This chapter demonstrates a direct measurement of the nanoparticle’s velocity distribution in its motional ground state. Due to the uncertainty principle, the position and momentum of a particle cannot be measured simultaneously with arbitrary precision. While previous studies inferred velocity from the time derivative of position signals obtained via optical scattering, these methods are inherently indirect and do not offer an independent measurement of momentum. To overcome this difficulty, we perform Time-of-Flight (TOF) measurements by releasing the particle from the optical trap. We determine its velocity from its displacement during free flight. The experiment reveals a previously unobserved coupling between translational and librational modes. This coupling, caused by slight asymmetries in the particle’s shape, broadens the velocity distribution. By cooling the librational motion, we successfully suppress the effect of this coupling on the TOF measurement. As a result, velocity distributions from TOF measurements narrow and closely match the theoretical distributions calculated using the occupation numbers derived from power spectral density analysis. These results provide a crucial step toward investigating quantum aspects of levitated nanoparticles via their velocity distribution.

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TOF Measurement of the Velocity Distribution

  • Mitsuyoshi Kamba

摘要

This chapter demonstrates a direct measurement of the nanoparticle’s velocity distribution in its motional ground state. Due to the uncertainty principle, the position and momentum of a particle cannot be measured simultaneously with arbitrary precision. While previous studies inferred velocity from the time derivative of position signals obtained via optical scattering, these methods are inherently indirect and do not offer an independent measurement of momentum. To overcome this difficulty, we perform Time-of-Flight (TOF) measurements by releasing the particle from the optical trap. We determine its velocity from its displacement during free flight. The experiment reveals a previously unobserved coupling between translational and librational modes. This coupling, caused by slight asymmetries in the particle’s shape, broadens the velocity distribution. By cooling the librational motion, we successfully suppress the effect of this coupling on the TOF measurement. As a result, velocity distributions from TOF measurements narrow and closely match the theoretical distributions calculated using the occupation numbers derived from power spectral density analysis. These results provide a crucial step toward investigating quantum aspects of levitated nanoparticles via their velocity distribution.