• Chinese Optics Letters
  • Vol. 17, Issue 6, 060901 (2019)
Yu Zheng1,2 and Fangwen Sun1,2,*
Author Affiliations
  • 1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
  • 2CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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    DOI: 10.3788/COL201917.060901 Cite this Article Set citation alerts
    Yu Zheng, Fangwen Sun, "Three-dimensional position measurement of a levitated nanoparticle in a vacuum by a Dove prism," Chin. Opt. Lett. 17, 060901 (2019) Copy Citation Text show less

    Abstract

    Forward-scattering-light interferometry has become the most commonly used position detection scheme in optical levitation systems. Usually, three-set detectors are required to obtain the three-dimensional motion information. Here, we simplify the three-set detectors to one set by inserting a Dove prism. We investigate the role of a Dove prism in the position measurement process with an optical levitation system in vacuum. The relationship between the power spectral density and the rotation angle of a Dove prism is experimentally demonstrated and analyzed. This work shows that the Dove prism can greatly reduce the complexity of the experimental setup, which can be applied to compact optical levitation systems for studies in metrology, quantum physics, and biology.
    IRIL=Nxx0,(1)

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    IR=0rmaxπ2π2I(r,θ,r0,θ0)dθdr,(2)

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    IL=0rmaxπ23π2I(r,θ,r0,θ0)dθdr,(3)

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    IR=0rmaxπ0I(r,θ,r0,θ0)dθdr,(4)

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    IL=0rmax0πI(r,θ,r0,θ0)dθdr.(5)

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    IRIL=IdownIup=Nyy0,(6)

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    IRφ0ILφ0=Nxx0cos(2φ0)Nyy0sin(2φ0),(7)

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    S(ω)=2kBTMΩ2Ω2Γ0(Ω2ω2)2+ω2Γ02,(8)

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    Γ0=6πηRM0.6190.619+Kn(1+cK),(9)

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    F(I0(t))=Nxcos(2φ0)F(x0(t))Nysin(2φ0)F(y0(t)),(10)

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    Sx(ω)=|F(x0(t))|2/Trec,(11)

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    Sy(ω)=|F(y0(t))|2/Trec,(12)

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    SI(ω)=|F(I0(t))|2/Trec={Nx2cos2(2φ0)|F(x0(t))|2+Ny2sin2(2φ0)|F(y0(t))|2NxNysin(2φ0)cos(2φ0)[F(x0(t))¯F(y0(t))+F(x0(t))F(y0(t))¯]}/Trec.(13)

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    F(x0(t))¯F(y0(t))+F(x0(t))F(y0(t))¯=0.(14)

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    SI(ω)=Nx2AxSx(ω)+Ny2AySy(ω),(15)

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