Feedback Cooling of a Cantilever’s Fundamental Mode below 5 mK

We cool the fundamental mechanical mode of an ultrasoft silicon cantilever from a base temperature of 2.2 K down to $2.9\pm 0.3\mathrm{mK}$ using active optomechanical feedback. The lowest observed mode temperature is consistent with limits determined by the properties of the cantilever and by the measurement noise. For high feedback gain, the driven cantilever motion is found to suppress or “squash” the optical interferometer intensity noise below the shot noise level.

Figure 1

(a) Schematic diagram of the experimental setup and (b) scanning electron micrograph of a representative Si cantilever.

Figure 2

Measured spectral density $S_{x+x_n}$ of cantilever 1 for different feedback gains $g$ as it is cooled from a base temperature $T=295\mathrm{K}$. Colored data points correspond to the mode temperatures (with an error of $\pm 10\%$) and gains of the same color shown to the right. Solid lines are fits to the data using (4).

Figure 3

Measured spectral density $S_{x+x_n}$ of cantilever 1 for different feedback gains $g$ as it is cooled from a base temperature $T=4.2\mathrm{K}$. Colored data points correspond to the mode temperatures (with an error of $\pm 10\%$) and gains of the same color shown to the right. Solid lines are fits to the data using (4).

Figure 4

Suppression of the thermal noise of cantilever 1 down to and below the measurement noise. Gray points represent the observed interferometer signal $S_{x+x_n}$ with the lever at a base temperature of $T=4.2\mathrm{K}$, solid lines are fits to this data using (4), and dashed lines are the corresponding spectra of the actual cantilever motion $S_x$ as defined in (3).

Figure 5

Measured spectral density $S_{x+x_n}$ of cantilever 2 for different feedback gains $g$ as it is cooled from a base temperature $T=2.2\mathrm{K}$. Colored data points correspond to the mode temperatures (with an error of $\pm 10\%$) and gains of the same color shown to the right. Solid lines are fits to the data using (4).

Figure 6

$T_{\mathrm{mode}}$ of our Si cantilevers as a function of feedback gain $g$. Solid lines show $T_{\mathrm{mode}}$ in (5) for the experimental parameters and the points represent $T_{\mathrm{mode}}$ extracted from three-parameter fits of (3) to spectra including those shown in Figs. 2, 3, 4, 5. Lines and points are color coded to correspond to the colored base temperature labels. The dashed line indicates $T_{\mathrm{mode},\min }=2.6\mathrm{mK}$ for cantilever 2 at $T=2.2\mathrm{K}$.