The ability to characterize static and time-dependent electric fields in situ with high sensitivity and high spatial resolution has profound applications for both fundamental science and technology. Precision sensing of electric fields and forces that couple to charge is the most direct way to search for deviations from Coulomb's law, which may be motivated by the presence of new forces under which dark matter could be charged. In addition, low-frequency electric field sensors are widely used in many fields such as geophysical exploration, electrical equipment detection and underwater communication.
It has become a research focus in the field of quantum precision measurement to carry out high-resolution electric field measurement on the microscopic scale and explore the electric field sensing mechanism suitable for various application scenarios. Recently emerging sensors based on Rydberg atom and quantum-entangled trapped ions have demonstrated the capabilities of electric field measurement with sensitivity superior than the order of 1μV⋅cm−1⋅Hz−1∕2 in the high-frequency band above MHz, which is hard to achieve and challenging for the detection scenario of the low-frequency band.
Recently the optically levitated nano-resonators have made many breakthroughs in the precision measurement of extremely weak force, torque, acceleration and ultra-small mass, and exhibited unique advantages in the development of mechanical sensors at the micro- and nanoscale. To develop levitated nano-resonators into electric field sensors, a joint research group led by Prof. Huizhu Hu from Zhejianglab and Zhejiang University reported a three-dimensional, high-sensitivity electric field measurement technology using the optically levitated nanoparticle with known net charge. The relevant research results were published in Photonics Research, Volume 11, No. 2, 2023 (Shaocong Zhu, Zhenhai Fu, Xiaowen Gao, Cuihong Li, Zhiming Chen, Yingying Wang, Xingfan Chen, Huizhu Hu. Nanoscale electric field sensing using a levitated nano-resonator with net charge[J]. Photonics Research, 2023, 11(2): 279).
As shown in Fig.1(a), the setup consisted of a single-beam optical trap, triaxial position detection and parametric feedback scheme, electric driving, and field measurement circuit. By scanning the electric field distribution between parallel electrodes, the three-dimensional electric field mapping capability of the system was demonstrated, as shown in Fig.1(b). Its measuring spatial resolution depends on the motion amplitude of the nanoparticle in the equilibrium position and the manipulation accuracy of the equilibrium position, which can reach the order of nanometers.
The electric field detection sensitivity is limited by thermal noise and the amount of net charge carried by the nanoparticle. The measured noise equivalent electric intensity at resonant frequency reached 7.5μV⋅cm−1⋅Hz−1∕2 at 1.4 × 10−7 mbar, and the bandwidth within 3 dB above the thermodynamic limit was 1.1kHz, as shown in Fig.1(c). Linearity analysis near resonance shows a linear range of more than 4 orders of magnitude with a largest detectable electric field of 65.5kV/m, which was merely limited by the maximum output of the test equipment.
Fig.1 (a) Schematic of the experimental setup. (b) Measured vector field in the x–z plane between two parallel plate electrodes. (c) Noise equivalent force and equivalent electric intensity in vacuum.
It is worth mentioning that the resonant frequency of the levitated resonator is naturally in the low frequency band, which can be adjusted from Hz to MHz according to size of particle and stiffness of the potential well, making it is a promising candidate for new electric field sensor in this frequency band. This method is most similar to electric field sensing with trapped ions that use mechanical oscillators as exquisite quantum tools to measure small displacements due to weak forces and electric fields. As schemes with optically levitated nanoparticles do not need an additional DC or AC electric field for a stable trap that is generally utilized in ions schemes, it can eliminate the influence of the existing electric field in the device on the electric field measurement as much as possible.
These results show that this technique has the advantage of adjustable resonant frequency (from Hz to MHz), vectorizable detection, high-spatial resolution and potential for miniaturization. Furthermore, the research group will improve the detection performance of the system and focus on solving the technical problem of stable and precise control of particle charge in high vacuum.
