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Nitrogen-vacancy center

May 03, 2024

The nitrogen-vacancy center (N-V center or NV center) is one of numerous photoluminescent point defects in diamond. Its most explored and useful properties include its spin-dependent photoluminescence (which enables measurement of the electronic spin state using optically detected magnetic resonance), and its relatively long (millisecond) spin coherence at room temperature.[1] The NV center energy levels are modified by magnetic fields,[2] electric fields,[3] temperature,[4] and strain,[5] 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.[6] It has also been explored for applications in quantum computing (e.g. for entanglement generation[7]) and spintronics.[8]

Simplified atomic structure of the NV center

Structure edit

 
Bottom images are spatial photoluminescence (PL) maps before and after application of +20 V voltage to a planar Schottky diode. The top image outlines the experiment. The PL maps reveal the conversion of individual NV0 centers into NV− centers that appear as bright dots.[9]

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−, are known from spectroscopic studies using optical absorption,[10][11] photoluminescence (PL),[12] electron paramagnetic resonance (EPR)[13][14][15] and optically detected magnetic resonance (ODMR),[16] which can be viewed as a hybrid of PL and EPR; most details of the structure originate from EPR. The nitrogen atom on one hand has five valence electrons. Three of them are covalently bonded to the carbon atoms, while the other two remain non-bonded and are called a lone pair. The vacancy on the other hand has three unpaired electrons. Two of them form a quasi covalent bond and one remains unpaired. The overall symmetry, however, is axial (trigonal C3V); one can visualize this by imagining the three unpaired vacancy electrons continuously exchanging their roles.

The NV0 thus has one unpaired electron and is paramagnetic. However, 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.[17]

The NV0 centers can be converted into NV− by changing the Fermi level position. This can be achieved by applying external voltage to a p-n junction made from doped diamond, e.g., in a Schottky diode.[9]

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. As in NV0, the vacancy electrons are "exchanging roles" preserving the overall trigonal symmetry. This NV− state is what is commonly, and somewhat incorrectly, called "the nitrogen-vacancy center". The neutral state is not generally used for quantum technology.

The NV centers are randomly oriented within a diamond crystal. Ion implantation techniques can enable their artificial creation in predetermined positions.[18]

Production edit

Main article: Crystallographic defects in diamond

Nitrogen-vacancy centers are typically produced from single substitutional nitrogen centers (called C or P1 centers in diamond literature) by irradiation followed by annealing at temperatures above 700 °C.[10] 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;[19] it therefore efficiently captures moving vacancies,[20] producing the NV centers.

 
Production of nitrogen-vacancy centers in diamond may require several steps. First, nitrogen must be introduced into the diamond lattice which can be accomplished via ion implantation or CVD delta doping. Secondly, vacancies must be introduced, which can be accomplished via laser irradiation, ion implantation, or electron irradiation. Alternatively, during the nitrogen introduction step, vacancies may also be introduced. Finally, a high-temperature annealing step can help promote NV formation.[21]

During chemical vapor deposition of diamond, a small fraction of single substitutional nitrogen impurity (typically <0.5%) traps vacancies generated as a result of the plasma synthesis. Such nitrogen-vacancy centers are preferentially aligned to the growth direction.[22][23] 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[24] or simulation.[25]

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.[10][26] Special care is taken to produce extremely sharp NV lines (line width ~10 MHz)[27] required for most experiments: high-quality, pure natural or better synthetic diamonds (type IIa) are selected. 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.[16][28]

 
Schematic energy level structure of the NV center. Electron transitions between the ground 3A and excited 3E states, separated by 1.945 eV (637 nm), produce absorption and luminescence. The 3A state is split by 2.87 GHz[29][30] and the 3E state by 1.42 GHz.[31] Numbers 0, ±1 indicate spin quantum number ms; splitting due to the orbital degeneracy is not shown.

Energy level structure edit

The NV center has a ground-state triplet (3A), an excited-state triplet (3E) and two intermediate-state singlets (1A and 1E).[note 1][32][33] Both 3A and 3E contain ms = ±1 spin states, in which the two electron spins are aligned (either up, such that ms = +1 or down, such that ms = -1), 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.

If an external magnetic field is applied along the defect axis (the axis which aligns with the nitrogen atom and the vacancy) of the NV center, it does not affect the ms = 0 states, but it splits the ms = ±1 levels (Zeeman effect). Similarly the following other properties of the environment influence the energy level diagram (further discussed under #Effects of external fields):

  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 (strain) or electric fields[34][35] have a much smaller but also more complex effects on the different levels.
  3. Continuous-wave microwave radiation (applied in resonance with the transition between ms = 0 and (one of the) ms = ±1 states) changes the population of the sublevels within the ground and excited state.[35]
  4. A tunable laser can selectively excite certain sublevels of the ground and excited states.[35][36]
  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.

The above-described energy structure[note 2] is by no means exceptional for a defect in diamond or other semiconductor.[37] It was not this structure alone, but a combination of several favorable factors (previous knowledge, easy production, biocompatibility, simple initialisation, use at room temperature etc.) which suggested the use of the NV center as a qubit and quantum sensor.

Optical properties edit

 
Optical absorption and emission of the NV− center at room temperature.

NV centers emit bright red light (3E→3A transitions), if excited off-resonantly by visible green light (3A →3E transitions). 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.[38]

As the relaxation time from the excited state is small (~10 ns),[39][40] 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 (ZPL).

An important property of the luminescence from individual NV centers is its high temporal stability. Whereas many single-molecular emitters bleach (i.e. change their charge state and become dark) after emission of 106–108 photons, bleaching is unlikely for NV centers at room temperature.[41][28] Strong laser illumination, however, may also convert some NV− into NV0 centers.[12]

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 edit

 
Spin dynamics in the NV center in diamond. The primary transition between the ground and excited state triplets is spin conserving. Decay via the intermediate singlets gives rise to spin polarization by converting spin from ms = ±1 to ms = 0. Both absorption and emission wavelengths are indicated,[42] since they differ due to Stokes shift.[43][44] Furthermore, the effect of a static magnetic field B0 along the defect axis and the resulting Zeeman shift is indicated. Here, γnv refers to the gyromagnetic ratio of the NV center. In many applications two of the ground-state levels are then used as a qubit.[45] Transitions in this effective two-level system, may be induced using a microwave field. 3E-1A and 1E-3A are non-radiative transitions.

Optical spin manipulation edit

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 (with equal spin) 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 diagram on the right shows the multi-electronic states of the NV center labeled according to their symmetry (E or A) and their spin state (3 for a triplet (S=1) and 1 for a singlet (S=0)). There are two triplet states and two intermediate singlet states.[46]

Spin-state initialisation edit

An important property of the non-radiative transition between 3E and 1A is that it is stronger for ms = ±1 and weaker for ms = 0. This provides the basis a very useful manipulation strategy, which is called spin state initialisation (or optical spin-polarization). To understand the process, first consider an off-resonance excitation which has a higher frequency (typically 2.32 eV (532 nm)) than the frequencies of all transitions and thus lies in the vibronic bands for all transitions. By using a pulse of this wavelength, one can excite all spin states from 3A to 3E. An NV center in the ground state with ms = 0 will be excited to the corresponding excited state with ms = 0 due to the conservation of spin. Afterwards it decays back to its original state. For a ground state with ms = ±1, the situation is different. After the excitation, it has a relatively high probability to decay into the intermediate state 1A by non-radiative transition[note 3][47] and further into the ground state with ms = 0. After many cycles, the state of the NV center (independently of whether it started in ms = 0 or ms = ±1) will end up in the ms = 0 ground state. This process can be used to initialize the quantum state of a qubit for quantum information processing or quantum sensing.

Sometimes the polarisability of the NV center is explained by the claim that the transition from 1E to the ground state with ms = ±1 is small, compared to the transition to ms = 0. However, it has been shown that the comparatively low decay probability for ms = 0 states w.r.t. ms = ±1 states into 1A is enough to explain the polarization.[48]

Effects of external fields edit

Microwave spin manipulation edit

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 (spin echo, Rabi oscillations, etc.) can be exploited by applying a carefully designed sequence of microwave pulses.[49][50][51][52][53] 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.[54][55] Its own resulting fluctuating fields may also be used to influence the surrounding nuclei[56] or protect the NV center itself from noise.[57] This is typically done using a wire loop (microwave antenna) which creates an oscillating magnetic field.[58]

Influence of external factors edit

If a magnetic field is oriented along the defect axis it leads to Zeeman splitting separating the ms = +1 from the ms = -1 states. This technique is used to lift the degeneracy and use only two of the spin states (usually the ground states with ms = -1 and ms = 0) as a qubit. Population can then be transferred between them using a microwave field. In the specific instance that the magnetic field reaches 1027 G (or 508 G) then the ms = –1 and ms = 0 states in the ground (or excited) state become equal in energy (Ground/Excited State Level Anticrossing). The following strong interaction results in so-called spin polarization, which strongly affects the intensity of optical absorption and luminescence transitions involving those states.[31]

Importantly, this splitting can be modulated by applying an external electric field,[34][35] in a similar fashion to the magnetic field mechanism outlined above, though the physics of the splitting is somewhat more complex. Nevertheless, an important practical outcome is that the intensity and position of the luminescence lines is modulated. Strain has a similar effect on the NV center as electric fields.[59]

There is an additional splitting of the ms = ±1 energy levels, which originates from the hyperfine interaction between surrounding nuclear spins and the NV center. These nuclear spins create magnetic and electric fields of their own leading to further distortions of the NV spectrum (see nuclear Zeeman and quadrupole interaction). Also the NV center's own spin–orbit interaction and orbital degeneracy leads to additional level splitting in the excited 3E state.

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

The Hamiltonian, a quantum mechanical equation describing the dynamics of a system, which shows the influence of different factors on the NV center can be found below.

 

Although it can be challenging, all of these effects are measurable, making the NV center a perfect candidate for a quantum sensor.[55]

Charge state manipulation edit

It is also possible to switch the charge state of the NV center (i.e. between NV−, NV+ and NV0) by applying a gate voltage.[60]

Applications edit

 
Scanning thermal microscopy using the NV center.
(a) Schematics of experimental setup. An electric current is applied to the arms of an AFM cantilever (phosphorus-doped Si, P:Si) and heats up the end section above the tip (intrinsic Si, i-Si). The bottom lens excites a diamond nanocrystal with a green laser light and collects photoluminescence (PL). The crystal hosts an NV center and is attached to the AFM tip. A wire on the sample surface serves as the microwave source (mw). The temperature of the cantilever Th is determined from the applied current and voltage.
(b) ODMR spectra of the NV center at three temperatures. The line splitting originates from a ~1 mT applied magnetic field.
(c) Thermal conductivity image of a gold letter E on sapphire. White circles indicate features that do not correlate with the AFM topography. (d) PL image of the AFM cantilever end and tip where the diamond nanocrystal appears as the bright spot. (e) Zoomed PL image of the NV center in d.[61]

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 (rather than lineshape), 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[62] or electric fields of about 10 V/cm[63] 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 (see image).[61]

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.[64][65][66][67][68]

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.[69] 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.[70]

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.[71][72] This application relies on good compatibility of diamond nano-particles with the living cells and on favorable properties of photoluminescence from the NV− centers (strong intensity, easy excitation and detection, temporal stability, etc.). Compared with large single-crystal diamonds, nanodiamonds are cheap (about 1 USD per gram) 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.[73] 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.[74] Those nanodiamonds are introduced in a cell, and their luminescence is monitored using a standard fluorescence microscope.[75]

Stimulated emission from the NV− center has been demonstrated, though it could be achieved only from the phonon side-band (i.e. broadband light) 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.[76]

The first continuous-wave room-temperature maser has been demonstrated.[77][78] 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 NV center can have a very long spin coherence time approaching the second regime.[79] This is advantageous for applications in quantum sensing[80] and quantum communication.[81] Disadvantageous for these applications is the long radiative lifetime (~12 ns[82][83] ) 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.[84]

Historical remarks edit

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[10] and on the electron paramagnetic resonance.[13][14] However, a minor error in EPR results (it was assumed that illumination is required to observe NV− EPR signals) resulted in the incorrect multiplicity assignments in the energy level structure. In 1991 it was shown that EPR can be observed without illumination,[15] which established the energy level scheme shown above. The magnetic splitting in the excited state has been measured only recently.[31]

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.[16] 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.

See also edit

Notes edit

  1. ^ Group theory results are used to take into account the symmetry of the diamond crystal, and so the symmetry of the NV itself. Followingly, the energy levels are labeled according to group theory, and in particular are labelled after the irreducible representations of the C3V symmetry group of the defect center, A1, A2, and E. The "3" in 3A2 and 3E as well as the "1" in 1A1 and 1E represent the number of allowable ms spin states, or the spin multiplicity, which range from –S to S for a total of 2S+1 possible states. If S = 1, ms can be −1, 0, or 1.
  2. ^ The energy level structure of the NV center was established by combining optically detected magnetic resonance (ODMR), electron paramagnetic resonance (EPR) and theoretical results, as shown in the figure. In particular, several theoretical works have been done, using the Linear Combination of Atomic Orbitals (LCAO) approach,[citation needed] to build the electronic orbitals to describe the possible quantum states, looking at the NV center as a molecule.
  3. ^ This is a phenomenon called intersystem crossing (ISC). It happens at an appreciable rate because the energy curve in function of the position of the atoms for the excited ms = ±1 state intersects the curve for the 1A state. Therefore, for some instant during the vibrational relaxation that the ions undergo after the excitement, it is possible for the spin to flip with little or no energy required in the transition.

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May 03, 2024
nitrogen, vacancy, center, nitrogen, vacancy, center, center, center, numerous, photoluminescent, point, defects, diamond, most, explored, useful, properties, include, spin, dependent, photoluminescence, which, enables, measurement, electronic, spin, state, us. The nitrogen vacancy center N V center or NV center is one of numerous photoluminescent point defects in diamond Its most explored and useful properties include its spin dependent photoluminescence which enables measurement of the electronic spin state using optically detected magnetic resonance and its relatively long millisecond spin coherence at room temperature 1 The NV center energy levels are modified by magnetic fields 2 electric fields 3 temperature 4 and strain 5 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 6 It has also been explored for applications in quantum computing e g for entanglement generation 7 and spintronics 8 Simplified atomic structure of the NV centerContents 1 Structure 2 Production 3 Energy level structure 4 Optical properties 5 State manipulation 5 1 Optical spin manipulation 5 1 1 Spin state initialisation 5 2 Effects of external fields 5 2 1 Microwave spin manipulation 5 2 2 Influence of external factors 5 3 Charge state manipulation 6 Applications 7 Historical remarks 8 See also 9 Notes 10 ReferencesStructure edit nbsp Bottom images are spatial photoluminescence PL maps before and after application of 20 V voltage to a planar Schottky diode The top image outlines the experiment The PL maps reveal the conversion of individual NV0 centers into NV centers that appear as bright dots 9 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 are known from spectroscopic studies using optical absorption 10 11 photoluminescence PL 12 electron paramagnetic resonance EPR 13 14 15 and optically detected magnetic resonance ODMR 16 which can be viewed as a hybrid of PL and EPR most details of the structure originate from EPR The nitrogen atom on one hand has five valence electrons Three of them are covalently bonded to the carbon atoms while the other two remain non bonded and are called a lone pair The vacancy on the other hand has three unpaired electrons Two of them form a quasi covalent bond and one remains unpaired The overall symmetry however is axial trigonal C3V one can visualize this by imagining the three unpaired vacancy electrons continuously exchanging their roles The NV0 thus has one unpaired electron and is paramagnetic However 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 17 The NV0 centers can be converted into NV by changing the Fermi level position This can be achieved by applying external voltage to a p n junction made from doped diamond e g in a Schottky diode 9 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 As in NV0 the vacancy electrons are exchanging roles preserving the overall trigonal symmetry This NV state is what is commonly and somewhat incorrectly called the nitrogen vacancy center The neutral state is not generally used for quantum technology The NV centers are randomly oriented within a diamond crystal Ion implantation techniques can enable their artificial creation in predetermined positions 18 Production editMain article Crystallographic defects in diamond Nitrogen vacancy centers are typically produced from single substitutional nitrogen centers called C or P1 centers in diamond literature by irradiation followed by annealing at temperatures above 700 C 10 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 19 it therefore efficiently captures moving vacancies 20 producing the NV centers nbsp Production of nitrogen vacancy centers in diamond may require several steps First nitrogen must be introduced into the diamond lattice which can be accomplished via ion implantation or CVD delta doping Secondly vacancies must be introduced which can be accomplished via laser irradiation ion implantation or electron irradiation Alternatively during the nitrogen introduction step vacancies may also be introduced Finally a high temperature annealing step can help promote NV formation 21 During chemical vapor deposition of diamond a small fraction of single substitutional nitrogen impurity typically lt 0 5 traps vacancies generated as a result of the plasma synthesis Such nitrogen vacancy centers are preferentially aligned to the growth direction 22 23 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 24 or simulation 25 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 10 26 Special care is taken to produce extremely sharp NV lines line width 10 MHz 27 required for most experiments high quality pure natural or better synthetic diamonds type IIa are selected 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 16 28 nbsp Schematic energy level structure of the NV center Electron transitions between the ground 3A and excited 3E states separated by 1 945 eV 637 nm produce absorption and luminescence The 3A state is split by 2 87 GHz 29 30 and the 3E state by 1 42 GHz 31 Numbers 0 1 indicate spin quantum number ms splitting due to the orbital degeneracy is not shown Energy level structure editThe NV center has a ground state triplet 3A an excited state triplet 3E and two intermediate state singlets 1A and 1E note 1 32 33 Both 3A and 3E contain ms 1 spin states in which the two electron spins are aligned either up such that ms 1 or down such that ms 1 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 If an external magnetic field is applied along the defect axis the axis which aligns with the nitrogen atom and the vacancy of the NV center it does not affect the ms 0 states but it splits the ms 1 levels Zeeman effect Similarly the following other properties of the environment influence the energy level diagram further discussed under Effects of external fields Amplitude and orientation of a static magnetic field splits the ms 1 levels in the ground and excited states Amplitude and orientation of elastic strain or electric fields 34 35 have a much smaller but also more complex effects on the different levels Continuous wave microwave radiation applied in resonance with the transition between ms 0 and one of the ms 1 states changes the population of the sublevels within the ground and excited state 35 A tunable laser can selectively excite certain sublevels of the ground and excited states 35 36 Surrounding spins and spin orbit interaction will modulate the magnetic field experienced by the NV center Temperature and pressure affect different parts of the spectrum including the shift between ground and excited states The above described energy structure note 2 is by no means exceptional for a defect in diamond or other semiconductor 37 It was not this structure alone but a combination of several favorable factors previous knowledge easy production biocompatibility simple initialisation use at room temperature etc which suggested the use of the NV center as a qubit and quantum sensor Optical properties edit nbsp Optical absorption and emission of the NV center at room temperature NV centers emit bright red light 3E 3A transitions if excited off resonantly by visible green light 3A 3E transitions 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 38 As the relaxation time from the excited state is small 10 ns 39 40 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 ZPL An important property of the luminescence from individual NV centers is its high temporal stability Whereas many single molecular emitters bleach i e change their charge state and become dark after emission of 106 108 photons bleaching is unlikely for NV centers at room temperature 41 28 Strong laser illumination however may also convert some NV into NV0 centers 12 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 edit nbsp Spin dynamics in the NV center in diamond The primary transition between the ground and excited state triplets is spin conserving Decay via the intermediate singlets gives rise to spin polarization by converting spin from ms 1 to ms 0 Both absorption and emission wavelengths are indicated 42 since they differ due to Stokes shift 43 44 Furthermore the effect of a static magnetic field B0 along the defect axis and the resulting Zeeman shift is indicated Here gnv refers to the gyromagnetic ratio of the NV center In many applications two of the ground state levels are then used as a qubit 45 Transitions in this effective two level system may be induced using a microwave field 3E 1A and 1E 3A are non radiative transitions Optical spin manipulation edit 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 with equal spin 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 diagram on the right shows the multi electronic states of the NV center labeled according to their symmetry E or A and their spin state 3 for a triplet S 1 and 1 for a singlet S 0 There are two triplet states and two intermediate singlet states 46 Spin state initialisation edit An important property of the non radiative transition between 3E and 1A is that it is stronger for ms 1 and weaker for ms 0 This provides the basis a very useful manipulation strategy which is called spin state initialisation or optical spin polarization To understand the process first consider an off resonance excitation which has a higher frequency typically 2 32 eV 532 nm than the frequencies of all transitions and thus lies in the vibronic bands for all transitions By using a pulse of this wavelength one can excite all spin states from 3A to 3E An NV center in the ground state with ms 0 will be excited to the corresponding excited state with ms 0 due to the conservation of spin Afterwards it decays back to its original state For a ground state with ms 1 the situation is different After the excitation it has a relatively high probability to decay into the intermediate state 1A by non radiative transition note 3 47 and further into the ground state with ms 0 After many cycles the state of the NV center independently of whether it started in ms 0 or ms 1 will end up in the ms 0 ground state This process can be used to initialize the quantum state of a qubit for quantum information processing or quantum sensing Sometimes the polarisability of the NV center is explained by the claim that the transition from 1E to the ground state with ms 1 is small compared to the transition to ms 0 However it has been shown that the comparatively low decay probability for ms 0 states w r t ms 1 states into 1A is enough to explain the polarization 48 Effects of external fields edit Microwave spin manipulation edit 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 spin echo Rabi oscillations etc can be exploited by applying a carefully designed sequence of microwave pulses 49 50 51 52 53 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 54 55 Its own resulting fluctuating fields may also be used to influence the surrounding nuclei 56 or protect the NV center itself from noise 57 This is typically done using a wire loop microwave antenna which creates an oscillating magnetic field 58 Influence of external factors edit If a magnetic field is oriented along the defect axis it leads to Zeeman splitting separating the ms 1 from the ms 1 states This technique is used to lift the degeneracy and use only two of the spin states usually the ground states with ms 1 and ms 0 as a qubit Population can then be transferred between them using a microwave field In the specific instance that the magnetic field reaches 1027 G or 508 G then the ms 1 and ms 0 states in the ground or excited state become equal in energy Ground Excited State Level Anticrossing The following strong interaction results in so called spin polarization which strongly affects the intensity of optical absorption and luminescence transitions involving those states 31 Importantly this splitting can be modulated by applying an external electric field 34 35 in a similar fashion to the magnetic field mechanism outlined above though the physics of the splitting is somewhat more complex Nevertheless an important practical outcome is that the intensity and position of the luminescence lines is modulated Strain has a similar effect on the NV center as electric fields 59 There is an additional splitting of the ms 1 energy levels which originates from the hyperfine interaction between surrounding nuclear spins and the NV center These nuclear spins create magnetic and electric fields of their own leading to further distortions of the NV spectrum see nuclear Zeeman and quadrupole interaction Also the NV center s own spin orbit interaction and orbital degeneracy leads to additional level splitting in the excited 3E state Temperature and pressure directly influence the zero field term of the NV center leading to a shift between the ground and excited state levels The Hamiltonian a quantum mechanical equation describing the dynamics of a system which shows the influence of different factors on the NV center can be found below nbsp Although it can be challenging all of these effects are measurable making the NV center a perfect candidate for a quantum sensor 55 Charge state manipulation edit It is also possible to switch the charge state of the NV center i e between NV NV and NV0 by applying a gate voltage 60 Applications edit nbsp Scanning thermal microscopy using the NV center a Schematics of experimental setup An electric current is applied to the arms of an AFM cantilever phosphorus doped Si P Si and heats up the end section above the tip intrinsic Si i Si The bottom lens excites a diamond nanocrystal with a green laser light and collects photoluminescence PL The crystal hosts an NV center and is attached to the AFM tip A wire on the sample surface serves as the microwave source mw The temperature of the cantilever Th is determined from the applied current and voltage b ODMR spectra of the NV center at three temperatures The line splitting originates from a 1 mT applied magnetic field c Thermal conductivity image of a gold letter E on sapphire White circles indicate features that do not correlate with the AFM topography d PL image of the AFM cantilever end and tip where the diamond nanocrystal appears as the bright spot e Zoomed PL image of the NV center in d 61 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 rather than lineshape 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 62 or electric fields of about 10 V cm 63 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 see image 61 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 64 65 66 67 68 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 69 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 70 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 71 72 This application relies on good compatibility of diamond nano particles with the living cells and on favorable properties of photoluminescence from the NV centers strong intensity easy excitation and detection temporal stability etc Compared with large single crystal diamonds nanodiamonds are cheap about 1 USD per gram 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 73 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 74 Those nanodiamonds are introduced in a cell and their luminescence is monitored using a standard fluorescence microscope 75 Stimulated emission from the NV center has been demonstrated though it could be achieved only from the phonon side band i e broadband light 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 76 The first continuous wave room temperature maser has been demonstrated 77 78 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 NV center can have a very long spin coherence time approaching the second regime 79 This is advantageous for applications in quantum sensing 80 and quantum communication 81 Disadvantageous for these applications is the long radiative lifetime 12 ns 82 83 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 84 Historical remarks editThe 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 10 and on the electron paramagnetic resonance 13 14 However a minor error in EPR results it was assumed that illumination is required to observe NV EPR signals resulted in the incorrect multiplicity assignments in the energy level structure In 1991 it was shown that EPR can be observed without illumination 15 which established the energy level scheme shown above The magnetic splitting in the excited state has been measured only recently 31 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 16 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 See also editCrystallographic defects in diamond Crystallographic defect Material properties of diamondNotes edit Group theory results are used to take into account the symmetry of the diamond crystal and so the symmetry of the NV itself Followingly the energy levels are labeled according to group theory and in particular are labelled after the irreducible representations of the C3V symmetry group of the defect center A1 A2 and E The 3 in 3A2 and 3E as well as the 1 in 1A1 and 1E represent the number of allowable ms spin states or the spin multiplicity which range from S to S for a total of 2S 1 possible states If S 1 ms can be 1 0 or 1 The energy level structure of the NV center was established by combining optically detected magnetic resonance ODMR electron paramagnetic resonance EPR and theoretical results as shown in the figure In particular several theoretical works have been done using the Linear Combination of Atomic Orbitals LCAO approach citation needed to build the electronic orbitals to describe the possible quantum states looking at the NV center as a molecule This is a phenomenon called intersystem crossing ISC It happens at an appreciable rate because the energy curve in function of the position of the atoms for the excited ms 1 state intersects the curve for the 1A state Therefore for some instant during the vibrational relaxation that the ions undergo after the excitement it is possible for the spin to flip with little or no energy required in the transition References edit Hanson R Gywat O Awschalom D D 2006 10 26 Room temperature manipulation and decoherence of a single spin in diamond Physical Review B 74 16 161203 arXiv quant ph 0608233 Bibcode 2006PhRvB 74p1203H doi 10 1103 PhysRevB 74 161203 S2CID 5055366 Maze J R 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