Surveying optically addressable spin qubits for quantum information and sensing technology

Abstract

Quantum technologies offer ways to solve certain tasks more quickly, efficiently, and with greater precision than their classical counterparts. Yet substantial challenges remain in the construction of sufficiently error-free and scalable quantum platforms needed to unlock any real benefits to society. Acknowledging that this hardware can take vastly different forms, our review here focuses on materials that bear an optically-addressable electron or nuclear spin to embody qubits. Towards helping the reader to spot trends and pick winners, we have surveyed the various families of optically addressable spin qubits and attempted to benchmark and identify the most promising ones in each. We go on to reveal further trends that demonstrate how qubit lifetimes depend on the material’s synthesis, the concentration/distribution of its embedded qubits, and the experimental conditions.

Introduction

Over the last 40 years, quantum computation has progressed from concept to hardware. In 2023, IBM reported the commissioning of a 1121-qubit superconducting quantum processor¹, while Honeywell demonstrated a quantum charge-coupled device architecture based on trapped ions². Despite such achievements, the scalability and, thus, ultimate utility of each species of hardware remains contested.

Recently, materials that harbour an unpaired electronic or nuclear spin have garnered attention as contenders for use as qubit media. The best of these materials offer coherence times exceeding milliseconds, albeit at cryogenic temperatures³. Progress in the field has made the dream of usefully storing quantum information and/or implementing quantum processing at scale with appropriately interacting spins more tangible. For example, the start-up company Quantum Brilliance recently demonstrated a room temperature qubit system based on nitrogen-vacancy (NV) centres in diamond⁴. Beyond computation, these same materials are already providing advantageous forms of quantum sensing, especially under ambient conditions where thermally-driven electronic and photonic noise present significant challenges for quantum applications⁵. Their advantages stem from the ability to optically initialise spin states into highly non-Boltzmann populations and, likewise, to implement optical readout routines that are less impacted by blackbody radiation.

In these quantum spin materials, information is most simply encoded in the spin state of a two-level system, but can be encoded across multiple levels in high-spin (S ≥ 1) systems; a property that may be used to facilitate certain error correction protocols⁶. For qubits, a magnetic or electric field is applied to split otherwise degenerate spin states. The higher and lower energy spin states, $∣0⟩$ and $∣1⟩$, form two orthogonal basis states. A pure state is formed as a coherent superposition of the two ($∣\psi ⟩=a∣0⟩+b∣1⟩$, see Fig. 1a). Geometrically, we can visualise any such state as a point on the surface of a Bloch sphere, the location being defined by a polar angle θ and an azimuthal angle ϕ⁷. The value of θ determines the probability amplitude of finding the qubit in either the $∣0⟩$ or $∣1⟩$ state, while ϕ determines the relative phase of the qubit between the $∣0⟩$ and $∣1⟩$ states.pdf.

Fig. 1. Quantum spin parameters important for quantum technology.

a Bloch sphere representation of a spin vector showing a quantum state composed of $∣\psi ⟩=\left(∣0⟩+∣1⟩\right)/\sqrt{2}$. b Spin-lattice relaxation T₁ transforms an ensemble of polarised spins to a Boltzmann (thermal) spin distribution, approximated by the equation shown, where ${\mathrm{N}}_{∣0⟩/∣1⟩}$ is the population of each state, $\mathrm{\Delta }{\mathrm{E}}_{∣0⟩-∣1⟩}$ is the energy difference between each state, k_B is the Boltzmann constant, and T is temperature. c Bloch sphere representing an incoherent collective superposition for an ensemble of spins after time T₂ has elapsed. d Homogeneous spin-resonance linewidth, demonstrating the impact of lowering T₂, and e the inhomogeneous linewidth broadened by neighbouring (α and β) magnetic spins; ν and B₀ represent the microwave frequency and magnetic field, respectively, as commonly used independent variables in quantum sensing.

To be useful, these materials must enable both reliable spin addressability and long storage times. These properties are, in turn, limited by the materials’ spin-lattice relaxation (T₁) and spin decoherence times (T₂, also known as phase memory time). T₁ and T₂ represent the time it takes for the “longitudinal” and “transverse” magnitude of the spin-state vector, respectively, to decay by a factor of e (Fig. 1a, c). In practical terms, T₁ is the lifetime of a non-Boltzmann spin population (Fig. 1b), and, put simply by DiVincenzo^8,9, T₂ characterises the interactions of a spin qubit with its environment. These quantities are fundamentally related by 1/T₂ = 1/2T₁ + 1/T_ϕ, where 1/T_ϕ stems from contributions of so-called “pure dephasing” due to factors such as 1/f noise¹⁰, spin-bath fluctuations, and other magnetic/electric field gradients. Hence, in an idealised “Markovian” system, T₂ is only the decoherence time constant due to energy exchange with the environment (with the limit 1/T₂ = 1/2T₁)¹¹, and can be estimated by the homogeneous linewidth of a spin transition’s resonant frequency (Δ_hom = 1/πT₂, Fig. 1d). In most cases, T_ϕ is significant and the transition linewidth becomes inhomogeneously broadened and can be used to estimate the overall spin dephasing, $1/T_2^{*}=1/T_2+1/T_{\varphi }={\mathrm{\Delta }}_{\mathrm{inhom}}/\pi$, Fig. 1e)¹². Sources of spin dephasing can arise from both intra- and intermolecular interactions, and T₂ is limited by several controllable factors in the material’s spin state, spin-orbit coupling (SOC), phonons, spin concentration, and spatial distribution of nuclear and electronic spins¹³. Spin-relaxation parameters are most commonly measured using electron paramagnetic resonance (EPR) techniques by measuring microwave absorptions and emissions from a material as a function of frequency or magnetic field strength, forming the basis for quantum spin technologies (Fig. 2).

Fig. 2. Prominent approaches for addressing quantum spins for quantum applications (inner circle) and their applications in quantum technologies (outer circle).

Optically-detected magnetic resonance (ODMR) spin measurements utilise spin-dependent luminescence with light/microwave-based spin manipulation (green third), whilst electron paramagnetic resonance (EPR) spin measurements can employ light to initialise a spin system into a spin-polarised state (pink third) or one can employ microwaves to manipulate a thermally polarised system with spin-dependent microwave readout (blue third).

Quantum systems capable of operating at room temperature open up many additional applications that the overhead of cryogenic operation precludes. But, achieving high fidelity (in the initialisation, gate operations and readout) of room temperature qubits remains extremely challenging. In this review, we have attempted to survey the available “fully-optically-addressable materials” (FOAMs) that are most directly relevant to quantum information and sensing technology¹⁴. We do not provide an exhaustive account of all reported spin systems and their limitations. Rather, we present the different approaches, materials-wise, that have shown promise and report the properties (where available) of the best-performing representatives of each approach.

Overview of candidate spin-qubit materials

FOAMs are an attractive option for quantum applications since they typically involve spin levels that are energetically separated by far more than k_BT and can be initialised using visible/near-infrared light to generate quasi-"pure” quantum states. Furthermore, optical signals, composed of photons with energies far larger than k_BT, are less affected by thermal noise and benefit from the availability of single-photon sources and detectors capable of operating at high levels of fidelity even at room temperature. FOAMS are often probed using ODMR spectroscopy, where the quantum sensing sensitivity for a.c. magnetic fields (for example), η, is proportional to $\sqrt{t_{\mathrm{overhead}}}/\left(C\sqrt{n_{\mathrm{spin}}{n}_{\mathrm{avgs}}}{T}_2^{*}\right)$, where t_overhead is the duration of the readout process, C is the measurement contrast, n_spin is the number of spins, and n_avgs is the number of scan averages. Relatively few FOAMs have been demonstrated so far and are often limited by either low photoluminescence yields or relatively short-lived spin polarisations (T₁) and spin coherences (T₂), which have been summarised in Fig. 3 to support our discussion. As a prerequisite for inclusion in Fig. 3, we have opted to follow the criteria put forward by Weber et al.¹⁵, for the realisation of an optically addressable solid-state spin qubit (that is usable)

1. A state must be paramagnetic and support two or more energy levels,

2. An optical pumping cycle can be used to initialise the qubit,

3. Luminescence to or from the qubit state varies by qubit sub-level in some differentiable way (i.e. intensity, wavelength, or other properties),

4. Optical transitions must not interfere with the electronic state of the host,

5. Differences between qubit sublevels must be large enough to avoid thermal excitation.

Fig. 3. A collection of reported temperature-dependent quantum spin parameters measured using pulsed-ODMR techniques.

a Spin-lattice relaxation, b spin coherence, c spin dephasing times, and d optical contrast. Not every parameter has been reported for each system and condition, hence not every material will be visible on all four plots. In each case, we have opted to include the highest measured parameter using standard inversion/saturation recovery, 3-pulse echo and Ramsey technique, regardless of applied magnetic field. Data adapted from: 0.1% Pc:PTP^121,123, M₂TTM-3FIr-M₂TTM¹³⁵, CH₃-m(TTM)₂¹³⁶, 2,$2^{\prime }$-dinaphthylcarbene¹⁹³, 1,2,4,5-tetrachlorobenzene¹¹², Cr⁴⁺ molecular systems^111,151; Rh³⁺ molecular systems¹⁴⁷, NV-diamond^24,194,195, isotopically enriched NV-diamond²⁵, SiV⁻diamond^45,196 SnV⁻diamond⁴⁷, GeV⁻diamond⁴⁶; ${\mathrm{V}}_{\mathrm{B}}^{-}$ in hBN⁹², carbon defects in hBN^96,98,101, monovacancies in 4H-SiC^57,67, isotopically purified SiC⁶⁸, divacancies in 4H-SiC^{69,73,74,197–199}, N_C V_Si (hh) in 4H-SiC⁵⁸, N_C V_Si (kk) in 4H-SiC⁵⁹, Cr⁴⁺ in 4H-SiC⁶⁰, Mo⁵⁺ in 6H-SiC⁶⁴, V⁴⁺ in 4/6H-SiC⁷⁹, Cr⁴⁺ in GaN⁶⁰, Eu³⁺ in Y₂O₃¹⁷³, Er³⁺ in Y₂O₃^178,200, Y₂SiO₅³, KTP¹⁷⁹, and LiNbO₄^178,201; Pr³⁺ in Y₂SiO₅¹⁶⁷ and La₂(WO₄)₃¹⁷⁷; Yb³⁺ in Y₂SiO₅¹⁸¹ and YAG¹⁸⁰; Ce³⁺:YAG^187,202. Rb in solid Ne²⁰³, T-centre in ²⁸Si²⁰⁴, EYFP protein¹⁴³, F-centre in CaO²⁰⁵.

3D spin-defect FOAMs

Diamond spin centres

A well-established example of a FOAM which satisfies the above criteria is the negatively charged NY centres in diamond (herein simply, NV-diamond or NV⁻-centres), which utilise a triplet ground state and the hyperfine splitting arising from the I = 1 ¹⁴N-nucleus. Initialisation (i.e., electron spin polarisation) is achieved by optical excitation with green light. The newly generated excited states either relax by emission of 637 nm light or undergo intersystem crossing (ISC) into a metastable singlet state (Fig. 4a). Repopulation of the ground state then follows an intermediate relaxation between two singlet states (with emission at 1042 nm) and finally spin-selective ISC into the T₀ sub-level, resulting in a strong spin polarisation. At zero-applied magnetic field (ZF), the T_±1 states are degenerate due to the defect’s C_3v symmetry. The application of a magnetic field lifts this degeneracy, which enables spin manipulation using microwave pulses, thereby modifying the fluorescence at characteristic Zeeman splitting frequencies (hν = g_eμ_BB₀), which can be detected following subsequent optical excitations and fluorescence back to T₀.

Fig. 4. Selected spin defects in diamond.

a Jablonski diagram for NV-diamond as a prototypical example of an optically addressable material; b low-temperature fluorescence spectrum for SiV⁻, SnV⁻ and GeV⁻ singlet spin centres showing electronic transitions between electronic and spin-orbit energy levels used for optically addressing spins; c example defect structure and energy level diagram for SiV⁻ and d GeV⁻ spin centres. Fluorescence data adapted from refs. ^36,48,206.

NV-diamond has been a cornerstone of ODMR-based quantum sensing due to its robust spin properties even at room temperature. Due to the relatively low spin densities (resulting in small dipolar coupling between spins) and the mismatch between diamond lattice vibrations (phonons) and the Larmor frequency of electron spins, its S = 1 ground state, NV-diamond can exhibit T₁s of several milliseconds at room temperature^16,17. The nature and mechanism of its spin-lattice relaxation as a function of temperature, which includes an “Orbach-like” process (dependent on the phonon density at the spin-transition frequency) and spin-phonon Raman scattering (of either first¹⁸ or else second¹⁷ order) scaling like T⁵, have been repeatedly investigated.

The material’s quantum spin properties are highly dependent on the NV⁻-centres’s depth (below the diamond’s surface)¹⁹, concentration²⁰, crystal strain²¹, and the presence of impurities such as ¹³C, N-centres or EPR-inactive neutral or positively charged NV-centres^22,23. Its popularity has seen a plethora of investigations to understand and modulate its spin properties. For example, high-field EPR spectroscopy and temperature-dependent measurements have demonstrated that decoherence from the ¹⁴N and ¹³C flip-flop fluctuations can be almost eliminated at low temperatures where the spin bath is polarised²⁴. Here, T₂ reached ≈ 250 μs at 2 K, following a sharp increase below 12 K in high-temperature high-pressure diamond samples. Achieving similar properties under low-field and higher temperature conditions with thermally polarised nuclei is challenging and requires meticulous materials preparation and/or the use of dynamical decoupling methods. For example, the impact of parasitic nuclear spins and impurities was shown most remarkably by Balasuramanian et al.²⁵. Careful growth by chemical vapour deposition (CVD) on a diamond substrate using isotopically enriched feedstock led to just 0.3% ¹³C abundance and low levels of other paramagnetic impurities, resulting in T₂ ≈ 1.8 ms at room temperature.

One limitation of NV⁻-centres in diamond is their propensity to undergo charge-state conversion into a neutral and magnetically inactive state, NV⁰, during high laser power excitation. This spin-independent process is reversible, but results in an EPR-inactive parasitic reservoir of NV⁰ that results in the loss of spin polarisation by up to 31% during pulsed measurements²⁶ and can even out-compete T₁ relaxometry²⁷.

More recently, increasing attention has been paid to using diamonds as a host for other spin defects owing to diamond’s wide bandgap, efficient thermal dissipation, and physical and chemical stability. As such, various magnetically-active colour centres have been investigated for quantum applications²⁸. These include HV²⁹, BV³⁰, OV³¹, so-called group-IV vacancy defects³² such as SiV^33,34, SnV^35,36, GeV³⁷, and PbV^38,39, and even transition metal defects originating as impurities like NiV⁴⁰. To our knowledge, spin polarisation has not been observed in HV or OV centres, whilst ODMR experiments on BV and PbV have not been reported. Despite this, PbV in particular, both in charged PbV⁻ and neutral PbV⁰ states, is expected to exhibit robust spin coherence properties up to 9 K⁴¹.

Metal-vacancy spin-centres typically exhibit strong spin-orbit coupling (several hundred GHz) that gives rise to zero-field splitting (ZFS) even for S = 1/2 species, as well as electron-nuclear spin coupling, making them qudit candidates (Fig. 4b–d). Moreover, group-IV defects exhibit useful photonic properties that make them attractive for quantum applications such as Fourier-limited zero-phonon line (ZPL) linewidths, high spectral stability, coherent photon emission, and strain-responsive bandgap engineering⁴².

For example, negatively charged SiV (S = 1/2 system, Fig. 4c) has enabled direct observation of photon interference⁴³. Outside of a dilution refrigerator, the spin coherence lifetimes are severely impacted by thermal acoustic phonon coupling. At 100 mK, T₁ reaches 1 second while the longest $T_2^{*}$ measured was 1.5 μs. Spin coherence could be maintained by dynamical decoupling up to 600 mK where the coherence time during a dynamical decoupling scheme (T_DD) measured 60 μs. $T_2^{*}$ can also be improved through strain engineering, which modifies the spin-orbit coupling and is responsible for inducing the ground-state splitting, and subsequently the spin-phonon coupling⁴⁴. By comparison, the neutral SiV (S = 1 ground state) demonstrates an impressive T₁ ≈ 25 s, T₂ ≈ 0.1 ms, even at 15 K, decreasing to 7.8 and 2 μs at room temperature⁴⁵. However, a route to reliably synthesising SiVs in diamonds remains elusive.

Negatively charged GeV (S = 1/2 ground state, Fig. 4d) has been investigated using ODMR for quantum memory applications at 300 mK and found to exhibit a T₂ ≈ 440 μs and $T_2^{*}$ ≈ 1.46 μs⁴⁶. These defects were found to be particularly responsive to dynamical decoupling protocols with T_DD reaching 24 ms, representing a significant improvement compared to negatively charged SiV.

SnV⁻s (S = 1/2 ground state) are also robust spin centres and have been the subject of spin control experiments. Rosenthal et al. report T₁ ≈ 20 ms and T₂ ≈ 170 μs when measured at 1.7 K in highly strained SnV-centres; these spin lifetimes afford significant improvement in operation fidelity⁴⁷. By comparison, Trusheim et al. report a longer T₁ ≈ 1.26 ms and $T_2^{*}$ ≈ 540 ns at 2.9 K in a less strained system⁴⁸.

Negatively charged NiV-centres (S = 1/2) are near-infrared emitters, making them especially interesting for quantum communications due to their compatibility with conventional optical cables²⁸. The S = 1/2 ground state of the negatively charged NiV-centre has a predicted 0.1 ms coherence time at 4 K⁴⁹, but only recently have steady-state ODMR studies been reported⁴⁰.

Silicon carbide spin centres

Beyond diamond, silicon carbide (SiC) also shows promising optical and coherence properties for quantum applications^50–55. SiC is a complex material with >200 polymorphs. It is also used commercially in electronics and hence benefits from decades of manufacturing maturation. So far, the study of quantum systems has been largely restricted to 3C-, 4H-, and 6H-SiC, where C and H signify cubic and hexagonal structures, respectively, and the preceding number designates its polytype⁵⁶ (see Fig. 5a). Pure SiC has a wide bandgap (≈2–3 eV), weak spin-orbit coupling, and a naturally low abundance of nuclear spins. Importantly, it is capable of harbouring several varieties of optically addressable colour centre with (often) near-infrared emission and record ODMR contrasts⁵⁷. The most commonly studied defects encompass monovacancies (V_C or V_Si), and divacancies, but other defects may include carbon antisite vacancies (C_Si V_C) (see Fig. 5b), charged NVs^58,59, Cr⁴⁺-^60,61, V³⁺, V^4+62,63, Mo⁵⁺⁶⁴, and Ti-centres^55,56,65. Further layers of complexity are added by consideration of additional charge states and crystallographic sites within each polytype. Understandably, studies often focus on the “best-performing” defect within a given sample, and seldom are single samples of SiC homogeneous. This lack of homogeneity is perhaps the material’s most significant practical limitation as a spin-qubit candidate compared to other platforms.

Fig. 5. Optically addressable point defects in SiC.

a Structures of the most commonly studied SiC polytypes, 3C-SiH, 4H-SiC and 6H-SiC showing the origin of divancancy nomenclature depending on the lattice substitution site; b 2D-depiction of selected SiC ODMR-active defects. c Photoluminescence spectrum from a SiC ensemble showing multiple individually addressable defect types (PL1-PL6). d Orbital distribution for the ground and excited states of the ${\mathrm{V}}_B^{-}$-defect with the corresponding quartet spin-level energy diagram with and without an applied magnetic field. Red and blue arrows indicate optical transitions that connect ${\mathrm{m}}_{\mathrm{s}}=∣1/2⟩$ and ${\mathrm{m}}_{\mathrm{s}}=∣3/2⟩$ states, respectively. e ODMR spectrum of 4H-SiC samples at 20 K and f 300 K (inset optical initialisation scheme), demonstrating the robust spin-optical properties of the PL8-defect (the highest contrast peak), g the corresponding room temperature Hahn-echo decay trace for PL8. Figure 1a–e–g were reproduced from refs. ^{57,74,207–209}, respectively, with permission from MDPI and the American Chemical Society under the open access Creative Commons licence.

Nevertheless, several defects exhibit outstanding spin-optical properties, and the fabrication challenges are beginning to be addressed. Negatively charged V_Si in isotopically purified (²⁸Si) 4H-SiC exhibits the largest ODMR contrast at ≈97% at 4 K⁵⁷. With an S = 3/2 ground state, its associated ZFS is a few MHz with degenerate pairs of $∣1/2⟩$ and $∣3/2⟩$ states (Fig. 5d). Under a magnetic field (≈82 mT) precisely aligned to the crystallographic c-axis, this degeneracy is lost, and in the excited, so-called “V1” state, $∣3/2⟩$ shifts higher in energy than the $∣1/2⟩$ states. To achieve ≈97% contrast, the authors first equilibrate the spin populations using a 40 μs off-resonance pump (at 730 nm), followed by an on-resonance pump (at 861 nm) lasting up to 80 μs. On-resonance optical pumping causes $∣3/2⟩$ states to selectively decay into a non-radiative metastable state, followed by spin-selective repopulation of $∣1/2⟩$ ground states. This leads to a spin polarisation of up to 90%, which is paired with record T₂s and $T_2^{*}$ s of 0.8 ± 0.12 ms and 30 ± 2 μs, respectively.

At room temperature, dynamic decoupling techniques can be used to extend T₂ from 8 μs to 47 ± 20 ms⁶⁶. More recently, it was shown that V_Si defects can be implanted into nanophotonic waveguides fabricated from 4H-SiC while also controlling the alignment of individual defects and maintaining excellent spin-optical properties⁶⁷. Here, $T_2^{*}$ of bulk V_Si-centres was measured at 34 ± 4 μs at 10 K, whilst those in the ≈1 μm diameter waveguides were measured at 9.4 ± 0.7 μs. The coherence properties can be further improved by a factor of 10 through a regime of isotopic purification, and another factor of 5 by reducing strain inhomogeneity through a regime of annealing. Using this combined approach, Lekavicius et al. enhanced $T_2^{*}$ from 400 ns to ≈20 μs at room temperature⁶⁸.

Divacancies also exhibit compelling spin-optical properties, including up to 94% optical contrast⁶⁹, albeit at generally lower temperatures. Divacancies are formed by annealing pre-irradiated SiC at over 700 °C, however, the conversion efficiency into divacancies only ever reaches a few percent^70,71, which may in part be due to counterproductive divacancy-dissociation back into V_C, V_Si, and potentially even antisite-C_Si V_C-centres under the right conditions⁷². Divacancies are most often given the generic label “V_Si V_C”, designating that these neutral defects occur when both a carbon and a silicon atom are missing from the lattice. However, it is important to note that depending on the polytype, there are several crystallographic sites available (Fig. 5a, b), and it is even possible to generate defects within stacking faults. Therefore, V_Si V_C-defects can exhibit either c-axis, C_3v, or basal-type, C_1h, symmetry. As a result, in 4H-SiC alone, there are at least eight unique divacancies, the best known examples of which are sometimes colloquially called PL1-8, and are all distinguishable by their unique ZPL emission frequency (Fig. 5c) and are mostly assigned to have S = 1 ground state due to their circa 1 GHz ZFS (Fig. 5e).

The kk-divacancy, PL2 in 4H-SiC, with natural isotopic abundance, can demonstrate T₂s of 1.3 ms at 20 K when decoupled from ¹³C and ²⁹Si nuclear spins under a 30 mT field⁷³; which is significantly longer than NV-diamond under similar conditions. Moreover, NV⁻-centres in 4H-SiC (N_C V_Si) have known kk, hh, hk and kh-type defects and also exhibit robust spin parameters at room temperature^58,59. However, unlike their diamond analogue, N_C V_Sis benefit from an NIR-emission with four distinct ZPLs between 1170 and 1250 nm, which is a preferred region for biosensing applications. Some of these divacancy centres also demonstrate remarkable insensitivity to temperature. For example, Yan et al. reported that despite having an unknown structure, PL8-centres exhibit similarly intense ODMR signatures at 1.4 GHz when measured at 20 K or room temperature⁷⁴ (Fig. 5e, f). This temperature insensitivity is also reflected in the quantum spin properties where T₂ and $T_2^{*}$ measure 15.6 ± 0.5 μs and 184 ± 10 ns at 20 K, respectively, and 9.1 ± 0.1 μs and 180 ± 9 ns at room temperature, respectively (Fig. 5g). This long-lived room temperature spin coherence is shared to a lesser extent by PL6-centres, which are thought to be hh-divacancies occupying a stacking fault and are distinguishable by their 1038 nm (vs PL8’s 1007 nm) ZPL emission. This demonstrates that several species in SiC are suitable for room temperature quantum applications. Moreover, divacancy systems were the first spin-centres demonstrated to be amenable to all-electrical spin-ensemble readout and initialisation schemes^75,76. These functionalities have since been discovered with monovacancies under ambient conditions⁷⁷, demonstrating a strong potential to avoid some of the difficulties associated with ODMR spectroscopy, such as pump-light stability and photon collection efficiency.

Beyond vacancy systems, several metal-ion centres have demonstrated interesting spin-optical properties when implanted into SiC. The best to date in terms of its optical addressability is Cr⁴⁺ in 4H-SiC. As an S = 1 species, this material exhibits T₁ > 1 second, with T₂ and $T_2^{*}$ = 81 μs and 317 ns, respectively, at 15 K⁶¹. Importantly, it also demonstrates a 79% contrast, marking it as a system with one of the highest optical readout fidelities. The spin-optical properties of the same ion are markedly impaired in GaN host, which demonstrates 27× broader emission linewidths due to interactions of Cr⁴⁺-centres with the surrounding spin bath⁶⁰.

V⁴⁺ is perhaps the most thoroughly studied ion with coherent manipulation of its S = 1/2 spin system reported in α-4H-SiC⁷⁸, β-4H-SiC, and γ-6H-SiC⁷⁹ host matrices. Whilst generally the spin-relaxation parameters are shorter than Cr⁴⁺, all V⁴⁺ defects emit ~1.3 μm with markedly narrow inhomogeneous emission linewidth (ca. 100 MHz) and resolvable hyperfine coupling of the electron spin to the I = 7/2 ⁵¹V nucleus, making them promising candidates for low-loss o-telecom band quantum applications⁸⁰. Unlike most of the spin-defects discussed so far, spin polarisation of V⁴⁺ is achieved using a magnetic field to lift the zero-field degeneracy of the m_s ± 1/2 states to generate two distinct spin-dependent ZPLs which can be selectively depopulated using circularly polarised light⁸¹. This scheme has been used successfully to generate strong ensemble spin polarisation, resulting in reported pulsed-ODMR contrasts of up to 90%⁸². Care is needed, however, since use of an on-resonance (with the ZPL) initialisation scheme generates V³⁺ states, which can be compensated for using an off-resonance green or UV repump protocol.

Mo⁵⁺ defects in 6H-SiC are another S = 1/2 spin defect demonstrated to enable coherent spin manipulation at cryogenic temperatures. Here, rather than being a hindrance, the strong SOC of the heavy Mo⁵⁺-ion is thought to protect it from parasitic phonon modes and spin-spin interactions, leading to T₁ of 2.7 seconds at 2 K⁶⁴, significantly longer than V⁴⁺. However, its ZPL is broader than vanadium at 24 GHz at 4 K, and shifted to 1120 nm⁸³, which is slightly outside the highly desirable telecom band.

2D- and van der Waals FOAMs

Van der Waals (vdW) materials are made of 2D-atomically thin layers weakly bound together through van der Waals interactions. These include graphene, hexagonal boron nitride (hBN) and transition metal dichalcogenides. Despite a range of remarkable materials having been identified as ODMR-active, the precise structure and even spin multiplicity of the spin species are often ambiguous. Nevertheless, like other defect spin-qubit systems, inhomogeneous broadening and spin-phonon interactions are the principal causes of spin decoherence.

The prototypical vdW material, graphene, was an early candidate for harbouring spin qubits; however, the metallic band structure of graphene is not conducive to forming luminescent spin centres. Instead, its isoelectronic analogue, hBN, has been the centre of remarkable advancement as a 2D-optically addressable platform at room temperature, building off its success as a single-photon source⁸⁴. Magnetically-active spin centres in hBN were identified by EPR in the 1960s, with hyperfine structures giving clues to their identity as S = 1/2 boron centres and carbon impurities^85–87. However, the first optically addressable spin centres were only identified recently as triplets stemming from a negatively charged vacancy, likely originating from a missing boron atom, so-called ${\mathrm{V}}_{\mathrm{B}}^{-}$-centres^88–91 (Fig. 6a). Similar to NV-diamond, optical initialisation is achieved by photoexcitation with 532 nm light, leading to ISC into a metastable singlet, which spin-selectively repopulates the fluorescent m_s = 0 state (T_Z at ZF, Fig. 6b). The readout of the spin state occurs through 850 nm fluorescence with pulsed-ODMR contrast of ≈1% at room temperature and almost ≈30% at 10 K, revealing a ZFS of ∣D∣ ≈ 3.5 GHz (Fig. 6c). Spin-relaxation and Hahn-echo measurements reveal a room temperature T₁ of 18 μs and T₂ of 2 μs⁹². These properties are particularly remarkable since both boron and nitrogen exhibit isotopically abundant nuclear spins (¹⁴N, I = 1, ¹⁰B, I = 3, and ¹¹B, I = 3/2). In the same work, suppression of the nuclear spin bath using a second microwave source centred on a hyperfine line was found to improve T₁ and T₂ up to 25 μs and 7.5 μs, respectively. Work continues optimising the synthesis conditions for hBN to enhance the quantum properties of the defects. For instance, the contrast of ${\mathrm{V}}_{\mathrm{B}}^{-}$-centres can be increased to ≈10% at room temperature by controlling the material purity and electron irradiation dose, though T₁ appears to remain phonon limited⁹³.

Fig. 6. Optically addressable spin defects in hBN.

a Proposed structure for the $V_{\mathrm{B}}^{-}$ triplet spin centre (purple atoms = N, cyan atoms = boron and grey atoms = carbon, with b its corresponding Jablonski diagram, and c variable temperature ODMR spectra at low-field, confirming the defect’s triplet character. d Proposed structures for selected carbon-based defects in hBN with e Jablonski diagram showing the involvement of two metastable states and repopulation of the g₁-state to achieve spin initialisation. f ODMR spectra for three carbon defects measured at 5 K showing g ≈ 2 doublet resonances corresponding to 154, 290, and 200 G for D1, D2, and D3-defects, respectively. g 2D-confocal map of hBN flakes showing fluorescent and ODMR-active (green dots) defect sites, with h histograms for 400+ carbon-based triplet defects. c, (f, data only), g, h were adapted from refs. ^90,96,98, respectively, with permission from Springer Nature under the open access Creative Commons licence.

Due to hBN’s potential as a tunable single-photon source, significant effort has been made to control substitutional-defect structures through careful synthesis. CVD-grown hBN has been found to contain a plethora of optically active carbon and oxygen-based spin species with stable ZFLs in the visible range^94,95; although most have yet to be structurally characterised, or even the multiplicity conclusively determined (see Fig. 6d for candidate structures and Fig. 6e for the spin initialisation scheme). For example, three distinct so-called “C_B”-defects, likely stemming from the substitution of a boron or nitrogen atom by carbon ("D1”, “D2”, “D3”, all likely S = 1/2), demonstrate similar spin relaxation and coherence quantum properties (T₂ ≈ 0.2 μs) with a continuous-wave (CW)-optical contrast up to 20% at 5 K⁹⁶ (Fig. 6f). Their inhomogeneous linewidths are also limited by the nuclear spin bath ($T_2^{*}\approx$ 40–60 ns), where local spins also bestow an apparent ZFS of between 8-10 MHz.

Though ensemble measurements remain challenging due to carbon-doped hBN’s broad emission profile, a recent report has shown that it is possible to survey over 400 defect centres in CVD-grown samples. Collectively known as “C_xy”-centres, careful measurements of individual spin-centres reveal distinctive triplet character with a ZFS of 15 MHz in contrast to most other accepted carbon-defects found in hBN⁹⁷. The triplet identity was later unambiguously characterised and confirmed for a series of defects with significantly larger ZFS with ∣D∣ ≈ 2 GHz and ∣E∣ ≈ 50 − 80 MHz⁹⁸ (Fig. 6g, h). The T₁ at room temperature was measured to be 200 ± 30 μs, T₂ ≈ 1 μs and $T_2^{*}\approx$100 ns, competitive with ${\mathrm{V}}_{\mathrm{B}}^{-}$ defects. However, these properties are matched with a remarkable ODMR contrast of almost 50% (though it decreases with an applied magnetic field), giving rise to projected D.C. magnetic field sensitivity of up to 3 μT Hz^−1/2. A recent survey of similar defects demonstrated that under high microwave and optical pump powers, the optical contrast could reach as high as 90%, though most exhibit < 50% despite similar ZFS, T₁ and T₂⁹⁹. The authors explore the potential of this material as a medium for D.C. vectorial quantum magnetometry by taking advantage of the defects’ low symmetry and in-plane quantisation axis. Though not yet experimentally verified, the authors hypothesise that applying a field bias along a different material axis corresponding to each of the three triplet states, T_x, T_y, and T_z, should result in subtle changes in contrast that can be related to particular T_n states to yield 3-vector components of the applied field.

More complex carbon species demonstrating similar coherent behaviour at room temperature have been explored using metal-organic vapour-phase epitaxy with carbon-based additives^100,101. The so-called “C_?”-defect (potential identity C₂C_N) is another potential S = 1/2 species or, two weakly coupled S = 1/2 centres, has recently been reported as being co-located with ${\mathrm{V}}_{\mathrm{B}}^{-}$-centres following electron irradiation of hBN flakes¹⁰¹. While their T₁ and T₂ are similar to C_B-species (≈13 μs and ≈80 ns, respectively), it can be used to “sense” ${\mathrm{V}}_{\mathrm{B}}^{-}$-centres through spin cross relaxation at an appropriate applied magnetic field. Due to its out-of-plane magnetic quantisation axis (versus the in-plane axis of ${\mathrm{V}}_{\mathrm{B}}^{-}$-centres), it can also be used more effectively to image magnetic structure on underlying substrates with an estimated DC magnetic sensitivity of ≈1 μT Hz^−1/2.

One limitation of hBN spin defects is their propensity to form dark “trap” states that lead to blinking luminescence^102,103. Unlike NV-diamond, the formation of these dark trap states is not dependent on laser power, and whilst the origin of this behaviour is still largely unknown, defects in multilayer hBN which are more protected from the environment are less prone to blinking¹⁰⁴. This suggests that atmospheric control may be a sensible approach to improve the reliability of spin-dependent luminescent readout.

Molecular FOAMs

p-block molecular spin centres

Molecular systems are becoming increasingly popular and offer an enticing opportunity to develop chemically tunable quantum materials catered to different applications^105–108. Ground-up synthesis enables the incorporation of particular functionalities such as stable radicals^109,110, modulation of triplet/singlet yields, enrichment with low or zero nuclear magnetic moments such as deuterium, oxygen and sulphur, or the targeted inclusion of nuclear spin-active elements such as nitrogen, phosphorous, transition metals, and lanthanides (vide infra). A synthetic approach also enables changes to the host matrix¹¹¹, spin concentration, defect orientation, and material processing approaches, which are limited for defect-based systems.

The first examples of ODMR performed on molecular systems focused on small organic molecules^112,113 and biologically relevant porphyrin molecules such as those found in chlorophyll and bacterial reaction centres. These molecules use photoexcited triplet states as the magnetically-active spin centres that spin-selectively relax through phosphorescence, or relax to the fluorescent single states^114,115 (Fig. 7a, b). Porphyrins may be coordinated with Mg²⁺ or Zn²⁺ ions, which, though affecting the yield of the photoexcited spin state, do not themselves directly harbour it due to their filled s- or d-orbitals. Until recently, studies on p-block FOAMs were typically limited to cw measurements at cryogenic temperatures and aimed at investigating the interplay between ground and excited states, the influence of the stereochemistry of the porphyrin dimer molecules¹¹⁶, and detecting triplet states in nanolayers¹¹⁷. A few groups did, however extend their work to pulsed measurements, including Breiland et al.¹¹², who measured the coherence properties of 1,2,4,5-tetrachlorobenzene in durene at 4 K, and found a T₂ of a few microseconds, which could be significantly extended to a millisecond or so using dynamic decoupling or spin-locking techniques.

Fig. 7. Fully optically addressable organic quantum materials.

a Molecular structures of known organic FOAMs. b Jablonski diagram for ground-singlet state materials, like Pc:PTP, with an inset doped structure crystal of p-terphenyl. The materials are excited/initialised using light. The spin centres subsequently relax by fluorescence (k_F) or populating the triplet states through intersystem crossing (k_ISC). Repopulation of the singlet ground state occurs in a triplet sub-level dependent manner (k_i, where i is the corresponding triplet sub-level) and gives rise to high-contrast spin-optical signals. c Bridgmann growth set up to manufacture doped organic crystals. d An example of a Bridgmann-grown single crystal of Pc:PTP. e ODMR spectrum of Pc:PTP and DAP:PTP demonstrates enhanced pulsed optical contrast due to modified spin dynamics. f Synthesis methodology to generate optically clear films (aka “foils'') of doped PMMA as an excellent amorphous host for radicals with spin-optical readout. g An example ODMR spectrum of CH₃-m(TMM)₃ in a PMMA host. Figure 1c–g were reproduced from refs. ^{126,136,141,210} with permission from MDPI and the American Chemical Society under the open access Creative Commons licence.

Single-molecule ODMR spectroscopy of pentacene molecules in a para-terphenyl matrix (Pc:PTP) has already been demonstrated at cryogenic temperatures in a series of remarkable works by Wrachtrup and colleagues^118–120. Only recently have pulsed experiments been performed to reveal contrast and spin coherence properties that are competitive with materials like NV − diamond at room temperature. The T_x-T_y spin transition of a 0.1% crystal of Pc:PTP, grown using the Bridgman technique (Fig. 7c, d), demonstrates T₁ ≈ 23 μs, T₂ ≈ 2.7 μs and $T_2^{*}\approx$500 ns^121,122. Investigations using the more strongly spin-polarised T_x-T_z transition in both crystals and 100 nm-thin films at 0.01% and 0.1%, respectively, reveal similar spin dynamics and also suggest an ability to modulate Pc:PTP’s spin properties according to sample thickness and spin concentration¹²³. These robust spin-optical properties can be maintained in Pc:PTP nanocrystals down to 200 nm with an optical contrast similar to equivalently sized NV-diamond nanoparticles¹²⁴. When coated with a Pluronic F-127 polymer, these nanoparticles also display excellent biocompatibility with low toxicity over 72 hours according to in vitro explorations, paving the way for their use in cell assay techniques.

The potential of using synthetic chemistry to modulate the spin dynamics to improve spin-optical properties has also been explored (see Fig. 7b). Substituting two carbon atoms on pentacene for nitrogen atoms resulted in 6,13-diazapentacene, which could be doped into a para-terphenyl host (DAP:PTP) by crystal growth and vapour deposition techniques^125,126. While maintaining a relatively long T₂ of 1.46 μs and strong triplet spin polarisation, DAP:PTP exhibited an enhanced contrast of up to 40%, surpassing the state of the art in NV-diamond platforms¹²⁶ (Fig. 7e). This improvement was attributed to the introduction of new low-energy non-bonding states that enhance vibrationally-induced spin-orbit coupling between the ground-state singlet and the metastable T_x state. It was also shown that direct solvent techniques can be used to grow ODMR-active DAP:PTP nanoparticles, which could be compatible with in vitro sensing experiments.

Further organic systems have demonstrated potential as optically addressable materials, though, to our knowledge, pulsed optically detected experiments have yet to be performed. For example, the room temperature steady-state ODMR contrast of a 1% crystal of pentacene-doped picene has been measured at 15%, representing a potentially significant improvement over the PTP matrix¹²⁷. Steady-state ODMR signals have also previously been reported at 2 K for (perdeutero)tetracene, 1,2-benzathracene, 1,2,3,4-dibenzanthracene¹²⁸ and dinaphtho-(2’,3’:1,2);(2",3":6,7)-pyrene¹²⁹. Interestingly, work by Corvaja, Pasimeni and Giometti et al. has shown that even highly spin-dense charge-transfer (CT) co-crystals can exhibit bright room temperature ODMR signals. Co-crystals comprised of donors such as biphenyl, fluorene, phenazine and acceptors such as 7,7’:8,8’-tetracyanoquinodimethane (TCNQ) and 1,2,3,4-tetrafluoro-TCNQ (F₄TCNQ) have been studied to elucidate their triplet state dynamics^130,131. These materials exhibit narrow resonance lines due to intermolecular site hopping of triplet excitons. The resonances for each site can become resolved at low temperatures where hopping is not thermodynamically favoured¹³⁰. Their high-spin densities (≈50%) are highly advantageous for quantum sensing, where the a.c. Sensitivity is proportional to the $\sqrt{n_{\mathrm{spin}}}$, though this is often concurrent with less robust quantum spin properties compared with dilute materials such as Pc:PTP. Moreover, these materials are also promising hosts for the study of exotic spin behaviours like singlet fission and triplet-triplet annihilation¹³². For example, at room temperature, the triplet states of phenazine:TCNQ are predominantly formed by singlet fission and using transient nutation EPR spectroscopy, the authors estimate T₁ and T₂ times of ≈1 μs and 600 ns, respectively, even at room temperature¹³³.

Several ground-state radical and diradical materials with an optical readout capacity have also been demonstrated^134–136, as have materials with quintet states^137–139. Diradical materials have the advantage of exhibiting a ground-state triplet, making their optical addressability protocol identical to NV-diamond. Optical readout is enabled by employing luminescent radical moieties based on tris(2,4,6-trichlorophenyl)methyl (TTM)¹⁴⁰, where the radical is sterically isolated on a carbon atom with only weak hyperfine coupling to neighbouring ¹³C and hydrogen atoms. As a result, these materials can benefit from relatively narrow resonance linewidths, long T₁s, and can be embedded in frozen solutions or optically transparent PMMA foils through simple solvent-based methods¹⁴¹ (Fig. 7f, g).

Additionally, ODMR has long been used to investigate genuine bio-molecules such as nucleotides and proteins using phosphorescence of pyridine dinucleotides or certain amino acid residues such as tryptophan^114,142, albeit at cryogenic temperatures. The emission wavelength-dependence of tryptophan’s ZFS parameters enabled investigators to distinguish between different proteins and even different tryptophan residues in the same protein molecule. The usefulness of these studies was restricted due to the perceived inability of these molecules to maintain long T₁s at room temperature, where dynamic effects occur. However, recently, fluorescent proteins have been demonstrated as a viable spin-qubit medium in vivo and in solution at room temperature. Feder et al. used ODMR spectroscopy to demonstrate that at 80 K the X-Z and Y-Z triplet transitions of enhanced yellow fluorescent protein demonstrated a 44% and 32% ODMR contrast, respectively¹⁴³. This corresponds with a zero-applied field T₁ of 141 μs (estimated from spin polarisation decay) and T₂ of 1.5 μs. Using Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling, the effective decoherence time (T_DD) reached 16 μs. The authors largely circumvent overhead limitations from long triplet lifetimes (ms) using an additional near-infrared pulse to induce T₁ to T₂ transitions to induce reverse ISC and delayed fluorescence from S₁. This interesting methodology could be suitable for other spin systems with quasi-resonant S₁ and T₂ electronic states, such as pentacene, to increase their sensitivity by increasing measurement repetition rates.

d-block molecular spin centres

Optically addressable d-block molecules have been investigated for several decades, though due to the weak oscillator strength of forbidden d-d transitions, the majority of ODMR studies focused on luminescence stemming from ligand-based triplet states generated following intramolecular ligand-to-ligand or metal-to-ligand charge transfer events^115,144. These studies have generally focused on the use of diamagnetic heavy metal centres such as Pd²⁺, Gd²⁺, Rh²⁺, Au⁺¹⁴⁵ where the extent of the metal-ligand orbital mixing is reduced. However, for elements with partially filled d-orbitals, the strong SOC stemming from the heavy metal centres plays a significant role in determining the spin-polarisation, spin-relaxation, and ZFS parameters. Accordingly, cryogenic temperatures are required to maintain the detectable transitions due to the strong SOC effects of the metal centres. One of the first attempts to investigate the quantum spin properties of these materials focused on Rh³⁺ biphenyl-type chelating ligands, where T_m was measured at a few microseconds at 1.4 K^146,147. Due to the deeply cryogenic conditions, T₁-type processes were assumed to be negligible.

In the early 2000s, further ODMR studies of transition metal complexes became far more scarce before lighter metal complexes regained attention in the 2010s. However, optically addressable materials with first row transition metal-spin centres were first reported using tris(aceylacetonato)Cr³⁺ (acac) supported in an Al(acac)₃ crystalline host matrix at 1.9 K. While the ODMR properties of the S = 3/2 ground state are not reported, on-resonance excitation to the lowest energy doublet state is sufficient to generate spin polarisation, with the ODMR signal detected through the vibronic side bands¹⁴⁸, making it a molecular analogue of earlier ruby ODMR experiments¹⁴⁹.

Optically addressable d-block molecules with a ground-state and zero-applied magnetic field spin manifold have only recently been demonstrated with Cr⁴⁺ (Fig. 8a). The Cr⁴⁺ spin-centre was realised with several tolyl-based ligand systems where modifications to the ligand structure and corresponding ligand-field strength can be used to control optical excitation frequency and the ZFS of the Cr⁴⁺ S = 1 ground state¹⁵⁰ (Fig. 8b, c). To reduce intermolecular dipole coupling, the spin-active moiety is diluted in a matrix with the S = 0 isostructural tin analogue in crystals grown from hexane solutions¹⁵¹. Optical spin polarisation is then achieved by exciting molecular spins from the S = 1 state to the S = 0 manifold, which fluorescently decays within a few microseconds to favourably populate the T_± states. Initial pulsed-ODMR experiments were performed on Cr⁴⁺(o-tolyl)₄ spins, which benefit from an E = 0 triplet and a relatively long T₁ of 0.22 ms and T₂ of 640 ns at 5 K. This permits several optical cycles to build spin polarisation and enhance the optical contrast up to 14%. The coherent properties can be significantly improved using a non-isostructural Sn(4-fluoro-2-methylphenyl)₄ host matrix¹⁵². Here, the ZFS is significantly increased, giving rise to clock transitions similar to those realised by the so-called “zero first-order Zeeman” (ZEFOZ) method, initially pioneered for lanthanide spin systems (see below). As a result, T₁ and T₂ are increased to ≈1.21 ± 0.02 ms and ≈10.6 ± 0.2 μs at 5 K, respectively, while the pulsed contrast can be improved up to 65%.

Fig. 8. Optically addressable Cr⁴⁺ molecular colour centres.

a Energy level illustration of spin initialisation and readout using resonant NIR-photoinduced ISC from the ground state triplet to an excited singlet state, followed by spin-selective fluorescence to T_± spin sublevels. b Molecular structures of three Cr⁴⁺ tolyl-type complexes, and c their corresponding cw-ODMR signals. a, c were adapted from ref. ¹⁵¹.

Work continues to explore alternative d-block elements where strong ligand-field interactions can enable optical excitation between spin manifolds and spin-dependent fluorescence^105,108. Candidates include Ni^2+153,154, Mo⁴⁺¹⁵⁵, V^3+155,156. Current challenges involve tuning the energy of the intermediate (e.g., singlet) state to provide the right conditions for spin polarisation, and identifying the appropriate ligand design to optimise photoluminescence.

f-block molecular spin centres

Lastly, there has been significant interest in f-block molecular systems. Here, we make a distinction between molecular systems where the ion is doped into a molecular lattice, and trapped ion systems where a single ion is levitated using electrostatic interactions to give rise to extremely long coherence times, but are not subject to qubit-quality improvements through molecular engineering^157–159.

Lanthanide spin centres benefit from highly shielded f-orbital electrons compared to d-orbital systems, leading to relatively long coherence times at low temperatures¹⁶⁰. The core-like nature of f-orbitals also means, compared to d-orbital systems, that the ligand-field environment has a much weaker influence on state energies (a few THz), compared to electron-electron interactions (≈800–1600 nm) and spin-orbit coupling (≈10s THz)^161,162 (see Fig. 9a). Lanthanide electron spins can also exhibit strong hyperfine coupling (tens of MHz) with I = 5/2 (Eu, Pr, ¹⁷³Yb), I = 1/2 (¹⁷¹Yb), I = 7/2 (¹⁴⁹Sm, ¹⁶⁷Er) nuclei, leading to a diverse spin-optical addressability schemes that can be further enhanced using applied magnetic fields. Moreover, strong spin-orbit coupling can lead to high magnetic anisotropy that can protect spin states from small magnetic fluctuations^163,164. Examples of optically active materials benefit from narrow and stable spin-dependent emission profiles at near-infrared frequencies, making them potentially compatible with conventional telecom fibre optics. Colour centres for which optical addressability has been established include Ce³⁺¹⁶⁵, Eu³⁺-¹⁶⁶, Pr³⁺-¹⁶⁷, Er³⁺-³, Yb³⁺-¹⁶⁸, and Sm³⁺:Y₂SiO₅¹⁶⁹ (Fig. 9c).

Fig. 9. Optically addressable lanthanide spin qubits.

a Generic energy level diagram showing energy level splitting due to electron-electron interactions (e-e, leading to ^2S+1L states), spin-orbit coupling (SOC, J), crystal field (m_j) and hyperfine interactions (A_I). b Example single crystal of Eu³⁺:Y₂SiO₄ grown by the Czochralski method. c Collated example photoluminescence spectra from purely inorganic lanthanide-doped crystal host systems demonstrating coverage of the visible and near-infrared spectrum. d Examples of a zero first-order Zeeman (ZEFOZ) transition for Eu³⁺:Y₂SiO₅ spin system with the transition region indicated, demonstrating equal energy-field gradients, resulting in magnetic field insensitivity, and e impact of the ZEFOZ method on spin decoherence time for Pr³⁺:Y₂SiO₅ showing $T_2^{\mathrm{start}}$ without ZEFOZ and $T_2^{\mathrm{opt}}$ with ZEFOZ. b, d, e were reproduced from refs. ^170,176,211, respectively, with permission from the American Physical Society and Elsevier. Data points for (c) were extracted from refs. ^{166,167,175,180,212}.

In the solid-state, Y₂SiO₅ has been favoured as host matrix due to the ability to grow large crystals with excellent optical properties using the Czochralski method¹⁷⁰ (Fig. 9b). However, as the only naturally occurring isotope, ⁸⁹Y harbours an I = 1/2 nuclear spin that ultimately limits decoherence times. To reduce the impact of the spin bath, various decoupling techniques have emerged^171–173. Perhaps the most successful is the so-called “ZEFOZ” technique, whereby a magnetic field is applied such that the magnetic field dependence of the spin-transition frequency is very close to zero¹⁷⁴ (Fig. 9d). In this “clock transition” regime, spins are first-order insensitive to small fluctuations in local magnetic fields. Using this technique with Eu³⁺:Y₂SiO₅, Zhong et al. demonstrated that it is possible to acquire T₂ ≫ 100 ms at 2 K, where spin-phonon coupling is negligible. Remarkably, combined with dynamic decoupling methods, T_DD was measured to be 370 ± 60 mins, reaching a critical milestone whereby the distance-dependent decoherence becomes less for spin-transport than it is during light-transport of quantum states¹⁷⁵.

Interestingly, the larger magnetic moment of Pr³⁺ can give rise to “frozen core”-type behaviour, whereby local Y-spins become dephased from the bulk crystal and hence exhibit reduced dephasing influence on the Pr³⁺ spins¹⁷¹. Equall et al. measured homogenous field-dependent and crystal structure site-dependent linewidths between 2.5 and 0.85 kHz, and a corresponding T₂ as high as 377 μs at 1.4 K¹⁶⁷. Combined with the ZEFOZ method, the T₂ can reach 82 ms at 1.5 K¹⁷¹ (see example Fig. 9e), and with further dynamical decoupling T_DD up to 1 min can be achieved, approaching the population lifetime limit¹⁷⁶. Coherence times can also be enhanced using a host matrix whereby the principal host ion (e.g., Y) has a more closely matched ionic radius to the dopant, leading to reduced crystallographic distortions. For example, in a Pr³⁺:La₂(WO₄)₃ system, a T₂ of 158 ± 7 ms has been measured at ≈ 4 K¹⁷⁷.

Spin coherence times of Er³⁺:Y₂SiO₅ have so far been shorter than the best-performing Eu³⁺ materials, with T₂ measured at 1.3 ± 0.01 seconds at 1.4 K, despite exhibiting the frozen core effect³. However, this was achieved without using the ZEFOZ method, and therefore, these times can likely be significantly extended. Er³⁺ has also been studied in a Y₂O₃ host with T₂ reaching ≈140 μs at 1.8 K and with an applied field of 4 T¹⁷⁸. Decoherence was dominated by phonon-driven dipole-dipole interactions and the nuclear spin bath at high fields, similar to Er³⁺:KTiOPO₄ where T₂ was measured at ≈ 200 μs under similar conditions¹⁷⁹.

¹⁷¹Yb³⁺ holds a unique position amongst the lanthanide ions discussed so far due to its S = 1/2 and I = 1/2 electron spin and hyperfine structure, resulting in a simple 4-level system. Of the ¹⁷¹Yb³⁺-doped materials¹⁸⁰, ¹⁷¹Yb³⁺:Y₂SiO₅ appears to exhibit the longest spin coherence times. This material was initially studied by X-band EPR spectroscopy and presented with an electron T₁ of ≈5 seconds at 2.5 K with an applied field of ≈90 mT. T₁ quickly increases above ≈4 K due to Raman relaxation, where T₂ becomes ultimately limited by T₁¹⁸¹. At 2.5 K, T₂ was optimised at ≈ 1 T to 73 μs and improved further by dynamical decoupling, reaching 550 μs. In the same experiments, the authors record nuclear T₁ and T₂ at 4.5 K of 4 and 0.35 ms, respectively. Using an optical approach, Ortu et al. improved the coherent properties of ¹⁷¹Yb³⁺:Y₂SiO₅ by employing the ZEFOZ method such that the electron T₂ remains above 100 μs at 5.6 K, and the nuclear T₂ extends to 1 ms¹⁶⁸. Using a different approach, Welinski et al. demonstrated that coherence can also be extended by first polarising host nuclear spins through spin diffusion. At 2 K, the authors first excite ¹⁷¹Yb spins before allowing them to equilibrate over a few seconds through spectral diffusion over the inhomogeneous linewidth. The result is an effective “hole burning” in the absorption spectrum of ¹⁷¹Yb³⁺:Y₂SiO₅ and up to 90% nuclear spin polarisation, thereby effectively generating mK spin temperatures and improving the optical T₂ from 0.3 to 0.8 ms¹⁸².

To our knowledge, pulsed optical decoherence studies have not been performed on Sm³⁺:Y₂SiO₅, however, its I = 7/2 nucleus and strong hyperfine coupling may be useful for qudit systems, and it is also predicted to be less sensitive to magnetic field fluctuations than Er^3+169,183.

Finally, in recent years, Ce³⁺:YAG has become a well-studied example of a potential lanthanide spin material that is readily available. As with the previous V⁴⁺ and Mo²⁺ spin centres found in SiC, Ce³⁺ exhibits a S = 1/2 ground state and is not initialised through ISC, but rather uniquely uses left- or right-handed circularly polarised light to selectively depopulate a spin-dependent ZPL¹⁸⁴. Moreover, unlike many lanthanide defects, this 4f- to 5d-orbital transition exhibits a high oscillator strength and can be excited using green light with yellow emission, generating a theoretical maximum of 99.7% spin polarisation in its excited state. This state only lasts ≈63 ns or so before relaxing back to the ground state with a reported ODMR contrast of 98%¹⁸⁵. Whilst maintenance of robust spin properties still requires low temperatures, in part due to the abundance of ²⁷Al (I = 5/2) in the YAG^186,187, detectable spin coherence is maintained up to 20 K–significantly higher than other lanthanides, and T₁ can even be measured at room temperature¹⁸⁴. Cross relaxation of commonly found co-impurities has been used to optically read out the spin-state of species like Tb³⁺ and Gb^3+188,189, demonstrating the capacity of Ce³⁺ to act as a spin readout relay for otherwise dark spins - an essential property for nanoscale sensing. Moreover, Ce³⁺:YAG may even demonstrate improved ODMR spin properties when manufactured into thin films, making it a promising platform for incorporation into devices¹⁹⁰.

Optimising performance of spin-qubit materials

From our review, it is clear that spin-based qubit candidates demonstrate potential in several fields of quantum technology. However, unsurprisingly, their spin coherence lifetimes are limited by temperature and the spin-bath dependence of the spin properties and optical contrast between different spin states. Across all material platforms, there is significant magnetic inhomogeneity that emerges from random local spin environments. To understand the extent to which inhomogeneity infects different materials, it could be instructive to consider the ratio of $T_2^{*}$/T₂ (Fig. 10, the so-called “inhomogeneity parameter”). Hence, a low ratio indicates that T₂ is close to $T_2^{*}$ and the materials are limited by dynamic, not static, sources of decoherence. Using the available data where $T_2^{*}$ and T₂ were measured under similar conditions, there appears to emerge a distinct advantage for molecules and van der Waals materials at higher temperatures despite their lack of isotopic enrichment. This likely stems from the use of molecular crystals and the inherent 2D-order associated with materials such as hBN, which helps to ensure that all molecules “feel” the same magnetic environment. Interestingly, despite the significant difficulties associated with synthesising aligned 3D spin defects in diamond, SnV⁻diamond (measured as single spins) exhibits the lowest ratio at low temperatures. Considering its robust quantum spin parameters, SnV⁻diamond could be a leading candidate for low-temperature applications.

Fig. 10. Comparison of T₂ and $T_2^{*}$ for different spin systems as a measure of inhomogeneity.

This ratio generally grows with temperature due to an increasing prevalence of dynamic decoherence including phonons and Johnson-Nyquist noise.

Spin parameters can be improved by positional engineering of defect centres. Clustering (or the straggling) of spin-active dopants in a substrate poses spin-spin coupling from the environment (nuclear spins), which decreases T₂. Controlled doping becomes crucial in decreasing spin density around spin-active defect centres. Eliminating unwanted spins like nuclear spins requires isotopic purity of substrate material or the careful doping of spin-active centres or defects within the host matrix. More recently, Plasma-Enhanced CVD methods have been used to achieve higher deposition rates while minimising the impact of energetic ions or electrons affecting the colour centres in NV and SnV diamonds¹⁹¹. Another novel method to precisely control the position of each defect is laser writing. Aberration-corrected optics allow for the precise positioning of vacancies in diamond systems, with a 45% success probability of a vacancy being located within 200 nm of a desired position¹⁹².

Due to their ability to effectively engineer the placement of molecules in 3D chemical systems, materials with charge transfer or hydrogen bonding motifs may yet demonstrate advantages. Moreover, as seen with Pc:PTP, and Pr³⁺:Y₂SiO₅ vs. the La₂(WO₅)₃ host, material engineers should avoid defect-site strain by selecting hosts with closely matched physical parameters to the defect. Finally, further improvements can be realised through dynamical decoupling methods that are tailored for each application. For example, while engineering clock transitions using magnetic fields or ZFS is appealing for quantum optics where spectral stability is prised, it is not necessarily useful for sensing or information processing. This is because the associated reduced magnetic field sensitivity would reduce the quantum operation fidelity. On the other hand, focused electromagnetic driving of parasitic impurities, such as N-centres in diamond, has yet to be significantly explored in molecular systems. Significant improvements in T₂ and $T_2^{*}$ would likely emerge from a combination of field-driving and pulsed refocusing methods such as CPMG.

Conclusion and outlook

Optically addressable spin systems show great potential as a diverse form of qubit media for quantum sensing, communications, and information processing applications. From this review, we have attempted to benchmark the different families of materials and identify useful investigative and experimental approaches that can be translated across the field. The most significant hurdles faced by chemists and materials engineers remain the strong temperature dependence of the spin-lattice relaxation and thermal polarisation of the spin bath, which renders most heavy atom-containing systems impractical above a few kelvin, but below which these materials demonstrate the longest coherence times by a significant margin. However, above liquid helium temperatures, it is clear that light-element materials such as colour centres in diamond, SiC and most recently, molecular systems demonstrate more robust quantum spin parameters. Nevertheless, significant advancements in dynamic decoupling techniques within the last 20 years and isotope engineering have enabled the realisation of remarkably competitive quantum spin properties. Within the next decade, it is expected that further advances and knowledge transfer between investigators of different material platforms will lead to devices capable of significantly impacting society, especially in the field of magnetic field sensors and coherent quantum optics. In particular, materials that are currently prised for their spectral stability and employed mainly for applications in quantum optics and communication or networking (e.g., f-block, heavy atom vacancy centres) will benefit from incorporating the relatively weak phononic sensitivity and high brightness found in materials primarily used for quantum sensing and information processing (e.g., defects in diamond, SiC, hBN and molecules), and vice versa. We also hope that by collating (meta)data on the available spin-qubit candidates, the field will eventually benefit from the processing and predictive power of machine learning and artificial intelligence approaches to materials discovery.

Author contributions

C.A.T. and M.A. curated the data. C.A.T., M.O., and M.A. contributed to the writing of the manuscript. All authors have read and approved the manuscript.

Data Availability

All data used in this review is available in the supplementary data in .xlsx format.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41535-026-00877-5.