a 532 nm green laser be used to both induce and monitor the NV 0 , the increase with green laser excitation strength is quadratic as shown in Figure 10b. As intensity is increased saturation occurs and the quadratic response is replaced by a near linear dependence. This tunneling situation has been reported previously in reference [32] and larger ranges of excitation intensities are illustrated.
It should be noted that upon exciting NV 0 there is no 'reverse' tunneling in the NV 0 excited state. To show this a tunable laser is swept in frequency from 565 nm to 585 nm. Through this wavelength region there is almost constant excitation of NV − (Figure 11b) and for a given excitation (a) . Spectra shown for increasing powers: 6mW, 36mW, 60mW, 100mW over 0.1cm 2 cross section. (100mW -> 1W/cm 2 ) Traces normalized to peak of vibronic band. The responses over a larger range of excitation intensities have been shown in reference [32]. (b) : Upper trace indicates increase of NV 0 with increasing red excitation at 620nm monitored by detection of NV 0 emission using a weak <1mW 532nm beam. Lower trace gives emission for increasing in green 532nm excitation whereas is a quadrativc fit to the lowest power values. Beam is over area of 0.1cm 2 Figure 10 (a) Excitation of NV 0 center at intensities of 3mW unfocused (noisy trace and zero level is noise) and 300mW focused (solid trace). Sample temperature is 10K and detection is at 600nm. (b) Laser is sweep in wavelength from 565nm to 585nm near the peak of the NV − vibrational sideband (shown by red box) and within this range there will be very little variation of NV 0 created through ionization.
(c) Detection for 11a is restricted by filters to only be between 595nm and 610nm within the vibrational sideband of NV 0 (shown by black box). The range of the excitation is repeated in red.  (Figure 11a). Should there have been reverse tunneling in the NV 0 excited state one would observe a change of NV 0 signal with excitation and a change of line shape. There is none and it can be concluded that there no linear photo-conversion of NV 0 in the excited state. Very different from the latter situation in the NV − excited state. The linear tunneling NV − -N + to attain NV 0 can be observed at intensities orders of magnitude less than that required to detect the two-photon ionization frequently reported in the case of single centres [33]. (At 532nm two-photon ionization observed at 10 6 W/m 2 whereas in general intensities here are < 10 5 W/m. 2 ) It is recognized that two-photon inter-conversion between NV − and NV 0 are intrinsic processes and when there is no tunneling will be the only mechanism whereby there can be NV − <->NV 0 conversion. With intensities adopted here no significant two-photon processes are observed.
The NV − to N + tunneling occurs in the excited state of NV − . As it is only in this state for 13 ns the rates must be fast to have a reasonable probability of tunneling within this time. Also as the rates will decrease exponentially with increasing separation of the NV − -N + pair the tunneling within the closer pairs will be favored. At low intensities it will mainly involve the very close pairs but with higher intensities the average time in the excited state can be increased to obtain contribution from more distant pairs. With continuous excitation a NV 0 population can be maintained dynamically and it is this population that is observed. The population attained following a step increase in excitation intensity has been measured previously [32]. When the excitation is switched off the population of NV 0 will not be maintained and all NV 0 will relax to their ground state. Once in the ground state there will be NV 0 -N 0 tunneling back to give the original NV − population. The rates for this recovery process has also been measured in previously publication [32]. Both rates, creation and decay, of NV 0 were found to varied from µs to minutes (and the fastest decay rates were probably instrument limited). The non-scalar rates are as expected for the enormous range of separations in a bulk crystal. So far it has not been possible to determine rates associate with any specific separations.
The tunneling will be a one photon process and in the molecular model as given in Figure 1 it is possible that NV 0 (e 2 a) in the ground state captures an electron from N 0 and tunnels directly to the NV − (e 2 a 2 ) ground state. However, in the excited state the reverse tunneling is unlikely to be direct to the NV 0 (e 2 a) ground state as this would involve a two electron transition. It is possible, therefore, that the decay from 3 E(e 3 a) involves tunneling to the meta-stable 4 A 2 (e 2 a) quartet level. However, the specific details of the tunneling transitions requires further theoretical consideration.
The last step of the tunneling cycle is the tunneling of an electron from N 0 to return the centre to the negative charge state. Regardless of the position of the original donor this latter process favors the faster rates and tunneling from the closest N 0 . Hence the cycle will create NV − centres with close N + donors. Should this be the only process optical excitation will always generate crystals with a predominance of NV − centres with close donors. However, this is not the only process. Optical excitation can also excites N 0 centres throughout the crystal. The excitation can ionize N 0 to give N + centres with an electron in the conduction band. The conduction electron is then trapped elsewhere in the lattice and although not the dominant process [37] can occasionally combine with one of the N + donors. Should this occur the consequence is that a N + is created at a random location and becomes the donor at the expense of the close donor. Therefore, with the optical excitation of substitutional nitrogen atoms there is a redistribution of the location of the N + donors with respect to the NV − centres and the process counteracts the situation of N + ions close to the NV − . This process can occur for single sites and give undesirable spectral diffusion [38], [39], [40], [41].
It is worthwhile mentioning an alternative process that is possible is where there is ionization of N 0 to create N + and the electron released is captured by a NV 0 centre to increase the concentration of NV − and N + . There is no evidence of this although the present samples have very low NV 0 concentrations and not optimal conditions for detecting such a process. With the samples investigated here this process is not considered further.
. Absorption line widths The competition between the two processes that alter the distribution of the donors result in observable changes of the line width of the low temperature 637nm zero-phonon line. The processes themselves are not temperature dependent and low temperatures are only necessary as the changes in line width are not observable at higher temperature due to phonon broadening of the zero phonon line. When the N + is close to the NV − the charge gives a Stark shift of the optical transition that varies from site to site and the combined effect is a Figure 12: . Transmission of 2ppm NV doped 1b diamond (115ppm) measured over 2mm 2 cross section. Between traces the sample was exposed to laser and the laser illumination at each wavelength between 637nm and 445nm was over the same area with an energy densities between 10 3 W/m 2 and 10 4 W/m 2 : exposure duration was approximately 1 minute. There is no other illumination during the transmission measurement. The sample is totally absorbing at 637.5nm.
broadening of the optical line distinguishable at temperatures < 77 K. On the other hand when the single-substitutional nitrogen are ionized and cause the redistribution of N + donors the average Stark shift is reduced and the zero-phonon line width becomes narrower. Equilibrium is established between the two processes and for a given sample the balance only depends on the wavelength of excitation. The magnitude of the effects vary from sample to sample dependent on the nitrogen concentration. The first process varies with the absorption of NV − and the second with the absorption of substitutional nitrogen [42] [43] and their variation as function of wavelength are shown in Figure 3. Due to the absorption dependence with wavelength the result is a broadening when the excitation is in the red as the wavelength favors NV − excitation and a narrowing when the excitation is in the blue favoring nitrogen ionization. The situation varies continuously between the red and blue and various intermediate wavelengths are illustrated in Figure 12 and also later in Figure 19b. Figure 12 presents a series of transmission measurements of NV − of the 115 ppm 1b diamond sample at 77K. Each measurement is the same: a measurement of transmission of the crystal in the spectral range of the 3 A 2 -3 E zero-phonon line from 630nm to 650nm using a low intensity white light source (that does not cause photo-ionization). The transmitted light is dispersed by a monochromator and detected with a photomultiplier. Other than the monitoring light there is no light on the sample at the time of the measurement. Prior to each measurement the sample is exposed to light of a given color. (The wavelengths used are the same as used in Figure 6.) The order of the color does not matter and the intensity and duration of exposure are also not of great significance usually being a few milliwatts for 10's of seconds. The wavelength determines the balance. After the light is switched off, relaxation and tunneling is largely complete within a minute. The situation is then stable and the absorption can be measured with the low intensity light source. As remarked above the processes occur regardless of temperature and the low temperatures are only required to monitor the situation via the changing width of the zero-phonon line.
The above assumes no other possibility for the variation in line width has been considered. The last step of the optical cycle where the optically induced population of NV 0 decays and there is a recovery of NV − [32] it is distinctly unlikely that this is not associated with tunneling of N 0 to NV 0 . Also this must favor fast tunneling and, hence, create close N + donors. The close nitrogen could introduce an extra strain but it is more likely to be the reverse as N + has the same electronic structure as carbon and so strain will be minimal. The N + replaces a N 0 and so the strain could be reduced but not sufficient to introduce a displacement of the ZPL from the mean. If this was  the case there would be a shift of transition frequency that is canceled by the optical cycle not the reverse. There maybe some minor changes in strain but undoubtedly the dominant effect is that of the Stark effect due to the introduction of the positive charges close to the NV − centres as asserted above.
There is only one previous report of broadening of 637 nm ZPL in single crystal diamond by Nishikoriet.al. [44]. in relation to a low temperature (60K) hole burning study An increase in line width of a 70 ppm nitrogen sample was observed using low temperature hole burning when exciting at or close to resonance at 637nm. The observations are consistent with that given here. The broadening was considered anomalous and the authors speculated on possible explanations. Similarly Wolters et.al. [45] observed fast frequency shifts of the zero-phonon line when the NV − centre was excited using correlation interferometry in a nanodiamond. The effect was attributed the diffusion of charge giving Stark effects that were linear with excitation intensity. The authors also noted a dependence on the wavelength of excitation. Their observations are consistent with the current measurements and as their sample were prepared from 1b diamond undoubtedly the effects are related and not restricted to the nano-scale.
One of the present authors has included a summary of the broadening effects and given a partial explanation in a book chapter by Zvyagin and Manson in 2012 [46].
Absorption line width with illumination The transmission measurements in Figure 12 are made without other light on the crystal during the individual measurements but this is not essential as illumination can be present without changing the observation. The creation of additional N + through ionization of the single-substitutional nitrogen does not give absorption. Also there is negligible change to the NV − ground state population through optical excitation. The result is that simultaneous modest optical illumination does not alter the transmitted light intensity. What is interesting is that when both colors are applied simultaneously the narrower line width as occurs for blue only illumination is obtained. This is because tunneling involves slow processes (many seconds) and is not competitive with ionization and fast electron migration in diamond. The rates in reaching equilibrium upon switching on red (620 nm) or blue (445 nm) are shown in Figures 13a and 13b. As with previous NV 0 ionization measurements there is a wide range of rates although the techniques adopted for the figures are biased towards observing the slower responses. This variation between red only excitation and simultaneous excitation with red and blue proves invaluable for further investigations and is an approach adopted for many measurements reported throughout the paper. It allows situations to be probed and compare the situations for close donors and dispersed donors. Figure 14: . The absorption of the 115 ppm sample at 10K. The low energy slope of the ZPL is shown on an expanded scale. The lowest trace shows the absorption after blue (445nm) illumination. The upper traces are measurement of absorption after red (620nm) illumination taken every two minutes. The X marks a zero phonon line at 658nm (1.885 eV associated with a Ni − impurity [19] and not part of the NV − spectrum. As well as Stark broadening of the zero-phonon line as in Figure 12 additional features are observed on the low energy side of the zero-phonon line. The features are very irregular on a sloping background termed 'moguls' are shown in Figure 14. The features are weak but repeatable as shown in the several traces in the Figure. After blue (445 nm) illumination the features are small or not present and this is given in the lowest trace of Figure 14. The features are attributed to optical transitions where optical frequencies are Stark shifted due to the charge of very close N + donors. The features are more pronounced with red illumination. In the 115 ppm nitrogen sample each mogul feature has an optical strength of less than OD < 0.01 compared with the zero-phonon line with an OD = 2.5 ( ie 1/4% of the parent transition). There is broadening to the high energy side of the zero-phonon line and it is anticipated that there will also be moguls on the high energy side. However, energy levels with split components displaced to higher energy will relax to lower energy and this process will result in broadening. Such features will be weak and no distinguishable features are observed. There are occasional irregularities in the background due measurement instability but the position of the mogul peaks are reproducible and this is illustrated by repetitions of the absorption measurement (given in preference to further averaging as due to irregularity of the spectra the response still 'looks like' noise).

Broadening and 'moguls'
The observation of moguls requires low temperature. They are distinguishable at 125 K and reach a minimum width by 50 K. This is shown in a series of traces in Figures 16a and 16b.  The moguls show variation in magnitude due to macroscopic inhomogenities in the samples. However, the wave lengths of spectral features are constant and features at the same wavelengths have been observed in both 115 ppm and 212 ppm high nitrogen concentration samples. They were too weak to obtain reliable time dependence although there was indication that the less shifted lines develop more slowly than the extreme lines. For example in Figure 14 a measurement was made at two minute intervals with red illumination after an initial illumination with blue. The lesser shifted features at 150 cm −1 (645 nm) increase slowly with time. In the other extreme the larger shifted lines such as those at 620cm −1 and 780 cm −1 (664 nm an 670.7 nm ) were more persistent and were still present with the blue illumination. This is consistent with the larger shifted lines being associated with closer N + ions, fast tunneling rates and more resistant to optical induced changes.
A sample with both high NV − and high N + concentrations was found to give prominent mogul structure that showed little modification with blue light (Figure 15). The moguls were significantly broader due to high concentrations but agreed in energy with those above. (The sample had irregular shape and not possible to obtain reliable concentrations from absorption and FTIR measurements). The shifts extended to 690nm, over 1200 cm −1 (150 meV) from the zero-phonon line as shown in Figure 15. The observations are attributed to Stark structure associated with a density of charge from NV − and N + giving higher electric fields than can be obtained with a single neighboring donor. There could also be higher electric fields from nickel, Ni − impurities plus N + compensation [35]  A simple Monte Carlo model was used to calculate the expected broadening and mogul structure due purely from N + Stark shifts. For 100 ppm nitrogen and 1 ppm NV − a volume within 8 nm of a given NV site is considered: a volume involving approximately 10 5 lattice sites. Within this volume each site for 100 ppm sample has a probability of 1/10 4 to be a nitrogen atom and each of these nitrogens for 1ppm NV − have a 1/10 2 to be positively charged. The remaining nitrogen sites likewise have a 1/10 2 chance being another NV − with -ve charge. The electric field due to the charges at the original NV site is summed. The site is assumed to contribute two narrow lines to the total, with positions given according to the field sensitivities given by Acosta et. al. [39] (Axial shifts of 4GHz for 10 4 V/cm and a splittings of 5 GHz for 10 4 V/cm although the authors expressed some reservations as only obtained for one centre. Screening due to dielectric constant is included in these values). Each of the lines is taken to be a Gaussian with FWHM of 0.3 nm, as this is the approximate line width of the narrowest mogul lines. Repeating this calculation 10 5 times and summing the resultant line gives the expected line-shape under blue illumination. For the situation of red illumination, we start with the blue situation already described. If the nitrogen site closest to the NV center is not already charged, then it is made to be charged and one of the charged sites is randomly chosen to be made neutral. The line widths for these situations are illustrated in Figure 17 for 100 ppm nitrogen with NV − concentrations of 1ppm (Results for calculation of 5 ppm and 25 ppm NV − are also included). The central feature is largely determined by the density of charges in the lattice and this gives the pronounced broadening as the NV − concentration increases, remembering that there is equal concentration of N + . The mogul structure at > 50 cm −1 is due to the N + charges that can be close to the central NV − and these are shown in more detail in Figure  18b.
There are a large number of moguls corresponding to donors at large distance from the NV and these features overlap and contribute to the ZPL line width as described above. A shift proportional to the calculated electric field should be valid for such cases where the donor is at large distances (>12 A 0 ). On the other hand there are a small number of sites that give well shifted mogul spectral features. The approach is less likely to be valid for the close neighbor sites as the   Figure 18b and this should be compared with the spectra given in Figure 18a associated with the moguls from the experimental trace in Figure 14. There is a reasonable degree of accord and gives support that the principle of the calculation and the mechanisms proposed are correct. Clearly more rigorous calculations are desirable. The weakness is that shifted features cannot yet be associated with specific NV − N + separations and there is some uncertainty of the electric field parameters [39]. Without such an information the calculations can only be expected to show the general correspondence rather than agreement.
(a) Emission spectra for six separate excitation wavelengths at 10K. The asymmetry is due to the Boltzmann factor. Dashed trace gives emission when blue illumination is included. Only the red at 620 nm in this example is chopped and in-phase signal detected. There is self absorption at the peak of the zero phonon line leading to unrelable line shape.     a) The excitation spectrum is obtained by sweeping the frequency of a tunable dye laser from 634 to 644nm (20mW) and detecting the emission at 680nm. Absorption is also included normalized to same peak height. Sample temperature is 10K. Signal to high energy side of 636nm is due to exciting/absorbing within vibrational sideband. (b) Upper traces give lifetime measurement of sample with 115 ppm nitrogen and lower traces that of sample with 212 ppm nitrogen using 639 nm (red) and 532 nm (green) excitation. The decay is not strictly exponential but it is noted that the lifetimes are shorter with red excitation (4.2 ns and 7.7 ns) than for 532 nm excitation (4.8 ns and 8 ns)

Visible Emission and Excitation
Emission line width The above analysis of the 3 A 2 -3 E ZPL in absorption has established the dynamics within the crystal that occur with optical illumination and this information is invaluable for the interpretation of emission spectra. Just as the 637 nm absorption line width varies with illumination wavelength, one might expect the emission line width to vary with excitation wavelength. Emission for various wavelengths of excitation is shown in Figure 19a and for convenience the absorption for the same wavelengths is given in the accompanying Figure 19b. The zero-phonon line in emission is broadest when excitation is in the red and narrowest in the blue and various intermediate wavelengths are also included in Figure 19a. The differences between red and blue are most obvious by comparing the limiting case and these are included in the lowest traces conveniently obtained by recording the emission using modulated red excitation with and without simultaneous excitation with blue light (see Figures 19a, 20a). The signal in both cases is that of NV − emission excited by the red (modulated) laser. What is changed is the distribution of N + donors caused by the irradiation: close N + donors in the case of red only excitation and random located N + donors when blue is applied simultaneously. These traces are repeated latter in Figure 20a shown with part of the vibrational sideband. The accompanying Figure 20b indicate the rate at which the spectra between the two situations change.
Emission intensity vs wavelength As well as a difference between red and blue excitation what is more significant is that in all cases the zero-phonon line in emission does not have the extremes of the absorption spectrum. Compare for example spectra given in Figures 19a and 19b for the case of 620 nm excitation/illumination (lowest traces). Comparison at the central frequencies of the zero-phonon line is unreliable owing to self absorption of the emission. Comparison in the wings is more informative and it is seen that there is negligible emission to the high energy of 636 nm ( shift = +40 cm −1 ) or low energy of 639.5 nm (shift = -50 cm −1 ) whereas there are responses in absorption (although weak) at these wavelengths. The lack of emission on the high energy side can be due to a Boltzman factor as measurements are at low temperature (10K) but this can not explain the lack of emission on the low energy side. Similar information is obtained from the excitation spectrum of the zero-phonon line. There is absorption at wavelengths shorter than 640 nm but at these wavelengths the laser does not excite the NV − centre. Hence, the excitation spectrum is narrower than the ZPL absorption spectrum (Figure 21a).
The explanation for the difference between the extreme widths of absorption and emission is a consequence of fast tunneling in the excited state when the donor is close. NV − centres can be excited but with fast tunneling to NV 0 the centres do not emit. Therefore, for centres with large Stark shifts prevalent with red excitation there will be a loss of radiative decay and a quenching of the emission. There are frequencies that give absorption but little or no emission and it is this that results in the more restricted range of the zero-phonon line in emission. The emission lifetime is also shortened and the shortening is again more pronounced with red excitation than with other wavelength such as 532 nm as shown in Figure 21b. The extreme case is that of the mogul features where the tunneling to NV 0 always occurs before any radiative decay. Excitation of the mogul features do not give emission. The NV 0 immediately decays to its ground state and tunnels back to NV − a sequence that occurs without emission. No emission is detected for wavelengths longer that 640 nm corresponding to a energy shift of -50 cm −1 implying the centres with NV − -N + separations of 12A 0 or closer (see mogul calculation) do not emit. With blue illumination giving the randomly distributed donors the centres that previously (with red) did not emit are shifted in frequency and now do emit. As a consequence with the addition of blue illumination more centres emit and for the same excitation intensity the total emission is increased by 10%. This is illustrated in Figure 20 where the increase is most obvious in the vibrational sideband.

Samples: variation with nitrogen concentration
In the above discussion the properties of NV − in 1b diamond have focused on one nitrogen concentration (115 ppm). It is anticipated that there will be variation of properties with nitrogen concentrations and it will be shown in this section that there are differences that arise from changes in average tunneling rates and NV-N separations.
Low intensity Firstly differences between samples can be detected using low excitation intensities. This is illustrated in Figure 22 where it can be seen that the ratio of NV 0 / NV − emission varies with (single substitutional) nitrogen concentration. The variation is a consequence of the different proximity of nitrogen donors altering the tunneling in the GROUND state. When there is a nitrogen atom within 'reasonable' distance of the NV an electron will tunnel to the NV to give an NV − centre. When the distances are such that this does not occur within a reasonable time scale the centre will 'remain' as NV 0 [31]. For the nitrogen concentration of 115 ppm (Figure 22) clearly the distance is too large for tunneling for only 1% of the NV centres. With lower nitrogen concentration the latter will be more common and for the 40 ppm sample NV 0 occurs for 15% of the NV centres, whereas with the higher nitrogen concentration of 212 pm NV 0 does not occur and all centres acquire an electron. The behavior is almost independent of the NV − concentration, well illustrated by Figure 4 of reference [47]. Their figure shows spectra for two nitrogen concentrations with widely varying NV − concentrations. For low nitrogen concentration NV 0 is observed in all examples whereas NV 0 is not observed at all with high nitrogen concentrations. The NV − concentration does have an influence but only as it will effect the average separation to substitutional nitrogen. High intensity Variation with nitrogen concentration tunneling in the EXCITED state is the reverse to that in the ground state. A density of NV 0 detected without being optically induced implies that there are large separation between NV − centres and substitutional nitrogen and tunneling rates are low. In such cases due to the large NV -N separations the tunneling in the excited state is too slow for the creation of NV 0 and there is only minimal increase in NV 0 concentration with optical excitation as seen in Figure 23a for the 40 ppm sample.(see also Figure 8 of reference [48]). This contrasts with the case of the 115 ppm sample where there are close donors with fast tunneling and for these centres tunneling in the excited state give rise to the increase in population of NV 0 as reported in the previous section (see Figure 10a). With higher concentrations such as with the 212 ppm sample there has to be a much larger fraction of close N + donors. Larger fraction of ionization and higher NV 0 concentration can be anticipated. However, there is a catch to observing this situation. The tunneling is such that as soon as the NV 0 decays to the ground state it immediately tunnels back to NV − so that a population of NV 0 cannot be maintained. Therefore in the case of the 212 ppm sample little NV 0 emission is observed at low intensities and also difficult to detect with higher excitation as illustrated in Figure 23b.
Absorption changes For all three samples when the excitation is switched off the centres decay and once in the ground state an electron tunnels from the N 0 to NV 0 's to restore the original NV − population. The tunneling 'selects' close donors and give Stark broadening of the zero-phonon line. The proportion of centres with close donors and associated broadening is large for the high nitrogen concentrations and small for the low nitrogen concentrations. Regardless of concentration the Stark broadening is reduced when there is a redistribution of donors with blue illumination. Spectra illustrating these trends are illustrated in Figures 24 and 25 .
Emission changes and lifetimes In absorption there are differences between the samples with nitrogen concentration. However, the difference in emission with nitrogen concentration is not obvious. This is because the emission of the largest shifted optical frequencies are quenched and   Figures 24, 25a and 25b).
For these three samples the fraction of centres where the emission is quenched and have shorter lifetimes is greater for the higher nitrogen concentration. The consequence is that the emission lifetimes are faster with the higher nitrogen concentration. For example it has been shown earlier in Figure 21b that the rate for the 212 ppm sample is faster than for the 115 ppm sample. Large variation in rates have been reported in the literature and for 1b diamonds the shorter lifetimes correlate with the higher nitrogen concentrations [47][48] [49] [50] [52]. Associated with shortening of the lifetimes and cycling involving NV 0 there is a reduction of spin polarization and this will be discussed in relation to infrared emission in Section 1.10.

Structure of infrared ZPL at 1042nm
Infrared line widths The infrared emission arises from inter-system crossing form the 3 E state and when there is visible emission from this state there is also inter-system crossing and infrared emission within the singlets (although weak). It is found is that some of the characteristics of the visible emission are also exhibited by the infrared emission. For example, the zero-phonon line at 1042 nm is broader when the excitation is in the red close to the 637 nm zero-phonon line and narrower when there is simultaneous illumination with blue light at 445 nm. Remembering that there is a 'normalizing' of the visible emission with nitrogen concentration and this results in only small variation of the infrared line width with nitrogen concentration. The infrared emission is from a orbital singlet and there is no Boltzman factor favoring one side of the zero-phonon line as occurs for the visible emission. The result is an infrared ZPL with slight Stark broadening in both 'wings' to high and low energy with little change of the central component. These effects are shown in Figures 26 for the three nitrogen concentrations 212 ppm, 115 ppm and 40 ppm.
Variation of IR ZPL with excitation wavelength The broadening analogous to the visible (although less) suggests a Stark effect and this was investigated using resonant excitation. A dye laser was tuned to various frequencies (Figure 27a) within the 637 nm optical zero-phonon line and the IR spectrum was recorded for each wavelength. To reduce the loss of emission via hole-burning small random frequency variation of the excitation laser was adopted. The signals although noisy were sufficient to identify structure in the infra red spectrum (27b). A splitting of the infrared zero-phonon line was observed and this splitting increased as the excitation is shifted from the central peak at 637 nm. The excitation selects subgroups of centres with specific electric fields and Stark shifts. As a consequence of these electric fields there is a Stark splitting of the infrared transition. The Stark effect for the infrared transition is factor 2.5 -3 smaller than that for the optical transition. With illumination of blue light although there is a reduction of the Stark splitting of both visible and infrared, the same ratio of shifts is maintained.
Where the excitation is resonant with the peak of the visible ZPL (0 cm −1 in Figure 27a ) there is no splitting of the infrared spectrum (black trace in 27b). The infrared acts as a diagnostic and indicates that the visible transition does not exhibit a splitting at this optical frequency. For all other excitation frequencies there is a splitting of the infrared line. A splitting can be expected particularly when the non-axial electric field parameters are larger than the axial parameter. It is concluded from the observations that there is a significant contribution from Stark effects to the infrared line width although no detailed fitting has been attempted.
The 1042 nm line width has been reported previously [53], but the line widths and splittings reported for a sample of <200 ppm nitrogen are more than a factor 2 larger than that given here for the 212 ppm sample. (width of 2.4 meV, 19 cm −1 compared to < 1 meV, 8 cm −1 and splittings of 1 meV, 8 cm −1 compared to 0.5 meV, 4 cm −1 ). The explanation is most likely due to additional impurities such as with A-centres in the sample discussed in Section 1.11. Should this be the situation the widths will be less from a Stark effect and more from random strain as given in their analysis. Figure 25: The lower traces give absorbance of samples at 10 K. Prior to these measurement (red traces) the samples have been illuminated with 100 mW red laser at 620 nm for approximately 1 minute. This is repeated (blue trace) but with prior illumination with 50 mW at 445 nm likewise for approximately 1 minute. For the upper traces the measurements are made with excitation present. For the red trace there is only red excitation at 620 nm. This is chopped and the in-phase emission detected. For the blue trace this is repeated but the blue illumination at 445 nm is added but not chopped.  Figure 28. When modified to the random donor case by simultaneously irradiating with the 445 nm laser the ODMR line width is similar but the separation of the double peak is reduce to 9 MHz as given by the lower trace of Figure 28. These observations suggest that the Stark effect may again play a role in (c) IR spectrum using resonant excitation at wavelengths marked by crosses (Figure 27a with blue light at 445nm also applied. The blue light inhibited any holeburning and resulted in larger emission signals but frequency range was greatly reduced as clear from the previous figure Figure 27: Variation of infrared line shape with optical excitation frequency. the spectral line shape. Figure 28: ODMR measured at zero field using red excitation at 620nm (upper traces) and same red excitation but with simultaneous illumination with blue light at 445nm. Vertical response corresponds to less emission. Traces repeated with changed order to ensure no memory effects.
Variation of ODMR with excitation wavelength It is found that the ODMR spectrum varies with detection wave length within the ZPL. For example, the separation of the double peak is slightly larger when detection is in the side (high or low) of the zero-phonon line and smaller when the detection is central. Similar observations are obtained using selective excitation at wavelengths within the ZPL and detect emission in the vibrational sideband at 680 nm. A well separated double peak is obtained when the excitation (or detection) is resonant with the wings of zero-phonon line and less separated when excitation is central to the zero-phonon line as shown in the traces in Figure  30. In both selective excitation and selective emission it is known from the study of the visible ZPL that subgroups of centres experiencing different Stark fields are involved and the observations indicate that the electric fields are indeed playing a role in determining the ODMR spectra. The visible emission line width can be 30 cm-1 (900GHz) (Figures 24 and 25)   The double peak in the ODMR has been reported numerous times and there has been comments that there has been difficulty in fitting to conventional line shapes. The best fit is given by Matsuzaki et. al [55] and with electric field considered as a parameter. However, fitting line shape where Stark effect is involved is not straightforward as indicated by Table 1.

Line shapes
For all transition it has been shown that Stark effect play a role in giving the line width but in no case has a satisfactory calculation of line shape been completed. The relative positions of the N + donors as attempted in Section 1.4 is always required. With knowledge of the Stark parameters the absorption spectra can be calculated and as these are known for the visible transition the principle of line shape calculation has been illustrated in Figure 17. All other spectra requires knowledge of the quenching effects associated with tunneling rates for the various N + -NV − separations and these are not known. Such information would allow emission line shapes to be determined. Likewise the infrared line shape although involves different Stark parameters and these have yet to be determined. ODMR line requires the information as for the visible emission but in addition a further set of Stark parameters are required. Spin polarization associated with position of N + donors needs also to be determined. Calculation of line shapes are clearly complex and the parameters necessary for calculation of the various line shapes is summarized in Table 1 1.10 Spin polarization and IR emission (a) Infrared emission of five samples with various nitrogen concentrations including ones from 20 ppm to 350 ppm. For these latter two samples nitrogen concentrations were obtained from FTIR measurements but the spectra indicated that there were other impurities. Therefore they are not simple 1b diamond and were not included in the more extensive experiments. Excitation involved 30 mW at 532 nm over sample area of 1 mm 2 . The emission traces are normalized to the 3 E -3 A2 at 930 nm. (b) The traces illustrated the change of emission with the application of a 500 gauss magnetic field and equivalent to figure 7b but at room temperature not low temperature. Loss of population for the 3 A2 -3 E transition and a gain of the infrared 1 A1 -1 E transition. The traces are for various samples and normalized for loss of visible emission. (For the 350 ppm sample there was negligible change of emission with field and so could not be included). The infrared shows a slight increase (30%) between 20ppm and 212ppm with increase of nitrogen concentration.

Figure 32: IR detection
From the earlier analysis it is recognized that NV − in the excited state can tunnel to NV 0 and subsequent tunneling in the NV 0 ground state returns the system to NV − . This optical cycle involving the charge conversion will not maintain spin polarization and, therefore, the tunneling will reduce spin polarization attained in a sample. The tunneling is most significant when the NV − and N + donors are close as occurs with the higher nitrogen concentrations and it is clear there will be a decrease of spin polarization with increasing nitrogen concentration. At very high nitrogen concentrations there are the centres that do not emit, cannot polarize and their presence in samples will further reduce the average spin polarization. This could be the situation with EPR measurements (see reference [30]). It is concluded that it is the occurrence of excited state tunneling to NV 0 that is the origin of reduced optically-induced spin polarization of NV − in 1b diamonds.
Measurement of spin polarization The reduction of ensemble spin polarization with nitrogen concentration can be conveniently monitored using infrared emission. This effect has been noted in the Introduction. The fraction of population that decay via the singlet levels and gives rise to the infrared emission increases as the spin polarization is reduced and such a trend is illustrated by Figure 32a. The observation provides a measure of spin polarization of emitting centres. Zero infrared emission corresponds to total polarization with no population in the m s = ± 1 spin state. On-the-other-hand the signal for no spin polarization can be obtained by applying a magnetic field (approximated by 500gauss along <001>). Between these limits the singlet emission gives a measure of the polarization. The values in Figure 32a correspond to the m s = 0 (and m s = ± 1) population varying from 35% (65% -almost unpolarized) to 75% (25%-high polarization) and these are plausible values compared to polarizations reported in literature.
The shortcomings of the techniques are recognized. One experimental issue is that when totally unpolarized as with a magnetic field all the samples should give the same ratio between infrared and visible emission and yet it is found that there are small departures from this situation. The reason is attributed to a small change of the strength of the infrared emission compared to nonradiative decay as illustrated by Figure 32b. Note the variation in Fig 32a indicates changes due to the different decay via optical and infra red whereas the variation in Figure32b is due to differences in the infrared and non-radiative decay. The latter change is almost certainly due to an increase of the infrared oscillator strength as it is very improbable the non-radiative transition would become weaker with added nitrogen impurities. The increasing nitrogen causing a variations of the oscillator strength has intriguing implications for the 1 A 1 -1 E transition and will require further investigation. The effect is 30% and although significant does not make the approach for determining spin polarization from the infrared emission invalid. Further investigations are merited and such an investigation could also establish whether there is a correlation between optical contrast, optical lifetime and the infrared emission.

Discussion
Samples The range of samples studied is limited. This is as a consequence of the samples not being prepared specifically for this study but rather the study relied on samples available from earlier investigations. The samples of interest are ones containing a concentration of nitrogen but focus on nitrogen that can act as a donor. Only substitutional nitrogen N 0 act as donors, the impurities that formally define 1b diamonds and, hence, the focus is on NV in 1b diamond. Other samples investigated had concentration of nitrogen but only a few had only substitutional nitrogen and these are the ones reported. The other samples included impurities that were not clearly identified and made any interpretation unsatisfactory. Other impurities may be studied at a later date to establish whether any new physics processes become relevant. There is one exception in that a sample that included A-centres (two nearest neighbor nitrogen atoms) in addition to single substitutional nitrogen was undertaken and reported in the next Section 1.12.
NV − concentration A concentrations of NV − centres can affect properties such as spin polarization but this has not been studied in any detail. No range of concentration was available and the ones studied had concentrations of only a few ppm very small compared to nitrogen concentrations of up to several hundred ppm. The present studies can be considered as investigations of NV interacting with an ensemble of nitrogen atoms and not to first order ensembles of NV centres. Consistent with this the only aspect where the NV − concentration is considered to influence the properties is that associated with optical line width included within the calculation given in Figure  17. This broadening is only as a consequence of higher electric fields than can be obtained for a single donor. When NV − concentrations are high there could be Förster resonant energy transfer (FRET) [51] between NV − centres and can lead to transfer to a non-emit or non-polarized centre. This would certainly reduce emission and spin polarization. There could also be energy transfer to the N 0 centres as has been suggested occurs with NV 0 [52], although this will be much less for NV − compared to NV 0 as the optical strength of N 0 is less at 637 nm compared to that at 575 nm (see Figures 3 and 6). In addition at high NV − densities spin-spin interaction can average the polarization effects as already studied by others [57].
However, a concentration n of NV − will necessitate crystals with a density of nitrogen and owing to this bath of nitrogen the NV − centres in the sample will have a range of emission strengths and spin polarization as indicated in the present studies. Consequently signal strengths will not increase with n and signal-to-noise will not increase as √ n. It will require samples with a range of NV and N 0 to establish which of the process dominate and how signals do vary with NV − concentration.
Spacial Other aspects not treated are spacial factors. These can be very important when detection is of a very small focused spot such as µ 3 as shown by Jayakumar et.al. [56]. Excitation at one location affects the adjacent environment via diffusion. This situation is avoided in the current study by exciting and detecting mm 3 volume that is relatively large and the effects from the adjacent crystal will be small. However, much smaller spot sizes are more relevant for applications and there is a need to investigate how the present observations are modified when the diffusion of electron and holes into and out of detected volume as in [56] become significant.

A-centre impurity
Spin polarization From FTIR measurements ( Figure 8) it was established that one sample contained nitrogen-pairs (A-centre) in addition to substitutional nitrogen (Compare figure 8 in [58]). The A-centres are generally neutrally charged and will not act as donors for NV − as the ionization energy is 4 eV. The donors associated with the NV − in this sample will still be the single-substitutal nitrogen atoms (N 0 or C-centres). It is only the N + donor that changes and controls the spin polarization and when the infrared emission of this sample is compared with other samples it suggests a 'nitrogen' concentration of <100ppm ( not included in Figure 32a). This is consistent with the measurement of the N 0 (C-centre) in the FTIR spectrum in Figure 8 but there is a large uncertainty due to the overlap of the A-centre absorption. The assertion is that even in this sample it is the concentration of singly substitutional nitrogen that determines spin polarization but confirmation whether this is always the case requires a wider range of samples.
Linewidth The presence of the A-centres introduces strain, non-local to the NV − and this is found to give significant broadening to the electronic transitions in the visible and infrared as shown in Figures 33. The broadening from the 192 ppm A-centres is larger than that associated with 212 ppm concentrations of substitutional nitrogen N 0 (C-centres). Indeed the broadening associated with the N 0 (C-centres) is found to be remarkably small as there is little additional width of the optical transition associated with the 212 ppm sample or the 115 ppm sample compared to that for the 40 ppm sample other than that attributed to N + Stark broadening. This suggests that the inclusion of the N 0 nitrogen introduces little non-local strain broadening. The best estimate is obtained from the width of the moguls lines where the widths must arise from non-local strain. In the 212 ppm sample the mogul widths are 4 cm −1 ( the Stark broadening is 24 cm −1 ) and this contrasts with 40 cm −1 line width for the sample incorporating 192 ppm A-centre nitrogen. It is concluded that the A-centre introduces more strain than the N 0 . This is not what was anticipated as the single nitrogen substitutes for carbon but undergoes a distortion and the distortion is thought to introduce strain. The normal consideration of strain as treated by Stoneham [59] is from such defects and the strain field is over a volume within the crystal and affect many centres. Davies [60,61] has treated optical line widths in diamond largely involved natural diamonds where A-centres would be the predominant nitrogen impurity. It is from his analysis that it has been concluded that nitrogen impurities contributed the dominant broadening of ZPL's in diamond samples. This maybe the case but it should be clarified as to which nitrogen impurities introduce the more significant broadening. Ideally an expanded study of line widths for all types of impurities would be worthwhile.

Other studies
Other color centres Photo-conversion between charge states of defects in diamond has been reported many times and long before this or our earlier work [19]. The processes are generally linear and must occur through some type of tunneling or charge hoping. It would be interesting to investigate whether the specific tunneling phenomenon reported here associated with N 0 donors occur in other centres in diamond. For example, there are silicon-vacancy centres SiV − (ZPL at 738nm, 1.68eV) [62] [63] and SiV 0 (ZPL at 946nm, 1.31 eV) [64], A-centre-vacancy centres H2 (NNV − at 989 nm, 1.25 eV) and H3 (NNV 0 at 503 nm, 2.46eV) [61] and vacancy centres GR1 (V 0 at 741 nm, 1.56 eV) and ND1(V 0 at 340nm, 2.37 eV) [19]. These centres exhibit photo-conversion between the charge states and the extra electron charge may well arises from single substitutional nitrogen. Questions arise as to whether donors can become adjacent in these other centres and give Stark broadening as observed here. Also concerning the NV centre is there anything that can be learned from these other systems?
Spin studies There are many investigations of the spin properties of the NV − centres including ones associated with ensembles that have relevance to the present optical study. For example Choi et.al. [57] in investigating the spin lifetime and decoherence of NV − have attributed the degrading of the spin properties to interaction with a fraction of NV − centres that are not spin polarized, termed 'fluctuators'. These effects may be related to optical cycle explained here where NV − are formed from NV 0 by tunneling as such NV − centres will not be spin polarized. In a separate study of nano-diamonds the spin polarization as indicated by the magnitude of spin contrast has been correlated with optical emission lifetimes [65]. This is a relationship where preliminary measurements have been undertaken here in relation to infrared emission in Section 1.10. Loretz et. al [66] in studying spin transfer for NV − to P1 (N 0 ) at 51 mT in a sample with 77 ppm nitrogen have observed a low spin polarization and saturation of the EPR signal at modest intensities. The authors attribute to the loss of signal and polarization to tunneling from the photo-excited NV − to adjacent donors consistent with processes proposed in this paper.
Optical In a study of ensemble of NV − in nano-diamonds created from 1b diamonds Wolters et.al. [45] observed fast frequency changes of the 637 nm zero-phonon line upon optical excitation and attributed the spectral diffusion to Stark shifts. The processes are associated with the excitation and they rule out two-photon processes. It was notable that the rates observed change with excitation wavelength -faster at higher energies. Their observations are consistent with present measurements. Related to these effects Janonneau et.al. [67] reported electric field fluctuation that contributed to the noise in the measurement of spin coherence of NV − in single spin systems. In a very different experiment Bradac et.al. [68] and Inam et.al. [69] have investigated very small nanodiamonds. They observed the emission of small nano-diamonds can be weak and exhibit blinking. The blinking in their cases are most likely related to surface effects as surfaces are a major concern in small diamonds. However, in very small diamonds there is the question whether it is possible to ever have a small number of close NV − -N + pairs that do not emit and give blinking. One can also speculate that there could be issues with close donors when trying to fabricate NV − centres very close to the diamond surface as achieved by Ofor-Okai el.al. [70].

Conclusions
The conclusions are: 1. The spin polarization that can be attained with NV − centres in 1b diamond is limited by the concentration of substitutional nitrogen.
• The process that limits the spin polarization is tunneling in the NV − excited state to NV 0 : linear in optical excitation 2. The properties of the separate centres in 1b diamond depend on NV − -N + separations.
• When the separation is large the NV − -N + pair centre has properties as reported for NV − single sites • When the separation is reduces the emission is weaker and spin polarization is reduced.
• When separation is less than 12 A 0 the pair centre does not emit and clearly there is no spin polarization.
3. Optical excitation alters the NV − -N + separations and with this the properties of the sample.
• Every observation depends on the excitation wavelength.
4. The N + donor gives an electric field at the NV − site that causes a Stark shift of the spectral transitions within the NV − system; optical, infrared and spin.
• The Stark effect in itself is of no particular significance for applications and the details are largely of academic interest. However, it is the study of the Stark effects that provides the vital insight into the properties and changing properties of the NV − -N + pair centre within 1b diamond.
• The vast majority of the study focuses on the variation of Stark effect on the electronic and spin transitions. Study involves nitrogen concentrations from 320 ppm to 20 ppm. Processes will occur at lower concentrations but could be harder to prove.

5.
No direct attention has been given to nano-diamonds, shallow implants or single sites but the knowledge of processes not previously considered may have implications in this wider area.
6. Most significantly the insight into the properties and processes associated with NV − in 1b diamond will enable better optimization of samples for applications.