Nitrogen-vacancy center


The nitrogen-vacancy center is one of numerous photoluminescent point defects in diamond. It consists of a nearest-neighbor pair of a nitrogen atom, which substitutes for a carbon atom, and a lattice vacancy.
The most explored and useful properties of an NV center include its spin-dependent photoluminescence, and its relatively long spin coherence at room temperature, lasting up to milliseconds. The NV center energy levels are modified by magnetic fields, electric fields, temperature, and strain, which allow it to serve as a sensor of a variety of physical phenomena. Its atomic size and spin properties can form the basis for useful quantum sensors.
NV centers enable nanoscale measurements of magnetic and electric fields, temperature, and mechanical strain with improved precision. External perturbation sensitivity makes NV centers ideal for applications in biomedicine—such as single-molecule imaging and cellular process modeling. NV centers can also be initialized as qubits and enable the implementation of quantum algorithms and networks. It has also been explored for applications in quantum computing, quantum simulation, and spintronics.

Production

Natural NV centers are randomly oriented within a diamond crystal. Ion implantation techniques can enable their artificial creation in predetermined positions, as follows.
Nitrogen-vacancy centers are typically produced from single substitutional nitrogen centers by irradiation followed by annealing at temperatures above 700 °C. A wide range of high-energy particles is suitable for such irradiation, including electrons, protons, neutrons, ions, and gamma photons. Irradiation produces lattice vacancies, which are a part of NV centers. Those vacancies are immobile at room temperature, and annealing is required to move them. Single substitutional nitrogen produces strain in the diamond lattice; it therefore efficiently captures moving vacancies, producing the NV centers.
During chemical vapor deposition of diamond, a small fraction of single substitutional nitrogen impurity traps vacancies generated as a result of the plasma synthesis. Such nitrogen-vacancy centers are preferentially aligned to the growth direction. Delta doping of nitrogen during CVD growth can be used to create two-dimensional ensembles of NV centers near the diamond surface for enhanced sensing or simulation.
Diamond is notorious for having a relatively large lattice strain. Strain splits and shifts optical transitions from individual centers resulting in broad lines in the ensembles of centers. Special care is taken to produce extremely sharp NV lines required for most experiments: high-quality, natural diamonds are selected, although synthetic diamonds are preferential. Many of them already have sufficient concentrations of grown-in NV centers and are suitable for applications. If not, they are irradiated by high-energy particles and annealed. Selection of a certain irradiation dose allows tuning the concentration of produced NV centers such that individual NV centers are separated by micrometre-large distances. Then, individual NV centers can be studied with standard optical microscopes or, better, near-field scanning optical microscopes having sub-micrometre resolution.

Structure

The nitrogen-vacancy center is a point defect in the diamond lattice. It consists of a nearest-neighbor pair of a nitrogen atom, which substitutes for a carbon atom, and a lattice vacancy.
Two charge states of this defect, neutral NV0 and negative NV−, exist. The NV0 centers can be converted into NV− by changing the Fermi level position with an external voltage.
On the one hand, the neutral state is not generally used for quantum technology. The NV− state is commonly, and somewhat incorrectly, called "the nitrogen-vacancy center". On the other hand, the modern, detailed structural understanding of the system originates from theoretical considerations and recent electron resonance and optically detected magnetic resonance studies on the paramagnetic NV0 state. Other spectroscopies used to describe the system's general structure include optical absorption and photoluminescence.
In the neutral NV0, the nitrogen atom has five valence electrons. Three are covalently bonded to adjacent lattice carbon atoms, while the other two remain a non-bonded lone pair.
The vacancy carries three valence electrons. Two of them form a quasi covalent bond and one remains unpaired. The overall symmetry, however, is axial ; one can visualize this by imagining the three unpaired vacancy electrons continuously exchanging their roles in a quantum superposition.
In the negative charge state NV−, an extra electron is located at the vacancy site forming a spin S=1 pair with one of the vacancy electrons. This extra electron induces spin triplet ground states of the form |3A⟩ and excited states of the form |3E⟩. There is an additional metastable state that exists between these spin triplets, that often manifests as a singlet. As in NV0, the vacancy electrons preserve the overall trigonal symmetry.

Energy levels

A NV center has a ground-state triplet, an excited-state triplet and two intermediate-state singlets. Both 3A and 3E contain ms = ±1 spin states, in which the two electron spins are aligned, and an ms = 0 spin state where the electron spins are antiparallel. Due to the magnetic interaction, the energy of the ms = ±1 states is higher than that of the ms = 0 state. 1A and 1E only contain a spin state singlet each with ms = 0.
As discussed below, many properties of the environment affect the precise energy levels and population of the system states:
  1. Amplitude and orientation of a static magnetic field splits the ms = ±1 levels in the ground and excited states.
  2. Amplitude and orientation of elastic or electric fields have a much smaller but also more complex effects on the different levels.
  3. Continuous-wave microwave radiation changes the population of the sublevels within the ground and excited state.
  4. A tunable laser can selectively excite certain sublevels of the ground and excited states.
  5. Surrounding spins and spin–orbit interaction will modulate the magnetic field experienced by the NV center.
  6. Temperature and pressure affect different parts of the spectrum including the shift between ground and excited states.

Electromagnetic coupling

The Hamiltonian dynamics of a NV center are approximated extremely well by the following sum of interactions with the electromagnetic field:
Each term in the Hamiltonian can be measured under the right conditions.

Optical properties

[Image:NVple.JPG|thumb|upright=1.1|Optical absorption and emission of the NV− center at room temperature.|left]
NV centers emit bright red light, if excited off-resonantly by visible green light. This can be done with convenient light sources such as argon or krypton lasers, frequency doubled Nd:YAG lasers, dye lasers, or He-Ne lasers. Excitation can also be achieved at energies below that of zero phonon emission.
As the relaxation time from the excited state is small, the emission happens almost instantly after the excitation. At room temperature the NV center's optical spectrum exhibits no sharp peaks due to thermal broadening. However, cooling the NV centers with liquid nitrogen or liquid helium dramatically narrows the lines down to a width of a few MHz. At low temperature it also becomes possible to specifically address the zero-phonon line.
An important property of the luminescence from individual NV centers is its high temporal stability. Whereas many single-molecular emitters bleach after emission of 106–108 photons, bleaching is unlikely for NV centers at room temperature. Strong laser illumination, however, may also convert some NV− into NV0 centers.
Because of these properties, the ideal technique to address the NV centers is confocal microscopy, both at room temperature and at low temperature.

State manipulation

Temperature and pressure directly influence the zero-field term of the NV center leading to a shift between the ground and excited state levels.

Radiative and non-radiative transitions

Optical transitions must preserve the total spin and occur only between levels of the same total spin. Specifically, transitions between the ground and excited states can be induced using a green laser with a wavelength of 546 nm. Transitions 3E→1A and 1E→3A are non-radiative, while 1A →1E has both a non-radiative and infrared decay path.
The non-radiative transition between 3E and 1A is stronger for ms = ±1 and weaker for ms = 0. This asymmetry enables optical spin-polarization, which initializes the quantum state of a qubit for quantum information processing or quantum sensing. To understand the process, first consider an off-resonance excitation which has a higher frequency than all transitions and thus couples to each transition through vibron excitation. A pulse of this wavelength will excite all spin states to 3E. Because the transition to 1A is weak for ms = 0, the spin-zero states radiate back to 3A. But states with ms = ±1 often decay nonradiatively to 1A, at which point the system is in a ms = 0 state. Further decay from 1A tends to preserve ms = 0, and after many cycles the system is in the ms = 0 ground state with high probability.

Static external fields

Microwave irradiation

The energy difference between the ms = 0 and ms = ±1 states corresponds to the microwave regime. Population can be transferred between the states by applying a resonant magnetic field perpendicular to the defect axis. Numerous dynamic effects can be exploited by applying a carefully designed sequence of microwave pulses. Such protocols are rather important for the practical realization of quantum computers. By manipulating the population, it is possible to shift the NV center into a more sensitive or stable state. Its own resulting fluctuating fields may also be used to influence the surrounding nuclei or protect the NV center itself from noise. This is typically done using a wire loop which creates an oscillating magnetic field.

Locally constant fields

If a magnetic field is oriented along the defect axis, the Zeeman effect splits the ms = +1 from the ms = -1 states. This technique is used to lift the spin degeneracy and use only two of the spin states as a qubit. In the specific instance that the magnetic field reaches 1028 G then the ms = –1 and ms = 0 states in the ground state become equal in energy. In such cases, the spin polarization technique detailed above becomes inefficient.
Zeeman splitting can also be modulated with an external electric field, although the physics of the splitting is somewhat more complex. Crystal strain has a similar effect on the NV center as electric fields.
The hyperfine interactions with nuclear spin also split the ms = ±1 energy levels. Optical pumping can coherently map of the spin states of the nitrogen nucleus to that of the NV center under the application of external magnetic field transverse to the NV symmetry axis. Also the NV center's own spin–orbit interaction and orbital degeneracy leads to additional level splitting in the excited 3E state.

Net charge

It is also possible to switch the charge state of the NV center by applying a gate voltage. The gate voltage electrically shifts the Fermi level at the diamond surface and changes its surface band bending. Upon varying the gate voltage, individual centers are allowed to switch from an unknown non-fluorescent state to the neutral charge state NV0. The ensemble of centers can be transitioned from NV0 to the qubit state NV−. The diamond surface termination additionally influences the charge state of near-surface NV centers. Oxygen termination is known to stabilize the NV−state by reducing surface conductivity and mitigating band bending. This improves charge state stability and coherence. In a similar capacity, nitrogen termination also affects surface properties and can optimize NV centers for specific sensing applications.
Optical excitation methods additionally play a role in charge state manipulation. Illumination with specific wavelengths can induce transitions between charge states. Near-infrared light at 1064 nm has been shown to convert NV0 to NV−, enhancing photoluminescence. Additionally, it has been demonstrated that NV+ centers can be switched to NV0 by photons with energies 1.23 eV.

Applications

The NV energy structure is by no means exceptional for a defect in diamond or other semiconductor. It was not this structure alone, but a combination of several favorable factors which suggested the use of the NV center as a qubit and quantum sensor.
The NV center can have a very long spin coherence time approaching the second regime. This is advantageous for applications in quantum sensing and quantum communication. Disadvantageous for these applications is the long radiative lifetime of the NV center and the strong phonon sideband in its emission spectrum. Both issues can be addressed by putting the NV center in an optical cavity.
The spectral shape and intensity of the optical signals from the NV− centers are sensitive to external perturbation, such as temperature, strain, electric and magnetic field. However, the use of spectral shape for sensing those perturbation is impractical, as the diamond would have to be cooled to cryogenic temperatures to sharpen the NV− signals. A more realistic approach is to use luminescence intensity, which exhibits a sharp resonance when a microwave frequency is applied to diamond that matches the splitting of the ground-state levels. The resulting optically detected magnetic resonance signals are sharp even at room temperature, and can be used in miniature sensors. Such sensors can detect magnetic fields of a few nanotesla or electric fields of about 10 V/cm at kilohertz frequencies after 100 seconds of averaging. This sensitivity allows detecting a magnetic or electric field produced by a single electron located tens of nanometers away from an NV− center.
Using the same mechanism, the NV− centers were employed in scanning thermal microscopy to measure high-resolution spatial maps of temperature and thermal conductivity.
Because the NV center is sensitive to magnetic fields, it is being actively used in scanning probe measurements to study myriad condensed matter phenomena both through measuring a spatially varying magnetic field or inferring local currents in a device.
Another possible use of the NV− centers is as a detector to measure the full mechanical stress tensor in the bulk of the crystal. For this application, the stress-induced splitting of the zero-phonon-line is exploited, and its polarization properties. A robust frequency-modulated radio receiver using the electron-spin-dependent photoluminescence that operated up to 350 °C demonstrates the possibility for use in extreme conditions.
In addition to the quantum optical applications, luminescence from the NV− centers can be applied for imaging biological processes, such as fluid flow in living cells. This application relies on good compatibility of diamond nano-particles with the living cells and on favorable properties of photoluminescence from the NV− centers. Compared with large single-crystal diamonds, nanodiamonds are cheap and available from various suppliers. NV− centers are produced in diamond powders with sub-micrometre particle size using the standard process of irradiation and annealing described above. Due to the relatively small size of nanodiamond, NV centers can be produced by irradiating nanodiamond of 100 nm or less with medium energy H+ beam. This method reduces the required ion dose and reaction, making it possible to mass-produce fluorescent nanodiamonds in ordinary laboratory. Fluorescent nanodiamond produced with such method is bright and photostable, making it excellent for long-term, three dimensional tracking of single particle in living cell. Those nanodiamonds are introduced in a cell, and their luminescence is monitored using a standard fluorescence microscope.
Stimulated emission from the NV− center has been demonstrated, though it could be achieved only from the phonon side-band and not from the ZPL. For this purpose, the center has to be excited at a wavelength longer than ~650 nm, as higher-energy excitation ionizes the center.
The first continuous-wave room-temperature maser has been demonstrated. It used 532-nm pumped NV− centers held within a high Purcell factor microwave cavity and an external magnetic field of 4300 G. Continuous maser oscillation generated a coherent signal at ~9.2 GHz.
The intermediate metastable states 1A and 1E play a crucial role in enabling ground state depletion (GSD) microscopy.

Historical remarks

The microscopic model and most optical properties of ensembles of the NV− centers have been firmly established in the 1970s based on the optical measurements combined with uniaxial stress and on the electron paramagnetic resonance. However, a minor error in EPR results resulted in the incorrect multiplicity assignments in the energy level structure. In 1991 it was shown that EPR can be observed without illumination, which established the energy level scheme shown above. The magnetic splitting in the excited state has been measured only recently.
The characterization of single NV− centers has become a very competitive field nowadays, with many dozens of papers published in the most prestigious scientific journals. One of the first results was reported back in 1997. In that paper, it was demonstrated that the fluorescence of single NV− centers can be detected by room-temperature fluorescence microscopy and that the defect shows perfect photostability. Also one of the outstanding properties of the NV center was demonstrated, namely room-temperature optically detected magnetic resonance.
Despite extensive efforts, electron paramagnetic resonance signals from NV0 avoided detection for decades until 2008. Optical excitation is required to bring the NV0 defect into the EPR-detectable excited state; the signals from the ground state are presumably too broad for EPR detection.