Nitrogen vacancy center

The nitrogen vacancy center is one of over 100 known defects in the diamond lattice . These defects are impurities in the pure carbon lattice of the diamond. It is one of the most prominent candidates for use as an emitter in a solid-state- based single-photon source at room temperature . Possible applications of such sources are in quantum cryptography and in quantum computer systems. The nitrogen vacancy center is also referred to as the NV center ( n itrogen- v acancy center).

Structure of the NV center

Structural sketch of a nitrogen (N) vacancy (V) center. Carbon atoms are shown in blue.

Both natural and synthetic diamonds ideally consist of only carbon atoms (see diamond structure ). However, contamination of this ideal structure must always be expected at the atomic level. Diamond can be classified into classes according to the degree of this contamination. An important class is type Ib diamond. Here the nitrogen is not present in agglomerations, but is evenly distributed over substitutional lattice sites. Therefore, nitrogen-based defects are also predominant and the defects currently (as of January 2010) the most investigated.

Among these defects, the NV center is one of the most promising for applications as a single photon emitter . This center is a complex formation from a single nitrogen atom in connection with a nearest neighbor defect in the carbon lattice of the diamond. Instead of the two naturally present adjacent carbon - atoms in the lattice, is accordingly in the NV-center at each of the position of a carbon atom, a nitrogen atom and at another position near the front of no atom. Together, these two positions in the diamond lattice form the defect - the NV center.

Charging the NV center

Spectroscopic examination: fluorescence image of a NV center in diamond. The two charge states of the center can be seen.

The nitrogen of the NV center is decisive for the electronic structure of the defect center and therefore also for the optical spectrum. However, spectroscopic examinations of the NV center showed the presence of two different NV centers with different charge states (see figure on the right). An exact explanation of the charge is attempted by taking a more detailed look at the atomic bond states in the defect center. If the defect is compared with a pure diamond lattice, including the nitrogen atom and the defect, this leads to unoccupied bonds. These are the three bonds to the surrounding carbon atoms and two bond electrons to the nitrogen atom. This results in a total of 5 electrons . From electron spin resonance experiments it is known, however, that the NV center must have an even number of electrons, a spin of . This problem of the different number of electrons has not yet been finally clarified. However, a model with 6 electrons is used as the working model of the NV center, whereby the missing electron could come from the surrounding grid. This means that the NV center takes on a negative charge. In such a case, the term- center is used and it is the state of charge of the NV center that is most frequently present. The further state of charge of the NV center is called the uncharged center. The occurrence of this center can be traced back to the fact that the mentioned electron donor, which supplies the electron required for the negatively charged center, is not present in the vicinity of the center. Usually, but strictly speaking incorrectly, the center is commonly referred to as the NV center without going into the different charge states. ${\displaystyle S=1}$ ${\displaystyle [NV]^{-}}$ ${\displaystyle [NV]^{0}}$ ${\displaystyle [NV]^{0}}$ ${\displaystyle [NV]^{-}}$ ${\displaystyle [NV]^{-}}$

State model of the NV center

As the simplest electronic model, a 3-level system can be cited for the NV center, i.e. a system that consists of three different electronic states. There is a basic state and an excited state and another energetically between these states . For the NV center, it can be concluded from the structural considerations that the ground state is a triplet state. By measuring the lifetime of the center, the excited state can also be determined as a triplet state. In the third state, a metastable singlet state is assumed. From investigations of the NV center in the infrared spectral range, conclusions can be drawn about the additional presence of this singlet state and it can be limited energetically between the ground state and the excited state. However, there is currently no precise knowledge of this metastable state. ${\displaystyle ^{3}A}$ ${\displaystyle ^{3}E}$ ${\displaystyle ^{1}A}$

Optical properties and detection

Energy diagram of the 3-level system of the NV center: denotes the ground state, denotes the excited state and the metastable singlet state. denotes the spin substates of the different triplet levels. ZPL is the zero phonon line. ${\displaystyle ^{3}A}$ ${\displaystyle ^{3}E}$ ${\displaystyle ^{1}A}$ ${\displaystyle m_{i}}$

The proof of the presence of NV centers can be accomplished with comparatively simple means. Standardized microscopy components can be used for purely spectroscopic examinations . An objective with a sufficient magnification factor from 60 and a high numerical aperture from 0.4 is the most important component in such an experiment. Thus, the simplest detection is given by photoluminescence examinations at the NV center.

The 3-level system is shown in simplified form in the illustration opposite. In this figure, the number 3 denotes the states and the number of permitted spin states . The spin multiplicity can assume values ​​of overall . Assuming the model of the NV center as described above, a number of 3 possible spin states results. can assume values ​​of . This leads to a Zeeman splitting of the emission line, which z. B. can be verified using an ODMR or ESR process. An analogous consideration applies to the single state , although this has never been observed directly in an experiment. The arrows show the excitation and decay channels in this system. Without the presence of a separate magnetic field as in ODMR examinations, however, only a split into two states is to be expected. In one case the spin of the electrons is parallel with and in the other case antiparallel with . The split of the ground state in this configuration is 2.88 GHz between the two states. ${\displaystyle ^{3}A}$ ${\displaystyle ^{3}E}$ ${\displaystyle m_{s}}$ ${\displaystyle 2S+1}$ ${\displaystyle S=1}$ ${\displaystyle m_{i}}$ ${\displaystyle [-1,0,+1]}$ ${\displaystyle ^{1}A}$ ${\displaystyle m_{i}=-1{,}1}$ ${\displaystyle m_{i}=0}$

In addition to resonant excitation, the transition to the center can also be excited by excitation to higher levels and a subsequent rapid relaxation to the level. This can be achieved, for example, by lighting using various laser systems . As the system reverts to its ground state, a photon is emitted after the excitation . Here, the energetic difference between the two energy levels of , or the wavelength of , is decisive for the frequency of the emitted photon. This applies to any level according to: ${\displaystyle ^{3}A}$ ${\displaystyle ^{3}E}$ ${\displaystyle [NV]^{-}}$ ${\displaystyle ^{3}E}$ ${\displaystyle 1{,}945\,\mathrm {eV} }$ ${\displaystyle 638\,\mathrm {nm} }$

${\displaystyle \lambda ={\frac {h\,c}{E_{2}-E_{1}}}}$,

where is Planck's quantum of action , the speed of light and the energy difference mentioned. The emission of this transition at 638 nm is also referred to as the zero phonon line and allows a clear optical characterization of the NV center. The zero phonon line arises at the transition of the NV center without interaction with the phonons of the surrounding diamond matrix. However, since the energy of a phonon in a solid matrix is ​​typically between 10 and , the thermal movement at room temperature has enough energy to excite a large number of phonons. It follows from this that the phonons can participate in an electronic transition. For this reason, at room temperature the exact energy of the transition under consideration cannot be predicted and the spectral lines are homogeneously broadened. This can lead to the fact that separate resolution of the line is no longer possible. The decay channel via the single state is not spin-conserving and can lead to a significant reduction in the emission from the NV center. An analogous consideration can be given for the center, the zero phonon line is attached to it . A clear differentiation of the charge states present is thus possible on the basis of the detection of the characteristic zero phonon line. ${\displaystyle h}$ ${\displaystyle c}$ ${\displaystyle E_{2}-E_{1}}$ ${\displaystyle 1000\;{\text{cm}}^{-1}}$ ${\displaystyle kT=300\;{\text{cm}}^{-1}}$ ${\displaystyle ^{1}A}$ ${\displaystyle [NV]^{0}}$ ${\displaystyle 575\;{\text{nm}}}$

Not classic behavior of the emission

One of the main advantages of the NV Center is to be understood as a 2-level system thanks to its idealization. If the NV center is optically excited, it can emit a photon. However, this is no longer possible until a renewed excitation has taken place, since the system first has to move from the basic state to the excited state before a photon can be emitted again. In quantum mechanics , an emission of this kind is described via Fock states of the photons. The photon statistics follow a sub-Poisson distribution. This means that each individually emitted photon can only be present in isolation. In the case of a thermal light source , for example, several photons are emitted at the same time. The proof of this special behavior of the NV center is achieved by measuring the correlation function according to the principle of a Hanbury Brown-Twiss structure. It can be determined in an interferometric setup that, with two detectors, the arrival of a photon is never registered on both detectors at the same time.

This behavior gives the individual photons of the NV center their potential useful value in quantum information processing . A quantum mechanical state can be assigned to each photon.

Manufacturing

The NV center occurs in both naturally occurring and synthetically produced diamond. However, it is also possible to create NV centers in a targeted manner. One of the simplest methods in diamond synthesis is the introduction of nitrogen during the CVD growth process. The nitrogen accumulates in the diamond and complexes with flaws are occasionally formed. However, more precisely controllable processes are based on irradiating the diamond with ions - ion implantation . A diamond substrate that is as pure as possible is bombarded with the desired ions . The dose can be defined very precisely and it is possible to generate individual defects with a high 3D spatial resolution. Since bonds in the diamond are broken by the bombardment, unoccupied grid positions remain. In this way, the flaw-based defect centers, such as the NV center, can be generated. This makes use of the fact that when the diamond is heated above 600 ° C after the ion implantation, these defect centers from foreign atoms and defects come together. This is due to the wandering of the imperfections in the diamond as a result of the heating. The activation energy for this diffusion was determined to be 2.4 eV for the NV center. This process can be represented as follows:

${\displaystyle 2\ N^{0}+V^{0}\rightarrow (NV)^{-}+N^{+}}$

As a result, the Fermi level shifts energetically down to the energy level of the centers, so that all nitrogen atoms have either been converted into or . ${\displaystyle [NV]^{-}}$ ${\displaystyle N^{+}}$ ${\displaystyle [NV]^{-}}$

Further irradiation leads to the formation of centers: ${\displaystyle NV^{0}}$

${\displaystyle 2\ (NV)^{-}+V^{0}\rightarrow (NV)^{0}+(NV_{2})^{-}}$ and

${\displaystyle NV^{-}+2\ V^{0}\rightarrow (NV)^{0}+V_{2}^{-}}$.

The occurrence of the and defects have not yet been observed experimentally (as of 1996). The theoretical state of the positively charged center also remains undiscovered. ${\displaystyle NV_{2}^{-}}$ ${\displaystyle V_{2}^{-}}$ ${\displaystyle [NV]^{+}}$

In this way, stable NV centers are created, for example, by bombarding a low-nitrogen class Ib diamond with a beam with a diameter of 0.3 μm consisting of 2 MeV ions. After bombardment, the diamond mainly shows the phosphorescence of the so-called GR1 defect. This is the emission from the neutral flaw in the diamond. If the sample is baked out, the GR1 emission goes down and the characteristic emissions of the NV center appear. ${\displaystyle N^{+}}$ ${\displaystyle V^{0}}$

See also

• Single photon source - The NV center is currently (as of Jan 2010) one of the best known defect centers spectroscopically. The theoretical models for this defect are also the most advanced. Because of its stable and strong emission at room temperature, it is therefore the most promising emitter in a solid-state single photon source . A first realization of such a source was presented in 2009.

• Biomarkers - NV centers can also be implemented in nanometer-sized diamonds on a scale of a few tens of nanometers . This results in new possibilities for use in medicine. Since diamond is not toxic to living tissue, it makes sense to use nanodiamonds as biomarkers. With suitable transport molecules, the fluorescence of defect-rich nanodiamonds can be used as a marker in tissue studies.

• For a further, somewhat more detailed overview - especially of the energy levels - and for access to further literature, it is recommended to also take a look at the English version of the article.

Individual evidence

1. ↑ J. Dynes, H. Takesue, Z. Yuan, A. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe and A. Shields: Efficient entanglement distribution over 200 kilometers . In: Opics Express . 17, 2009. doi : 10.1364 / OE.17.011440 .
2. ↑ A. Nizovtsev, S. Kilin, F. Jelezko, T. Gaebal, I. Popa, A. Gruber and J. Wrachtrup: A Quantum Computer Based on NV Centers in Diamond: Optically Detected Nutations of Single Electron and Nuclear Spins . In: Optics and Spectroscopy . 99
3. ↑ Element Six: Classification of Diamond ( Memento of March 31, 2009 in the Internet Archive )
4. ^ J. Loubser and J. van Wyk: Electron spin resonance in the study of diamond . In: Rep.Prog.Phys. . 41, 1978. doi : 10.1088 / 0034-4885 / 41/8/002 .
5. ^ Y. Mita: Change of absorption spectra in type-ib diamond with heavy neutron irradiation . In: Phys.Rev.B . 53, 1996. doi : 10.1103 / PhysRevB.53.11360 .
6. ↑ A. Lenef and S. Rand: Electronic structure of the nv center in diamond: Theory . In: Phys.Rev.B . 53, 1996. doi : 10.1103 / PhysRevB.53.13441 .
7. ↑ P. Tamarat, N. Manson, J. Harrison, R. McMurtrie, A. Nizovtsev, C. Santori, R. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup: Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy center in diamond . In: New Journal of Physics . 10, 2008. doi : 10.1088 / 1367-2630 / 10/4/045004 .
8. ↑ A. Collins, M. Thomaz, and M. Jorge: Luminescence decay time of the 1.945ev center in type ib diamond . In: Solid State Physics . 16, 1983. doi : 10.1088 / 0022-3719 / 16/11/020 .
9. ↑ L. Rogers, S. Armstrong, M. Sellars, and N. Manson: Infrared emission of the nv-center in diamond: Zeeman and uniaxial stress studies . In: New Journal of Physics . 10, 2008. doi : 10.1088 / 1367-2630 / 10/10/103024 .
10. ↑ G. Balasburmanaian, IY Chan, Roman Kolesov, Mohannad Al-Hmoud, Julia Tisler, Chang Shin, Changdong Kim, Aleksander Wojcik, Philip R. Hemmer, Anke Krueger, Tobias Hanke, Alfred Leitenstorfer, Rudolf Bratschitsch, Fedor Jelezko & Jörg Wrachtrup : Nanoscale imaging magnetometry with diamond spins under ambient condition . In: Nature Lett. . 455, 2008. doi : 10.1038 / nature07278 .
11. ^ G. Fuchs, V. Dobrovitski, R. Hanson, A. Batra, C. Weis, T. Schenkel, D. Awschalom: Excited-State Spectroscopy Using Single Spin Manipulation in Diamond . In: Phys.Rev.Lett. . 101, 2008. doi : 10.1103 / PhysRevLett.101.117601 .
12. ↑ J. Martin, R. Wannemacher, J. Teichert, L. Bischoff and B. Kohler: Generation and detection of fluorescent color centers in diamond with submicron resolution . In: Applied Physics Letters . 75, 1999. doi : 10.1063 / 1.125242 .
13. ↑ F. Jelezko and J. Wrachtrup: Single defect centers in diamond: A review . In: Phys.Stat.Sol.A . 203, 2006. doi : 10.1002 / pssa.200671403 .
14. ^ Y. Mita: Change of absorption spectra in type-Ib diamond with heavy neutron irradiation . In: Phys. Rev. B . 53, No. 17, 1996, pp. 11360-11364. doi : 10.1103 / PhysRevB.53.11360 .
15. ↑ J. Meijer, B. Burchard, M. Domhan, C. Wittmann, T. Gaebel, I. Popa, F. Jelezko and J. Wrachtrup: Generation of single color centers by focused nitrogen implantation . In: Applied Physics Letters . 87, 2005. doi : 10.1063 / 1.2103389 .
16. ↑ QCV - Quantum Computing Victoria
17. ↑ S. Yu, M. Kang, H. Chang, K. Chen and Y. Yu: Bright fluorescent nanodiamonds: No photobleaching and low cytotoxicity . In: J.Am.Chem.Soc. . 127, 2005. doi : 10.1021 / ja0567081 .

literature

Some reviews and overview articles on NV centers in general and in particular on the spectroscopy of NV defects:

• DD Awschalom, R. Epstein, R. Hanson: Spintronik mit Diamant , In: Spectrum of Science, December 2007, pp. 112-120
• F. Jelezko and J. Wrachtrup: Single defect centers in diamond: A review . In: Phys.Stat.Sol.A . 203, 2006. doi : 10.1002 / pssa.200671403 .
• F. Jelezko, C. Tietz, A. Gruber, I. Popa, A. Nizovtsev, S. Kilin and J. Wrachtrup: Spectroscopy of Single NV Centers in Diamond . In: Single Molecules . 2, 2001. doi : 10.1002 / 1438-5171 (200112) 2: 4 <255 :: AID-SIMO255> 3.0.CO; 2-D .
• A. Lenef, S. Brown, D. Redman and S. Rand: Electronic structure of the NV center in diamond: Experiments . In: Phys.Rev.B . 53, 1996. doi : 10.1103 / PhysRevB.53.13427 .
• A. Lenef and S. Rand: Electronic structure of the NV center in diamond: Theory . In: Phys.Rev.B . 53, 1996. doi : 10.1103 / PhysRevB.53.13441 .