The duration of chorus elements is an important parameter to understand chorus excitation and to quantify the effects of nonlinear wave-particle interactions on energetic electron dynamics. In this work, we analyze the duration of rising tone chorus elements statistically using Van Allen Probes data. We present the distribution of chorus element duration () as a function of magnetic local time (MLT) and the geomagnetic activity level characterized by auroral electrojet (AE) index. We show that the typical value of for nightside and dawnside is about 0.12 s, smaller than that for dayside and duskside by about a factor of 2 to 4. Using a previously developed hybrid code, DAWN, we suggest that the background magnetic field inhomogeneity might be an important factor in controlling the chorus element duration. We also report that is larger during quiet times and shorter during moderate and active periods; this result is consistent with the MLT dependence of and the occurrence pattern of chorus waves at different levels of geomagnetic activity. We then investigate the correlation between and the frequency chirping rate (Γ). We show that, from observation, scales with Γ as ∝ Γ −1.1 , suggesting that statistically the frequency range of chorus elements (Γ) should be roughly the same for different elements. These findings should be useful to the further development of a theoretical model of chorus excitation and to the quantification of nonlinear wave-particle interactions on energetic electron dynamics.

Searching for new particles beyond the standard model is crucial for understanding several fundamental conundrums in physics and astrophysics. Several hypothetical particles can mediate exotic spin-dependent interactions between ordinary fermions, which enable laboratory searches via the detection of the interactions. Most laboratory searches utilize a macroscopic source and detector, thus allowing the detection of interactions with submillimeter force range and above. It remains a challenge to detect the interactions at shorter force ranges. Here we propose and demonstrate that a near-surface nitrogen-vacancy center in diamond can be utilized as a quantum sensor to detect the monopole–dipole interaction between an electron spin and nucleons. Our result sets a constraint for the electron–nucleon coupling, , with the force range 0.1–23 μm. The obtained upper bound of the coupling at 20 μm is  < 6.24 × 10−15.

Quantum control of systems plays an important role in modern science and technology. The ultimate goal of quantum control is to achieve high-fidelity universal control in a time-optimal way. Although high-fidelity universal control has been reported in various quantum systems, experimental implementation of time-optimal universal control remains elusive. Here, we report the experimental realization of time-optimal universal control of spin qubits in diamond. By generalizing a recent method for solving quantum brachistochrone equations [X. Wang et al., Phys. Rev. Lett. 114, 170501 (2015)], we obtained accurate minimum-time protocols for multiple qubits with fixed qubit interactions and a constrained control field. Single- and two-qubit time-optimal gates are experimentally implemented with fidelities of 99% obtained via quantum process tomography. Our work provides a time-optimal route to achieve accurate quantum control and unlocks new capabilities for the emerging field of time-optimal control in general quantum systems.

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