Quantum Defects as Sensors, Single-Photon Emitters, and Qubits

A quantum defect is an atom-scale imperfection in an otherwise periodic crystal whose electronic states are localized strongly enough to behave like a small artificial atom. The host provides mechanical support, thermal contact, optical access, and fabrication routes. The defect provides the quantum degrees of freedom: a spin, an optical transition, a local charge state, or a combination of these.

The negatively charged nitrogen-vacancy center in diamond, NV$^-$, is the canonical example. It consists of a substitutional nitrogen next to a missing carbon atom. In the useful charge state it has a spin-triplet ground state, an optical transition in the visible, and spin-dependent fluorescence. That combination is rare: we can initialize the spin optically, manipulate it with microwaves, read it out optically, and let it interact with magnetic fields, electric fields, strain, temperature, photons, and nearby nuclear spins.

This note is organized around three applications and one design question:

1. quantum sensing: how a defect turns fields into phase shifts or resonance shifts;
2. single-photon emission: how one localized optical transition emits one photon at a time;
3. quantum computing: how a defect spin becomes a qubit and couples to memories or photons;
4. computational discovery: how screening requirements tighten from ground-state stability to excited-state dynamics.

The same defect can support all three applications, but the requirements are not equally strict. A useful sensor can be an ensemble with broad optical emission. A single-photon source must be bright, photostable, and antibunched. A scalable quantum-computing or networking defect usually needs coherent spin control, high-fidelity initialization and readout, reproducible optical transitions, and an interface to either nearby spins or photons. The funnel becomes narrow quickly.

1. Quantum Sensing

The basic sensing idea is simple: use a well-controlled quantum transition as a clock, then let the environment shift that clock. A magnetic field, electric field, strain field, temperature change, or nearby spin changes the defect Hamiltonian. If we can prepare a superposition, wait, and read out the accumulated phase, the defect becomes a local probe.

For the NV$^-$ center, the ground state has total spin $S=1$. A minimal spin Hamiltonian is

Here $D/2\pi\approx 2.87$ GHz is the zero-field splitting between $m_s=0$ and $m_s=\pm1$, $\gamma_e$ is the electron gyromagnetic ratio, $H_{\rm strain}$ describes local crystal distortion and electric-field-like perturbations, and $H_{\rm hf}$ describes hyperfine coupling to nuclei such as the host $^{14}$N or nearby $^{13}$C spins. Along the NV axis, the Zeeman term shifts the $m_s=\pm1$ levels in opposite directions:

Measuring the microwave resonance frequency is therefore a magnetometer. The physics is a solid-state version of spectroscopy:

The remaining question is practical: how do we measure the spin state of one atomic-scale defect? The answer is that light gives different photon counts for different spin projections.

For this discussion, write the useful ground-state spin levels as

Here $m_s=0$ is not a singlet. It is one component of the same $S=1$ triplet. In a collinear DFT calculation one often represents the triplet by the high-spin determinant with total moment near $2\mu_B$; the experimental spin Hamiltonian then describes the $m_s=0,\pm1$ sublevels inside that triplet.

Now separate the electronic state from the spin projection. Write

for the ground and optically excited triplet states with the same spin projection $m_s$. Green light mainly drives

This optical excitation is approximately spin-conserving: the photon changes the orbital/electronic configuration, but it usually does not flip $m_s$.

After excitation, the defect can come down by two routes.

First, the bright route emits a red photon:

Here $k_{\rm rad}$ is the radiative decay rate. Larger $k_{\rm rad}$ means more red photons.

Second, the dark route goes through singlet states:

Here $\lvert s\rangle$ denotes intermediate singlet states, $k_{\rm ISC}$ is the intersystem-crossing rate from the excited triplet into those singlets, and $k_s$ is the decay rate from the singlets back to the ground triplet. This route is “dark” because the photons from this path are weak, shifted, or not collected in the same red fluorescence channel used for NV readout.

The crucial NV fact is

This is why the $m_s=\pm1$ states are darker. They are not darker because they absorb much less green light. They are darker because after green excitation they are more likely to leave the bright triplet-to-triplet cycle:

instead of emitting the usual red photon. The microscopic reason is spin-orbit coupling: it couples the excited $m_s=\pm1$ triplet components more strongly to nearby singlet states than it couples the excited $m_s=0$ component. In a compact rate model, the photon probability from a spin projection is roughly

where $k_{\rm nr}$ is any other nonradiative decay rate. If $k_{\rm ISC}$ is larger, $p_\gamma$ is smaller. Therefore

So the expected photon number during a short readout pulse satisfies

That inequality is the whole reason optical readout works. A bright signal means the spin was more likely in $m_s=0$; a darker signal means it was more likely in $m_s=\pm1$.

The same dark route also initializes the spin. The singlet path tends to decay back into $\lvert g,0\rangle$, so repeated laser cycles pump population into $m_s=0$:

Here $\rho$ is the spin density matrix and $\rho_{00}$ is the population in $\lvert g,0\rangle$. In words, the laser does two useful things at once:

Now add microwaves. A microwave does not vaguely “mix” states. It resonantly drives population back and forth between two spin sublevels when its frequency matches their energy splitting:

On resonance, the driven two-level Hamiltonian is

so population oscillates as

Here $\Omega$ is the Rabi frequency. If the microwave is off resonance, it barely transfers population, the laser keeps the spin mostly in bright $m_s=0$, and fluorescence is high. If the microwave is on resonance, it transfers some population into darker $m_s=\pm1$, and fluorescence drops:

This is optically detected magnetic resonance, or ODMR. The name sounds heavier than the experiment: shine laser light, sweep microwave frequency, and record where the red fluorescence dips. The dip position gives $f_\pm$, and $f_\pm$ gives the local field.

There are two common ways to use this physics.

Resonance-Shift Sensing

The simplest mode measures the frequency of the fluorescence dip:

This works with one NV center, but it is also natural for ensembles. With many NV centers in each camera pixel, one can image a spatially varying magnetic field by fitting the dip frequency pixel by pixel. The cost is that an ensemble usually has broader lines because different defects see slightly different strain, fields, and local environments.

Phase-Accumulation Sensing

For weaker fields, it is often better to use the spin as an interferometer. Prepare

wait for a time $\tau$, and then read out the spin optically. During the wait time, the field changes the relative phase:

The final microwave pulse converts this phase into population:

So the measured photon count is ultimately a measurement of accumulated phase. Ramsey, echo, and dynamical-decoupling sequences are different choices of microwave pulses during the wait time. They decide which time-dependence of $\delta\omega(t)$ the NV is most sensitive to.

The useful chain is therefore

The sensor does not need a perfect optical transition. For magnetometry, a broad but bright room-temperature optical cycle can be enough, as long as the photon count still depends on the spin state and the spin survives long enough to accumulate a measurable shift.

2. Single-Photon Emission

A single-photon emitter is a localized quantum system that emits at most one photon per excitation cycle. If a defect is in its ground state and absorbs one photon, it can be promoted to an excited state. It then relaxes by emitting one photon and returns to the ground state. Until it is excited again, it cannot emit a second photon. That saturation of one localized emitter is the physical origin of antibunching.

The standard diagnostic is the second-order correlation function

For an ideal single-photon source, $g^{(2)}(0)=0$: two photons are not detected at the same time. Experimentally, $g^{(2)}(0)<1/2$ is the usual signature that the light is dominated by a single emitter rather than a classical or multi-emitter source.

For NV$^-$, the optical transition connects the triplet ground state $^3A_2$ to the triplet excited state $^3E$. At room temperature, much of the emission goes into a broad phonon sideband, while the zero-phonon line is near 637 nm. The broad sideband is fine for confirming single-photon emission and for many sensing readout schemes. It is less ideal for interference-based photonic quantum information, where photons from different emitters should be indistinguishable.

The distinction is important:

A localized defect can be a robust single-photon source even if it is not an ideal quantum-network node. The early NV single-photon experiments were important because they showed a stable solid-state source that did not photobleach like many molecules. But NV$^-$ also illustrates a limitation: only a modest fraction of its emission is in the zero-phonon line. For indistinguishable photons, researchers often use cavities to enhance the zero-phonon-line channel, work at cryogenic temperatures, or search for alternative defects such as group-IV vacancy centers in diamond, divacancies in SiC, rare-earth ions, or defects in two-dimensional materials.

The physical design question is therefore not just “does it glow?” It is whether a localized excited state, radiative decay, weak spectral wandering, and efficient collection can combine into useful quantum light.

Computationally, that means one has to care about optical excitation energies, relaxed excited-state geometries, electron-phonon coupling, nonradiative pathways, and how strongly the transition dipole couples to the optical mode. Ground-state defect levels are only the first filter.

3. Quantum Computing

For quantum computing, the defect must supply at least one controllable two-level subsystem. In NV$^-$, the natural qubit is a pair of spin sublevels in the $S=1$ ground state, often $\lvert0\rangle\equiv\lvert m_s=0\rangle$ and $\lvert1\rangle\equiv\lvert m_s=-1\rangle$ under a bias magnetic field. Microwave pulses drive rotations between them:

As with other qubit platforms, resonant drive amplitude sets the rotation angle, drive phase sets the rotation axis in the $xy$ plane, and detuning gives a $z$ rotation in the rotating frame.

Side Note: Why Use $S=1$ Instead of $S=1/2$?

A spin-$1/2$ defect is the cleanest qubit on paper:

That is a perfectly valid defect-qubit design. The reason NV$^-$ is so famous is not that $S=1/2$ is bad. It is that $S=1$ gives an extra handle: the three spin projections

are split even at zero magnetic field:

For $S=1/2$, $S_z^2=1/4$ for both states, so this axial zero-field-splitting term cannot separate the two qubit states. A magnetic field is needed:

For NV$^-$, the $S=1$ triplet has a zero-field splitting $D/h\approx2.87$ GHz, so the transition $\lvert m_s=0\rangle\leftrightarrow\lvert m_s=\pm1\rangle$ is microwave-addressable even when $B=0$. Even more importantly, optical excitation treats these sublevels differently: $m_s=0$ is bright, while $m_s=\pm1$ more easily decay through singlet states. That is what gives initialization and optical readout:

So the short version is:

For sensing and optically read out qubits, $S=1$ is convenient. For a mathematically minimal qubit, $S=1/2$ is absolutely natural.

The NV electron spin can also couple to nearby nuclear spins through hyperfine interactions:

Nearby $^{13}$C nuclei or the intrinsic nitrogen nuclear spin can act as longer-lived memory qubits. The electron spin is easy to initialize, manipulate, and read out optically; nuclear spins are slower but can store coherence for longer. This gives a small quantum register around a single defect.

There are three levels of ambition.

Local Registers

A single defect plus nearby nuclei can implement a few-qubit register. The electron spin acts as an ancilla for control and readout, while nuclear spins provide memory. This is enough for demonstrations of entanglement, simple algorithms, error-correction primitives, and nanoscale sensing protocols that use a memory qubit to preserve information while the electron spin interacts with the environment.

Coupled Defects

Two nearby electronic spins can couple magnetically through dipole-dipole interactions. The scale is roughly

This interaction is conceptually clean but hard to scale: the coupling becomes strong only at nanometer separations, while too many nearby spins also create decoherence. Fabrication must place defects accurately and control the spin environment.

Networked Qubits

A more scalable route is optical networking. If a defect has spin-selective optical transitions, photons can become entangled with the spin. Interfering photons from remote defects can then herald entanglement between distant spin qubits. In this mode, the optical transition is no longer just a readout channel. It becomes the quantum interconnect.

That is why the quantum-computing requirement is harsher than the sensing requirement. A magnetometer can tolerate inhomogeneous broadening if the resonance is still measurable. A networked qubit needs optical linewidths narrow enough for photon indistinguishability, stable charge states, low spectral diffusion, good spin coherence, efficient collection, and high-fidelity operations.

The full qubit checklist looks like this:

NV$^-$ is excellent for room-temperature spin control and sensing. It is also a serious qubit and network node, especially with nuclear-spin memories and cryogenic resonant excitation. But it is not perfect: optical spectral diffusion, collection efficiency, and the small zero-phonon-line fraction motivate both nanophotonic engineering and the search for new defects.

4. What Defect Papers Actually Compute

The computational workflow is less mysterious if we separate the outputs by what calculation produces them. Most papers do not compute “a quantum technology score.” They compute a table of defect quantities, then decide which application those numbers support.

Here is the quick way to read the numbers. The ranges are not universal laws; they are the scale one usually hopes for before spending harder calculations or experiments on the defect.

4.1 Ground-State Supercell Calculations

Start with a relaxed supercell containing the defect. For each charge state $q$ and spin constraint, calculate a total energy. The standard formation energy is

Here $E_{\rm tot}(D^q)$ is the DFT total energy of the defective supercell, $E_{\rm tot}({\rm bulk})$ is the total energy of the pristine supercell, $n_i$ counts atoms of species $i$ added to the cell, $\mu_i$ is the atomic chemical potential, $E_F$ is the Fermi level measured from the valence-band maximum $E_{\rm VBM}$, and $E_{\rm corr}$ corrects finite-size electrostatics for charged defects.

For synthesis, smaller $E_f$ is better. As a rough equilibrium-growth scale, $E_f\lesssim1$-$2$ eV is friendly; much larger values usually mean low thermal concentration unless the defect is created non-equilibrium by implantation, irradiation, plasma growth, or annealing.

The charge-transition level between charge states $q$ and $q’$ is the Fermi level where their formation energies are equal:

This answers a concrete question: for which Fermi-level range is NV$^-$ stable rather than NV$^0$ or another charge state?

The ideal result is a wide Fermi-level window where the desired charge state is the lowest-energy one. If $\epsilon(q/q’)$ sits too close to the actual operating $E_F$, the defect can blink or switch charge state under illumination.

For the spin state, a collinear DFT calculation usually fixes or initializes

For the NV$^-$ triplet, the usual high-spin representative has $N_\uparrow-N_\downarrow=2$, so $M_z\approx2\mu_B$. This is how VASP sees the $S=1$ electronic configuration. The experimental labels $m_s=0,\pm1$ are then sublevels of this same triplet in the effective spin Hamiltonian.

For magnetic sensing or spin qubits, $S=0$ is usually not useful because there is no electronic spin to control. $S=1/2$ is the simplest qubit. $S\ge1$ is useful when one wants zero-field splitting or spin-selective optical pumping.

One also checks whether the defect state is localized. A simple orbital localization measure is the inverse participation ratio

A more localized state has larger ${\rm IPR}$. In practice, papers also plot the defect Kohn-Sham orbitals or the spin density

Large ${\rm IPR}$ and compact $\sigma(\mathbf r)$ are good signs for a point-defect qubit because the state is not just a band-edge state spread over the whole supercell. But “larger is always better” is not quite true: extreme localization can also mean strong coupling to local distortions, charge traps, and phonons.

At this level the calculation gives: stable charge state, relaxed geometry, spin multiplicity, gap levels, and localization. This is the loose screen.

4.2 Spin-Hamiltonian Parameters

After the electronic state is identified, compute the parameters in a spin Hamiltonian:

Every tensor in this equation is computable.

The zero-field-splitting tensor $\mathbf D$ describes how the spin sublevels split even when $\mathbf B=0$. For the spin-spin contribution,

Here $\rho_2$ is the two-electron spin density matrix. In DFT codes this is usually approximated from occupied Kohn-Sham orbitals. For an approximately axial $S=1$ defect, this tensor is often summarized by one number:

For NV$^-$, this is the origin of the $m_s=0$ versus $m_s=\pm1$ splitting near $2.87$ GHz.

For ODMR, $D/h$ should be large enough to resolve cleanly, usually at least MHz scale, but still experimentally addressable by microwave hardware. GHz-scale splittings, like NV$^-$, are very convenient. For an ideal $S=1/2$ center, this quantity is absent rather than small.

The $g$ tensor tells how a magnetic field shifts the spin levels:

If $\mathbf g=g_e\mathbf I$, the spin behaves like a free electron with $g_e\approx2.0023$. In a crystal, spin-orbit coupling and the local electronic structure make $\mathbf g$ slightly anisotropic. Formally,

So $\mathbf g$ is the derivative of the energy with respect to magnetic field direction and spin direction. Computationally it is a relativistic response property, often treated with PAW/GIPAW or related methods.

For many defect electron spins, $g\approx2$ is expected. Large shifts or anisotropy are not automatically bad: they can help identify the orbital character and orientation. But strong spin-orbit mixing can also increase relaxation, so the ideal $\mathbf g$ is application-dependent and should be stable from device to device.

The hyperfine tensor $\mathbf A^{(K)}$ tells how the defect electron spin couples to nucleus $K$:

It has a contact part from spin density at the nucleus and a dipolar part from spin density around it:

Here $\mathbf R_K$ is the nuclear position, $\mathbf I_K$ is the nuclear spin operator, $g_K$ is the nuclear $g$ factor, and $\mu_N$ is the nuclear magneton. The vector $\mathbf r$ is measured from nucleus $K$. Large hyperfine couplings identify nearby nuclei that can either disturb the electron spin or act as memory qubits.

For an unwanted nuclear-spin bath, smaller $\mathbf A^{(K)}$ is better. For a chosen memory nucleus, one wants a resolved coupling: often kHz-MHz, depending on whether the goal is long storage or fast gates.

4.3 Optical Quantities

For single-photon emission, the next calculation is an excited-state calculation. Let $Q_g$ be the relaxed nuclear geometry of the electronic ground state, and $Q_e$ the relaxed geometry of the excited state. Then

This is the zero-phonon-line energy: the photon energy if the electronic transition happens without changing vibrational quantum number.

The useful $E_{\rm ZPL}$ must fit inside the host band gap. If it lies too close to a band edge, optical excitation can ionize the defect instead of cycling it. Visible wavelengths are convenient for microscopes and detectors; telecom wavelengths are attractive for fiber networks.

The vertical absorption and emission energies are

From these one gets the relaxation energies

The transition dipole is

It controls the radiative decay rate. A common estimate is

where $\omega=E_{\rm ZPL}/\hbar$ and $n$ is the refractive index of the host.

The Huang-Rhys factor measures how much the atoms move between the two electronic states. In a one-effective-mode approximation,

Here $\alpha$ labels atoms, $M_\alpha$ is the atomic mass, $\mathbf R_{g,\alpha}$ and $\mathbf R_{e,\alpha}$ are relaxed positions in the ground and excited states, and $\Omega$ is an effective phonon frequency. In a many-mode treatment,

The Debye-Waller factor is the fraction of optical intensity in the zero-phonon line:

Small $S_{\rm HR}$ means less phonon sideband and a larger zero-phonon-line fraction. For a simple single-photon source, one mainly wants a stable optical transition and antibunching. For photon-mediated quantum computing, one wants a large radiative rate into a narrow optical line, so $E_{\rm ZPL}$, $\boldsymbol\mu_{eg}$, $S_{\rm HR}$, and ${\rm DW}$ matter a lot.

Because ${\rm DW}\approx e^{-S_{\rm HR}}$, the direction is unambiguous:

NV$^-$ is excellent as a spin defect but weak as a bare indistinguishable-photon source because ${\rm DW}\sim0.03$. For photonic quantum networking, ${\rm DW}\gtrsim0.3$ is much more attractive, and values near unity are ideal.

4.4 Ground-State Coherence: $T_1$ and $T_2$

The optical rates above are not the same thing as spin coherence. They describe what happens after optical excitation. For sensing and qubits, one also cares about the ground-state spin density matrix after the laser is off.

For a two-level spin subspace, write the density matrix as

$T_1$ is the longitudinal relaxation time. It tells how fast population relaxes:

For a spin defect, $T_1$ is often set by spin-phonon coupling. A phonon slightly changes the spin Hamiltonian,

where $Q_k$ is phonon normal coordinate $k$. If the phonon-induced perturbation connects two spin states, Fermi’s golden rule gives a transition rate

Then, schematically,

The computational inputs are phonon modes $\omega_k$, spin-Hamiltonian derivatives such as $\partial\mathbf D/\partial Q_k$ or $\partial\mathbf g/\partial Q_k$, and sometimes magnetic-noise models. This is much harder than computing $\mathbf D$ at one relaxed geometry.

$T_2$ is the transverse coherence time. It tells how fast the off-diagonal phase coherence disappears:

It is bounded by $T_1$ but also includes pure dephasing:

Here $T_\phi$ is pure dephasing: loss of phase without population relaxation. In real NV samples, $T_\phi$ often comes from slowly fluctuating nuclear spins, paramagnetic impurities, charge noise, strain noise, or temperature noise. Some of these can be estimated from first principles, but many papers use experiment or a separate bath model.

Sensing papers also often quote $T_2^*$, the inhomogeneous dephasing time measured in a Ramsey experiment without refocusing pulses. Usually

$T_2^*$ is shortened by static sample-to-sample or position-to-position disorder. Hahn echo and dynamical decoupling remove part of that slow disorder, so they measure a longer $T_2$.

So the relation is:

They meet during measurement. Optical readout must happen before the spin information is lost, but optical decay rates are not equal to $1/T_1$ or $1/T_2$.

For a useful spin qubit or sensor, the desired direction is simple:

NV$^-$ is strong here because its ground-state electron spin can keep coherence for long times in clean diamond, especially with isotopic purification and dynamical decoupling.

4.5 Spin-Dependent Optical Cycle

This part is not a routine output of ordinary defect-formation papers. It is a specialized calculation done when one wants to explain NV-like optical spin polarization and ODMR contrast. For NV$^-$, detailed models were developed by combining excited triplet and singlet electronic states, spin-orbit coupling, Jahn-Teller/vibronic coupling, and measured or computed energy gaps.

The question is not merely “is there an optical transition?” It is whether the optical cycle distinguishes spin states. A minimal rate model uses

Here $\Gamma_{\rm rad}$ is the photon-emitting decay rate, $\Gamma_{\rm nr}$ is a non-photon nonradiative optical decay rate inside the same spin manifold, and $\Gamma_{\rm ISC}$ is the rate for the excited triplet state to cross into singlet states. These are optical-cycle rates, not ground-state $T_1$ and $T_2$ rates.

The radiative rate is the easiest one. It comes from the optical transition dipole between an initial excited state $\Psi_i$ and a lower final state $\Psi_f$:

Then

The nonradiative rate is harder because the missing energy becomes phonons instead of a photon. For an initial electronic state $\Psi_i$ and final electronic state $\Psi_f$, Fermi’s golden rule gives

Here $\chi_{i\nu}$ and $\chi_{f\mu}$ are vibrational wavefunctions on the initial and final electronic potential-energy surfaces, $\nu$ and $\mu$ label vibrational states, $P_{i\nu}$ is the thermal occupation of initial vibrational state $\nu$, and $H_{\rm ep}$ is the electron-phonon coupling operator.

A common first-principles workflow rewrites this as

$W_{if}$ is the electronic coupling, often computed from the change of the Kohn-Sham potential along a configuration coordinate $Q$:

$F_{if}(\Delta E,T)$ is the Franck-Condon weighted phonon factor: it counts how well many-phonon vibrational states can conserve energy when the electronic gap is $\Delta E=E_i-E_f$. This is where the relaxed geometries, phonon frequencies, and Huang-Rhys factors enter. For a bright emitter, one wants

The intersystem-crossing rate is a special nonradiative rate where the electronic spin manifold changes, for example triplet to singlet. The electron-phonon part supplies vibrational overlap, while spin-orbit coupling supplies the spin change:

Here $H_{\rm SO}$ is the spin-orbit coupling operator and $F_{\rm ISC}$ is again a vibrational overlap factor. To compute it, one needs triplet and singlet excited-state energies, spin-orbit matrix elements, relaxed geometries, and phonon overlaps. This is why $\Gamma_{\rm ISC}$ is usually a specialized NV-style calculation, not a standard line in ordinary defect screening tables.

The optical quantum yield is then

For a plain single-photon emitter, one wants $\eta\rightarrow1$. For NV-like sensing, one also wants $\Gamma_{\rm ISC}$ to depend strongly on $m_s$, because that spin dependence is what creates optical spin contrast.

For optical spin readout, the desired inequality is

or the reverse, as long as the two spin states produce different photon counts. What matters experimentally is large contrast:

If $C\approx0$, the defect may still emit single photons, but it is not an optically readable spin qubit in the NV sense.

So the practical order is:

1. compute $E_f(D^q)$ and $\epsilon(q/q’)$ to find stable charge states;
2. compute $S$, $\sigma(\mathbf r)$, gap levels, and localization;
3. compute $\mathbf D$, $\mathbf g$, and $\mathbf A^{(K)}$ for the spin Hamiltonian;
4. for coherence, compute or model spin-phonon coupling and spin-bath noise to estimate $T_1$ and $T_2$;
5. compute $E_{\rm ZPL}$, $\boldsymbol\mu_{eg}$, $\Gamma_{\rm rad}$, $S_{\rm HR}$, and ${\rm DW}$ for optical emission;
6. only for NV-like optical spin readout, compute or model the rates $\Gamma_{\rm rad}^{(m_s)}$, $\Gamma_{\rm nr}^{(m_s)}$, $\Gamma_{\rm ISC}^{(m_s)}$, and the contrast $C$.

That is the loose-to-harsh rationale in computational language. Formation energy and spin density are relatively routine. ZFS, hyperfine, and $g$ are specialized but well-defined spin-Hamiltonian outputs. $T_1$ and $T_2$ require dynamical noise mechanisms, so they are less often predicted from a single static DFT calculation. ZPL and Huang-Rhys require excited-state geometries. Spin-selective readout requires the most detailed excited-state and vibronic information, and is usually done only for deeply studied platforms such as NV$^-$.

References

• A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. von Borczyskowski, “Scanning Confocal Optical Microscopy and Magnetic Resonance on Single Defect Centers,” Science 276, 2012-2014 (1997): DOI:10.1126/science.276.5321.2012.
• C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable Solid-State Source of Single Photons,” Phys. Rev. Lett. 85, 290-293 (2000): DOI:10.1103/PhysRevLett.85.290.
• F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillations in a Single Electron Spin,” Phys. Rev. Lett. 92, 076401 (2004): DOI:10.1103/PhysRevLett.92.076401.
• P. Neumann et al., “Multipartite Entanglement Among Single Spins in Diamond,” Science 320, 1326-1329 (2008): DOI:10.1126/science.1157233.
• J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Quantum Computing with Defects,” PNAS 107, 8513-8518 (2010): DOI:10.1073/pnas.1003052107.
• E. Togan et al., “Quantum Entanglement Between an Optical Photon and a Solid-State Spin Qubit,” Nature 466, 730-734 (2010): DOI:10.1038/nature09256.
• L. Robledo et al., “High-Fidelity Projective Read-Out of a Solid-State Spin Quantum Register,” Nature 477, 574-578 (2011): DOI:10.1038/nature10401.
• M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. L. Hollenberg, “The Nitrogen-Vacancy Colour Centre in Diamond,” Physics Reports 528, 1-45 (2013): DOI:10.1016/j.physrep.2013.02.001.
• C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle, “First-Principles Calculations for Point Defects in Solids,” Rev. Mod. Phys. 86, 253-305 (2014): DOI:10.1103/RevModPhys.86.253.
• A. Alkauskas, Q. Yan, and C. G. Van de Walle, “First-Principles Theory of Nonradiative Carrier Capture via Multiphonon Emission,” Phys. Rev. B 90, 075202 (2014): DOI:10.1103/PhysRevB.90.075202.
• C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum Sensing,” Rev. Mod. Phys. 89, 035002 (2017): DOI:10.1103/RevModPhys.89.035002.
• G. Thiering and A. Gali, “Theory of the Optical Spin-Polarization Loop of the Nitrogen-Vacancy Center in Diamond,” Phys. Rev. B 98, 085207 (2018): DOI:10.1103/PhysRevB.98.085207.
• J. Gugler, T. Astner, A. Angerer, J. Schmiedmayer, J. Majer, and P. Mohn, “Ab Initio Calculation of the Spin Lattice Relaxation Time $T_1$ for Nitrogen-Vacancy Centers in Diamond,” Phys. Rev. B 98, 214442 (2018): DOI:10.1103/PhysRevB.98.214442.
• V. Ivady, I. A. Abrikosov, and A. Gali, “First Principles Calculation of Spin-Related Quantities for Point Defect Qubit Research,” npj Computational Materials 4, 76 (2018): DOI:10.1038/s41524-018-0132-5.
• A. Gali, “Ab Initio Theory of the Nitrogen-Vacancy Center in Diamond,” Nanophotonics 8, 1907-1943 (2019): DOI:10.1515/nanoph-2019-0154.
• G. Wolfowicz et al., “Quantum Guidelines for Solid-State Spin Defects,” Nature Reviews Materials 6, 906-925 (2021): DOI:10.1038/s41578-021-00306-y.
• Z. Fang and Q. Yan, “Towards the Predictive Design of Quantum Defects for Next-Generation Quantum Technologies,” Communications Materials 7, 155 (2026): DOI:10.1038/s43246-026-01225-7.