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 ${\mathrm{\Omega }}_0$, this measurement backaction adds quanta $\hslash {\mathrm{\Omega }}_0$ to the oscillator’s energy at a rate ${\mathrm{\Gamma }}_{\text{recoil}}$, a process called photon recoil heating, and sets bounds to coherence times in cavity optomechanical systems. Here, we use an optically levitated nanoparticle in ultrahigh vacuum to directly measure ${\mathrm{\Gamma }}_{\text{recoil}}$. By means of a phase-sensitive feedback scheme, we cool the harmonic motion of the nanoparticle from ambient to microkelvin 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.

Figure 1

Illustration of photon recoil heating. A particle with mass $m$ is trapped at the focus of a laser beam by means of the optical gradient force. The particle’s center-of-mass temperature is cooled by parametric feedback and heated by individual photon momentum kicks. ${\mathrm{\Omega }}_0/2\pi$ is the mechanical oscillation frequency and $\hslash {\omega }_0$ is the photon energy. The incident light is polarized along the $x$ direction.

Figure 2

Power spectral densities under feedback cooling. The Lorentzian curves correspond to the motion of a particle with radius $R=49.8\mathrm{nm}$ along $y$ for three different vacuum pressures: $6.6\times {10}^{-4}$, $1.1\times {10}^{-5}$, and $2\times {10}^{-8}\mathrm{mbar}$. $n$ indicates the mean occupation number. The center-of-mass temperature of the $n=63$ peak is $T_{\mathrm{cm}}=450\mu \mathrm{K}$. Note that ${\tilde{S}}_{yy}$ is the single sided PSD [31].

Figure 3

Steady state under feedback cooling. Mean occupation number along the three principal axes ($x$, $y$, $z$) as a function of gas pressure measured under constant feedback cooling for an $R=49.8\mathrm{nm}$ particle with focal power $P_0=70\mathrm{mW}$. The solid curves are fitting functions of the form $a+b{P}_{\text{gas}}$.

Figure 4

Reheating time traces. Particle reheating along the $y$ axis for different particle sizes and laser powers. (a) Reheating for $R_1=52.7\mathrm{nm}$ and $R_2=71.6\mathrm{nm}$ nanoparticle. The pressure is $3\times {10}^{-8}\mathrm{mbar}$ and the focal power is 70 mW. (b) Reheating for a particle with radius $R=68.0\mathrm{nm}$ measured for two different focal powers, $P_0^{(1)}=30.5\mathrm{mW}$ and $P_0^{(2)}=80.0\mathrm{mW}$, at a pressure $7\times {10}^{-9}\mathrm{mbar}$. The experimental data are obtained by averaging 500 individual reheating trajectories. The shaded areas reflect one standard error above and below the mean phonon value.