🔬 applied physics

Intermediate Excited State Relaxation Dynamics of Boron Vacancy Spin Defects in Hexagonal Boron Nitride

This study experimentally measures the temperature-dependent relaxation dynamics of the intermediate excited state in boron vacancy spin defects in hexagonal boron nitride, revealing a 24.0 ns room-temperature lifetime that enables optimized pulse sequences for enhanced spin manipulation and quantum sensing sensitivity.

Original authors: Paul Konrad, Mehran Kianinia, Lesley Spencer, Andreas Sperlich, Lukas Hein, Selin Steinicke, Igor Aharonovich, Vladimir Dyakonov

Published 2026-07-30

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CC BY 4.0

Original authors: Paul Konrad, Mehran Kianinia, Lesley Spencer, Andreas Sperlich, Lukas Hein, Selin Steinicke, Igor Aharonovich, Vladimir Dyakonov

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 authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of quantum physics as a high-tech playground where tiny particles act like magical switches. These switches, called "spin defects," can be flipped on and off using light and radio waves. Scientists have long used these switches inside 3D crystals, like diamonds, to build super-sensitive sensors that can detect magnetic fields or temperature changes. But there's a catch: because these crystals are thick, the sensors are buried deep inside, far away from the tiny things they are trying to measure. It's like trying to listen to a whisper from the other side of a brick wall.

Enter hexagonal boron nitride (hBN), a material that is as thin as a single sheet of paper. It's a 2D world where these magical switches sit right on the surface, ready to listen to whispers from the immediate neighborhood. However, to make these switches work perfectly, scientists need to understand exactly how they behave when they get excited. When you shine a light on them, they jump up to a higher energy level, but they don't just bounce back down immediately. They often get stuck in a "waiting room" state before returning home. If you don't know how long they stay in that waiting room, you might try to flip their switch at the wrong time, missing the chance to read their message. Understanding this timing is the key to turning these thin materials into the ultimate quantum sensors.

This paper is like a detective story where the researchers are trying to figure out exactly how long a tiny quantum switch gets "stuck" in a waiting room before it's ready to work again. The switch in question is a missing piece of a puzzle in a sheet of hexagonal boron nitride, known as a boron vacancy. When you shine a laser on it, the defect gets excited and then tries to relax back to its resting state. But on its way down, it often gets trapped in a mysterious "Intermediate State" (IS). Think of this IS like a busy coffee shop line: the electrons (the customers) get excited by the laser, go to the counter, and then get stuck in the line before they can finally leave and go back to their seats (the ground state).

The big mystery was: how long does it take for these electrons to get out of that line? Previous guesses were just that—guesses based on math models. This team decided to measure it directly. They used a super-fast laser that could turn on and off in the blink of an eye (less than 2.5 nanoseconds) and watched how the light coming from the sample changed. They noticed something cool: when they turned the laser off and then back on, the light didn't just start at a normal level; it shot up in a bright "overshoot" before settling down. This overshoot happened because, while the laser was off, the electrons were finally clearing out of that coffee shop line (the IS) and flooding back into the ground state, ready to be excited again.

By timing how long it took for this overshoot to happen, the researchers measured the "waiting time" of the intermediate state. They found that at room temperature, it takes about 24.0(3) nanoseconds for the electrons to clear out of the IS and return to the ground state. They also checked what happens when it's freezing cold (down to 4 Kelvin). In the cold, the electrons seem to linger a bit longer, taking about twice as much time to clear out, reaching up to 56 nanoseconds.

The paper also argues against the idea that you can just zap these switches with microwaves immediately after turning off the laser. If you try to flip the switch while the "coffee shop line" is still full of stuck electrons, your microwave pulse will only affect the few electrons that are already in the right spot, missing the rest. The team showed that if you wait just a little bit—specifically, a "buffer" time of about 150 nanoseconds—you let the line clear out completely. When you do this, your microwave pulse hits a much larger group of electrons, making the signal much stronger. In fact, this simple waiting period boosted the effectiveness of their spin-flipping pulse by nearly 26%.

The researchers used computer simulations to back up their measurements, showing how the population of electrons moves between the ground state, the excited state, and that tricky intermediate state. They confirmed that their direct measurement of the 24 ns lifetime is reliable and doesn't depend on guessing unknown rates. They also ruled out the idea that the laser itself was heating the sample too much to get accurate results at room temperature, though they noted that at cryogenic temperatures, laser heating is a bigger factor to watch out for.

In short, this paper didn't just guess how long the boron vacancy waits; it measured it. By understanding that this "waiting room" takes about 24 nanoseconds to empty at room temperature, scientists can now design better experiments. They know exactly when to pause and let the electrons settle before trying to control them. This makes the quantum sensors based on these 2D materials much more sensitive and efficient, bringing us one step closer to using these ultra-thin sheets to sense the tiniest changes in our world.

Technical Summary: Intermediate Excited State Relaxation Dynamics of Boron Vacancy Spin Defects in Hexagonal Boron Nitride

Problem Statement
Optically addressable spin defects in hexagonal boron nitride (hBN), specifically the negatively charged boron vacancy ( $V_B^-$ ), offer significant potential for 2D quantum sensing due to their atomic-scale proximity to target samples. However, the excited-state dynamics of these defects remain poorly understood. While theoretical models and indirect rate-model fittings have suggested the existence of a shelving intermediate state (IS) and estimated transition rates, direct experimental measurement of the relaxation rates from this IS back to the ground state (GS) has been lacking. The lack of precise, experimentally verified rate constants hinders the optimization of pulse sequences for coherent spin control and limits the sensitivity of quantum sensors based on $V_B^-$ .

Methodology
The authors employed a combination of time-resolved photoluminescence (PL) and optically detected magnetic resonance (ODMR) techniques to directly probe the relaxation dynamics of the $V_B^-$ spin system.

Sample Preparation: Defects were created in hBN flakes using a 30 keV nitrogen ion beam with fluences up to $1.15 \times 10^{15}$ ions/cm².
Room Temperature Measurements: A high-power (300 mW) continuous-wave 473 nm diode laser with fast on-off modulation capabilities (<2.5 ns rise time) was used in a confocal microscope. Time-correlated single-photon counting (TCSPC) captured PL dynamics. The experimental protocol involved a composite pulse train where an initialization laser pulse was followed by a variable "dark period" ( $\tau$ ) before a read-out pulse.
Cryogenic Measurements: Similar measurements were conducted in a closed-cycle cryostat (down to 4 K) using an acousto-optical modulator (AOM) for laser control, allowing for the study of temperature dependence.
Coherent Control: Pulsed ODMR experiments were performed using resonant microwave pulses to manipulate spin populations. The efficiency of these manipulations was tested by varying the delay (buffer) between the laser turn-off and the microwave pulse.
Simulation: A 5-level rate model simulation was developed to interpret the experimental data, tracking the population evolution of the ground state (GS), excited state (ES), and intermediate state (IS).

Key Results

Direct Measurement of IS Lifetime: By analyzing the "PL overshoot" observed immediately after the read-out laser pulse turns on, the authors directly measured the relaxation time from the IS to the GS. The PL overshoot intensity increases with the length of the dark period as shelved electrons repopulate the GS. Fitting this exponential growth yielded an IS relaxation time of 24.0(3) ns at room temperature. This value was consistent across a wide range of laser powers and did not rely on fitting a rate model with unknown parameters.
Temperature Dependence: At cryogenic temperatures (4 K), the IS lifetime approximately doubled to 56 ns. The authors note that laser heating effects at low temperatures complicate the exact determination of the local sample temperature, suggesting the 56 ns value represents a lower bound for the IS lifetime at 4 K. Additionally, the PL lifetime of the excited state increased from ~1.44 ns at 300 K to ~2.99 ns at 4 K.
Spin Polarization Dynamics: Simulations revealed that under continuous excitation, a significant portion of the spin population (up to ~96% at high powers) becomes shelved in the IS. The ratio of relaxation rates from the IS to the GS ( $\kappa_0/\kappa_1$ ) determines the maximum achievable spin polarization in the $m_s=0$ state.
Optimization of ODMR Sequences: The study demonstrated that the efficiency of coherent control is heavily dependent on the depletion of the IS. When microwave manipulation is performed immediately after the laser turns off, a large fraction of spins remains shelved in the IS and is unaffected by the microwaves, reducing ODMR contrast. Introducing a deliberate delay (buffer) of ~150 ns (approximately $6 \times T_{IS}$ ) allows the IS to fully relax and repopulate the GS. This optimization resulted in a 26% relative increase in ODMR contrast (a 2% absolute increase) and improved the effectiveness of $\pi$ -pulses in flipping spin polarization.

Significance and Claims
The paper claims that the direct experimental measurement of the IS lifetime provides a critical parameter for designing efficient quantum control sequences for $V_B^-$ defects. By accounting for the IS relaxation time, researchers can optimize the timing of laser and microwave pulses to maximize the number of addressable spins. The authors state that this optimization leads to a substantial improvement in the sensitivity of quantum sensors based on boron vacancies, particularly for applications involving pulsed ODMR techniques like dynamical decoupling. The work bridges the gap between theoretical rate models and experimental reality, offering a validated guide for initializing and manipulating $V_B^-$ spin systems in 2D van der Waals materials.

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