⚛️ quantum physics

Quartet state of the neutral nitrogen-vacancy center in diamond and optimized spin readout under near-infrared two-photon excitation

Using tunable femtosecond laser two-photon optically detected magnetic resonance, researchers determined that the neutral nitrogen-vacancy center's metastable quartet state lies 0.54 eV above its ground state, enabling optimized spin readout in the near-infrared tissue window (1060–1075 nm) with significantly enhanced sensitivity.

Original author: Nikoletta Jegenyes, Pál Maák, Vladimir Verkhovlyuk, László Himics, Tamás Váczi, Miklós Veres, Ádám Gali

Published 2026-11-03

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Original author: Nikoletta Jegenyes, Pál Maák, Vladimir Verkhovlyuk, László Himics, Tamás Váczi, Miklós Veres, Ádám Gali

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the crystal lattice of a diamond, a tiny flaw can act as a sensitive sensor for the magnetic fields of the world around it. This flaw, known as a nitrogen-vacancy center, occurs when a nitrogen atom sits next to a missing carbon atom in the diamond's structure. When this defect carries a negative electric charge, it behaves like a tiny magnet that can be manipulated with light and radio waves, making it a powerful tool for measuring temperature, pressure, and magnetic fields with extreme precision. Scientists have long used these centers to peer into biological tissues, where near-infrared light can penetrate deeper than visible light. However, when researchers shine intense pulses of this light to read the magnetic state of the defect, they sometimes accidentally knock an electron loose, changing the defect's charge and scrambling the very information they are trying to measure. Understanding exactly when and how this happens is crucial for building better sensors.

A team of researchers in Hungary has now mapped out the precise energy levels where this charge-changing event occurs, revealing a hidden state of the defect that had been suspected but never directly measured. By tuning a laser to scan across a range of near-infrared wavelengths, they observed the exact moment the diamond defect loses an electron and becomes neutral. They found that this ionization process does not simply return the defect to its lowest energy state; instead, it often leaves the defect in a specific, higher-energy configuration where the spins of its electrons are all aligned in the same direction. This state, known as a quartet state, acts as a trap that disrupts the magnetic reading. The researchers measured the energy required to reach this state with high precision, determining it sits about 0.54 electronvolts above the defect's ground state. This value was derived by measuring the threshold for ionizing the ground state and the threshold for ionizing the excited state in the same experiment, ensuring the result was not skewed by temperature changes or other variables.

The discovery of this specific energy threshold allowed the team to identify the perfect window for reading the magnetic spin without causing damage. They found that using a laser wavelength between 1060 and 1075 nanometers provides the clearest signal. At this specific range, the laser is energetic enough to excite the defect but not so energetic that it triggers the ionization channels that destroy the spin information. This sweet spot offers a significant improvement over previous methods, which used slightly shorter wavelengths around 1030 to 1040 nanometers. By shifting to this new range, the sensitivity of the measurement increases by roughly 26 to 37 percent, meaning researchers can either detect weaker signals or use less laser power to achieve the same result. This is particularly important for biological applications, as lower power reduces the risk of heating or damaging living tissue, while the near-infrared light continues to penetrate deep into cells.

The study also clarified what happens when the laser is too strong or tuned to the wrong color. The researchers demonstrated that if the light is too energetic, it strips an electron from the excited defect, leaving it in a neutral state with a different spin arrangement that no longer responds to the magnetic readout. They ruled out several other potential pathways that could have explained the loss of signal, confirming that the primary culprit is the transition to this specific quartet state. Furthermore, they showed that the defect can be recharged back to its original state, but only if the laser energy is carefully controlled. By mapping these transitions, the team provided a clear guide for future experiments, showing that the optimal strategy is to stay just below the energy level where the quartet state begins to form. This work transforms a previously uncertain variable into a known quantity, allowing scientists to tune their instruments with greater confidence and extract more detailed information from the microscopic world inside a diamond.

Technical Summary: Quartet State of the Neutral Nitrogen–Vacancy Center in Diamond and Optimized Spin Readout under Near-Infrared Two-Photon Excitation

Problem Statement
The negatively charged nitrogen–vacancy center (NV⁻) in diamond is a premier solid-state quantum sensor. While two-photon excitation in the near-infrared (NIR) offers advantages for deep-tissue imaging and intrinsic optical sectioning, intense femtosecond excitation induces photoionization, converting NV⁻ to the neutral state (NV⁰). This process degrades spin contrast, the metric for spin readout sensitivity. A critical gap in understanding exists regarding the specific ionization channels opened by NIR excitation. Specifically, photoionization of the excited state ( $^3E$ ) leaves the neutral defect in a metastable quartet state ( $^4A_2$ ), the energy of which relative to the neutral ground state ( $^2E$ ) has remained uncertain. Previous estimates varied significantly (0.4–0.68 eV), and the optimal excitation wavelength for maximizing spin readout sensitivity while minimizing ionization-induced contrast loss had not been spectrally resolved.

Methodology
The authors employed tunable two-photon optically detected magnetic resonance (ODMR) using a femtosecond laser (680–1300 nm) on a single-crystal diamond sample containing an ensemble of NV centers.

Spectral Scanning: They performed wavelength scans across the NIR range (specifically 910–1130 nm) at varying power levels (40 mW to 500 mW).
Signal Metrics: At each wavelength, they measured the photoluminescence ( $S$ ), the spin signal ( $\Delta S$ , the decrease in $S$ on resonance), and the spin contrast ( $C = \Delta S/S$ ). They also calculated the shot-noise-limited figure of merit ( $\Delta S/\sqrt{S}$ ).
Rate Modeling: To interpret the experimental data, the authors developed a comprehensive rate model tracking populations across ten energy levels, including the sublevels of the NV⁻ triplet states ( $^3A_2$ , $^3E$ ), singlet states ( $^1A_1$ , $^1E$ ), and the NV⁰ states ( $^2E$ , $^2A_2$ , and the quartet $^4A_2$ ). The model incorporated two-photon excitation, photoionization, recharge channels, intersystem crossing, and electron tunneling from nearby nitrogen donors.
Threshold Determination: By fitting the model to the measured contrast loss (defined as the deviation from a reference contrast at 1075 nm at equal photoluminescence), they spectrally resolved the onset of the $^3E \to NV^0(^4A_2)$ ionization channel and the ground-state ionization threshold.

Key Results

Quartet State Energy: The study spectrally resolved the onset of the photoionization channel from the excited state $^3E$ to the quartet state $^4A_2$ . The threshold energy ( $E_Q$ ) was determined to be 1.23 ± 0.02 eV.
Ground-State Ionization Potential: Using the same experimental setup and sample, the ionization potential of the ground state ( $IP(^3A_2)$ ) was measured as 2.63 ± 0.03 eV.
Quartet Energy Relative to Ground State: Combining these thresholds with the known zero-phonon line ( $E_{ZPL} = 1.945$ eV), the energy of the quartet state relative to the neutral ground state ( $^2E$ ) was calculated as 0.54 ± 0.04 eV. This value aligns with high-level theoretical calculations (HSE06 and PBE functionals) and resolves previous uncertainties.
Optimal Excitation Window: The authors identified that the optimal excitation wavelength for two-photon spin readout lies between 1060 and 1075 nm. In this window:
- The spin contrast loss is minimized (near zero relative to the reference).
- The shot-noise-limited sensitivity ( $\Delta S/\sqrt{S}$ ) is maximized.
- Compared to the previously used 1030–1040 nm range (typical for Yb sources), this window offers a 26–37% higher sensitivity.
Ionization Channels: The data confirmed that at wavelengths longer than 1080 nm, the dominant ionization route is $^3E \to NV^0(^2E)$ (Channel I), which destroys spin contrast. At shorter wavelengths, the $^3E \to NV^0(^4A_2)$ channel (Channel Q) becomes active, also reducing contrast. The optimal window sits between the broadened onset of Channel Q and the fall-off of the two-photon absorption cross-section.

Significance and Claims
The paper claims to provide the first spectral resolution of the $^3E \to NV^0(^4A_2)$ ionization threshold, thereby fixing the energy of the metastable quartet state with high precision. This resolves a long-standing uncertainty in the energy level structure of the NV center.

Furthermore, the work establishes a practical "recipe" for optimizing two-photon spin readout in biological media. By shifting the excitation wavelength to the 1060–1075 nm range, researchers can achieve significantly higher sensitivity (shortening acquisition time by a factor of 1.6–1.9 or reducing power requirements by 30–40%) while maintaining operation within the near-infrared tissue transparency window. The authors emphasize that these findings apply directly to sensing with nanodiamonds in biological environments, where minimizing photodamage and maximizing signal-to-noise are critical.

The study also clarifies the role of competing ionization channels, demonstrating that the $^3E \to NV^0(^2E)$ channel is non-negligible at longer wavelengths and is the primary source of contrast loss in that regime. The results are consistent with independent cavity experiments and theoretical predictions, reinforcing the validity of the derived energy levels.

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