THE QUANTUM INTELLIGENCER

Probing NV-NV Interactions in Diamond Using Dynamical DEER: A Path to Quantifying Quantum Spin Concentrations In Plain English: Scientists use tiny defects in diamond, called nitrogen-vacancy (NV) centers, to build ultra-sensitive sensors for magnetic fields and temperature. When many of these defects are packed close together, they can start to interfere with each other, reducing their performance. This study looked at how these defects interact by using a special sequence of microwave pulses to 'listen' to their magnetic conversations. They found that the way these defects affect each other doesn’t follow simple rules, but they can still use the strength of this interaction to count how many defects are present. This helps researchers make better sensors by understanding and managing the crowd of defects inside the diamond. Summary: This paper presents a systematic experimental study of mutual interactions between nitrogen-vacancy (NV) centers in diamond using dynamical double electron-electron resonance (DEER) techniques. While decoherence in NV ensembles is commonly attributed to extrinsic paramagnetic impurities such as carbon-13 nuclei and P1 centers, the role of direct NV-NV interactions—particularly in dense ensembles—remains poorly characterized. The authors employ both three- and four-pulse DEER sequences to directly observe and quantify these interactions. They analyze both the phase evolution and amplitude decay of the NV spin state, providing a complete picture of NV-induced decoherence. The three-pulse sequence exhibits a distinct phase jump, attributed to non-commuting quantum rotations within the pulse sequence—an effect arising from the specific timing and orientation of control pulses. Crucially, the observed decay rate of the state vector deviates significantly from theoretical predictions for a simple spin-1/2 system, indicating more complex many-body dynamics. Despite this deviation, the decay rate in the DEER sequence correlates reliably with the concentration of NV centers, provided that the magnetic transition of the NV centers is saturated. This establishes the DEER-based measurement as a viable method for determining NV density in diamond samples, offering both fundamental insights into spin-spin interactions and a practical tool for optimizing quantum sensor fabrication. Key Points: - Nitrogen-vacancy (NV) centers in diamond are used in quantum sensors, but their performance depends on how they interact when packed densely. - Direct NV-NV interactions are less understood compared to decoherence from other impurities like carbon-13 or P1 centers. - The study uses dynamical double electron-electron resonance (DEER) with 3- and 4-pulse sequences to probe NV-NV coupling. - Phase jumps in the 3-pulse sequence result from non-commuting quantum rotations during the pulse sequence. - The amplitude decay of the spin state does not follow standard spin-1/2 decoherence models, indicating complex interaction dynamics. - Despite model deviations, the measured decay rate in DEER reliably reflects NV center concentration when magnetic transitions are saturated. - This enables DEER as a method to quantify NV density, useful for sensor development and quantum material characterization. Notable Quotes: - "The nature of the phase jump in the 3-pulse sequence was attributed to the effect of non-commuting rotations within the sequence." - "It was shown that the rate of the state vector decay differed significantly from predictions for a spin 1/2 system." - "However, the decay rate observed in the DEER sequence remained a reliable indicator of the concentration of bath spins and could be used to measure NV center concentration..." Data Points: - Study involves two types of dynamical DEER sequences: one with 3 pulses, another with 4 pulses. - Magnetic transition of NV centers must be saturated for decay rate to reliably indicate concentration. - No quantitative values (e.g., decay rates, concentrations, or coherence times) are provided in the abstract. Controversial Claims: - The claim that NV-NV interaction-induced decoherence deviates significantly from spin-1/2 predictions may challenge simplified models used in current quantum sensor designs, implying that existing simulations may underestimate collective effects. Additionally, the assertion that DEER decay rates can reliably measure NV concentration—despite non-standard decoherence behavior—might be contested if unaccounted environmental factors (e.g., strain, temperature gradients, or other spin baths) influence the signal in real-world samples. Technical Terms: - Nitrogen-vacancy (NV) centers, diamond, quantum sensors, decoherence, paramagnetic impurities, carbon-13 isotopes, P1 centers, NV-NV interaction, dynamical double electron-electron resonance (DEER), 3-pulse sequence, 4-pulse sequence, non-commuting rotations, phase jump, state vector rotation, amplitude decay, spin 1/2 system, bath spins, magnetic transition saturation, coherent properties, spin ensemble —Ada H. 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