• Photonics Research
  • Vol. 11, Issue 2, 279 (2023)
Shaocong Zhu1, Zhenhai Fu1、3、*, Xiaowen Gao1、4、*, Cuihong Li1, Zhiming Chen1, Yingying Wang1, Xingfan Chen2, and Huizhu Hu1、2、5、*
Author Affiliations
  • 1Quantum Sensing Center, Zhejiang Lab, Hangzhou 310000, China
  • 2State Key Laboratory of Modern Optical Instruments, College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
  • 3e-mail: fuzhenhai@zju.edu.cn
  • 4e-mail: gaoxw@zhejianglab.com
  • 5e-mail: huhuizhu2000@zju.edu.cn
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    DOI: 10.1364/PRJ.475793 Cite this Article Set citation alerts
    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 Copy Citation Text show less

    Abstract

    The nanomechanical resonator based on a levitated particle exhibits unique advantages in the development of ultrasensitive electric field detectors. We demonstrate a three-dimensional, high-sensitivity electric field measurement technology using the optically levitated nanoparticle with known net charge. By scanning the relative position between nanoparticle and parallel electrodes, the three-dimensional electric field distribution with microscale resolution is obtained. The measured noise equivalent electric intensity with charges of 100e reaches the order of 1 μVcm-1Hz-1/2 at 1.4×10-7 mbar. Linearity analysis near resonance frequency shows a measured linear range over 91 dB limited only by the maximum output voltage of the driving equipment. This work may provide an avenue for developing a high-sensitivity electric field sensor based on an optically levitated nano-resonator.
    SE=2mSxel(ωdr)[(ωdr2ωx2)2+Γx2ωdr2]Nqe  (inVm1Hz1/2).

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    χ˜Fcool(ω)=1m(ωx2ω2+jΓxω).

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    mx¨+mΓxx˙+kx=Fth(t)+Fel(t).(A1)

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    Felx=NqeEx.(A2)

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    Sxel(ω)=Svxel(ω)/cx/V2=2Felx2τsinc2[2(ωωdr)τ]m2[(ω2ωx2)2+Γx2ω2],(A3)

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    Ex=mSvxel(ωdr)[(ωdr2ωx2)2+Γx2ωdr2]/(2τ)cx/VNqe.(A4)

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    xel(ω)=Nqem[(ωx2ω2)+jΓxω]Ex(ω)=χ˜el(ω)Ex(ω).(C1)

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    χ˜el(ω)=Nqeχ˜F(ω).(C2)

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    Eth=2kBT0mΓxNqe.(C3)

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    χ˜elcool(ω)=Nqem[(ωx+δω)2ω2+j(Γx+δΓ)ω].(C4)

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    Ethcool=2kBTcoolm(Γx+δΓ)Nqe.(C5)

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    Tcool=T0ΓxΓx+δΓ.(C6)

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    xsn=TV/iRi/Pcx/VSPP1/2=TV/iRi/Pcx/V2hvPaη.(C7)

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    Esn(ω)=TV/iRi/Pcx/V2hvPaη|χ˜elcool(ω)|1.(C8)

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    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
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