Cold Damping of an Optically Levitated Nanoparticle to Microkelvin Temperatures

We implement a cold-damping scheme to cool one mode of the center-of-mass motion of an optically levitated nanoparticle in ultrahigh vacuum (${10}^{-8}\mathrm{mbar}$) from room temperature to a record-low temperature of $100\mu \mathrm{K}$. The measured temperature dependence on the feedback gain and thermal decoherence rate is in excellent agreement with a parameter-free model. For the first time, we determine the imprecision-backaction product for a levitated optomechanical system and discuss the resulting implications for ground-state cooling of an optically levitated nanoparticle.

Figure 1

Experimental setup. A silica nanoparticle (nominal diameter 136 nm) carrying a finite net charge $q$ is optically trapped in a vacuum using a laser beam (wavelength 1064 nm) focused by an objective. To measure the $y$ motion of the particle, the backscattered light is rerouted by a free-space circulator, mixed with a local oscillator (frequency shifted by 1 MHz relative to the trap laser), and sent to a balanced split detection scheme, yielding the out-of-loop signal $y_{\mathrm{ol}}$. The forward-scattered light is detected in another balanced split detection scheme and yields the in-loop signal $y_{\mathrm{il}}$, which is processed by a linear, digital filter $H$. The resulting feedback signal is applied as a voltage to a capacitor enclosing the trapped particle.

Figure 2

(a) Single-sided power spectral densities ${\tilde{S}}_{yy}^{\mathrm{ol}}$ of the motion of the nanoparticle measured by the out-of-loop detector for different feedback damping rates ${\gamma }_{\mathrm{FB}}$. The solid lines are Lorentzian fits to the data. The black data points denote the measured shot-noise level ${\tilde{S}}_{\nu \nu }$ on the out-of-loop detector. (b) Mode temperature $T_y$ derived from the out-of-loop signal $y_{\mathrm{ol}}$ as a function of feedback gain ${\gamma }_{\mathrm{FB}}$. The black circles denote the measured values at a pressure of $1.4\times {10}^{-8}\mathrm{mbar}$. At a damping rate of ${\gamma }_{\mathrm{FB}}=2\pi \times 1\mathrm{kHz}$, we observe a minimum temperature of $100\mu \mathrm{K}$. The solid black line is a parameter-free calculation according to Eq. (3). The blue (red) dashed line denotes the contribution of the first (second) term in Eq. (3). The gray triangles and line show measured and calculated mode temperatures, respectively, at a higher pressure of $1.2\times {10}^{-7}\mathrm{mbar}$. Inset: Power spectral densities ${\tilde{S}}_{yy}^{\mathrm{il}}$ measured by the in-loop detector for the same settings as in (a). Photon shot noise ${\tilde{S}}_{nn}$ is shown as black data points. In contrast to (a), for a large feedback gain (${\gamma }_{\mathrm{FB}}=2\pi \times 3.0\mathrm{kHz}$) we observe noise squashing; i.e., the measured signal drops below the noise floor.

Figure 3

(a) Ring-down and reheating experiment. For the ring-down experiment, we start with the oscillation mode at an elevated temperature, reached by reducing the feedback gain. At time $t=0$, we switch the feedback damping rate to ${\gamma }_{\mathrm{FB}}$ and measure the decay of the mode temperature $T_y(t)$ (blue triangles). We fit $T_y$ with a single exponential decay (black dashed line) and extract the decay constant, which yields ${\gamma }_{\mathrm{FB}}=2\pi \times 47\mathrm{Hz}$. For the reheating experiment, we turn off the feedback cooling at time $t=0$ and measure the increasing mode temperature $T_y(t)$ (red circles). A linear fit (dash-dotted line) to the data yields the reheating speed $d{T}_y/dt=\gamma T_{\mathrm{bath}}$. (b) Feedback damping rate ${\gamma }_{\mathrm{FB}}$ (blue triangles) and reheating speed $d{T}_y/dt$ (red circles) as a function of the pressure. The feedback damping rate is independent of the pressure and solely determined by the gain of the feedback circuit. Within our pressure range, the reheating follows a linear trend (indicated as the dash-dotted line).