Optically Detected Electron Spin Echo Envelope Modulation on a Photoexcited Triplet State in Zero Magnetic Field—A Comparison between the Zero-Field and High-Field Limits

Optically detected nuclear quadrupolar interaction ofN14in nitrogen-vacancy centers in diamond

“…The experimental spectrum acquired with the Hahn spin-echo sequence showed excellent quantitative agreement with the simulated spectrum at ß5 MHz. Simulation and experimental data also showed a spectral peak at ß10 MHz, consistent with the fact that ESEEM gives envelope modulation at frequencies ω 0 , ω + , ω 0 − ω + , and ω 0 + ω + , where ω 0 and ω + stand for the transition frequencies of the nuclear spin associated with the electron spin states |ψ z and |ψ y , respectively [26].…”

“…The modulation frequencies due to the hyperfine interaction with 13 C nuclei could be greatly modified from the secular term A zz of the hyperfine interaction, since the net contribution of the hyperfine interaction to transition frequencies is a function of magnetic field strength and orientation when a static magnetic field is misaligned from the NV quantization axis. This has been well studied in the literature and is not a focus of our discussion [26,37,38].…”

“…In a magnetic field applied parallel to the electron spin quantization axis, the anisotropic terms of the hyperfine interaction, such as S z A zx I x , give different nuclear spin eigenstates for different states of the electron spin. A transition of the electron spin projects the nuclear spin onto a different set of eigenstates, and as a result, the envelope of the electron spin echo is modulated at frequencies determined by the hyperfine interaction, the nuclear quadrupolar interaction, and the nuclear Zeeman interaction [26]. The 14 N nuclear spin associated with NV center, however, does not induce any modulation in the electron spin-echo envelope when a magnetic field is applied parallel to the NV quantization axis.…”

“…A transition of the electron spin projects the nuclear spin onto a different set of eigenstates, and as a result, the envelope of the electron spin echo is modulated at frequencies determined by the hyperfine interaction, the nuclear quadrupolar interaction, and the nuclear Zeeman interaction. 26 The 14 N nuclear spin associated with NV center, however, does not induce any modulation in the electron spin-echo envelope when a magnetic field is applied parallel to the NV quantization axis. This is because the quantization axis of the 14 N nuclear spin is parallel to the NV quantization axis, and the nuclear spin eigenstates are independent of the electron spin state, so any effect of the frequency shifts due to interactions involving the nuclear spin is completely removed by the spin echo.…”

Room temperature coherent control of spin defects in hexagonal boron nitride

“…The ESEEM frequencies evolve linearly with the magnetic field B following the law 𝜈 tuttv = |𝜈 c ± 𝛾𝐵| , where 𝛾 = 4.54 ± 0.59𝑘𝐻𝑧/𝑚𝑇 and 𝜈 c = 382.9 ± 4.4 𝑘𝐻𝑧 is the frequency at B = 0. In the absence of magnetic field, the nuclear Zeeman splitting is zero and ESEEM arises only from the nuclear quadrupole and/or hyperfine interactions 29 and can be used to determine the quadrupole coupling as Q= 𝜈 c = 383 kHz (Eq.1), as shown in Fig. 3c.…”