Direct Measurement of Photon Recoil from a Levitated Nanoparticle

The momentum transfer between a photon and an object defines a fundamental limit for the precision with which the object can be measured. If the object oscillates at a frequency $\Omega_0$, this measurement back-action adds quanta $\hbar\Omega_0$ to the oscillator's energy at a rate $\Gamma_{\rm recoil}$, a process called photon recoil heating, and sets bounds to quantum coherence times in cavity optomechanical systems. Here, we use an optically levitated nanoparticle in ultrahigh vacuum to directly measure $\Gamma_{\rm recoil}$. By means of a phase-sensitive feedback scheme, we cool the harmonic motion of the nanoparticle from ambient to micro-Kelvin temperatures and measure its reheating rate under the influence of the radiation field. The recoil heating rate is measured for different particle sizes and for different excitation powers, without the need for cavity optics or cryogenic environments. The measurements are in quantitative agreement with theoretical predictions and provide valuable guidance for the realization of quantum ground-state cooling protocols and the measurement of ultrasmall forces