Sub-Kelvin Feedback Cooling and Heating Dynamics of an Optically Levitated Librator

Rotational optomechanics strives to gain quantum control over mechanical rotors by harnessing the interaction of light and matter. We optically trap a dielectric nanodumbbell in a linearly polarized laser field, where the dumbbell represents a nanomechanical librator. Using measurement-based parametric feedback control in high vacuum, we cool this librator from room temperature to 240 mK and investigate its heating dynamics when released from feedback. We exclude collisions with residual gas molecules as well as classical laser noise as sources of heating. Our findings indicate that we observe the torque fluctuations arising from the zero-point fluctuations of the electromagnetic field.

Figure 1

(a) Pictorial representation of radiation torque shot noise. An anisotropic scatterer in a linearly polarized light field experiences a fluctuating torque that arises from the vacuum fluctuations, illustrated as entering the unused port of the polarizing beam splitter (PBS). (b) Schematic of the experimental setup. Inside a vacuum chamber, we focus a laser beam (propagating along $z$, linearly polarized along $x$) with an aspheric lens to form an optical trap. In the forward direction, the light is collected and split into two paths with a beam splitter (BS). One half of the optical power is sent to a center-of-mass (COM) motion detector. The other half is used to measure the libration angle $\theta$ in a balanced detection scheme. The measurement is recorded with a data-acquisition card (DAQ). The intensity of the laser beam (focal power $P=1205(23)\mathrm{mW}$) is modulated with an electro-optic modulator (EOM) using feedback signals derived from the COM and the libration detector, respectively. (c) The blue line shows the measured power spectral density $S_{\theta \theta }$ of the uncooled libration motion at a pressure of $p_{\mathrm{gas}}=7.0(7)\mathrm{mbar}$. The broad spectrum is a result of coupling between the angular degrees of freedom. The black line shows $S_{\theta \theta }$ at $p_{\mathrm{gas}}=1.1(1)\times {10}^{-8}\mathrm{mbar}$ and with feedback cooling engaged for COM and librational motion, where the signal of the libration detector reduces to a single resonant line. The additional peaks are electronic noise from our data-acquisition card.

Figure 2

Reheating experiment at $p_{\mathrm{gas}}=1.1(1)\times {10}^{-8}\mathrm{mbar}$. (a) Cooled libration spectrum right after feedback cooling is turned off. (b) Libration spectrum after 950 ms, just before the feedback cooling is turned back on. (c) Libration energy (blue circles) as a function of time. A linear fit to the data is shown as the solid line.

Figure 3

Heating rate (blue circles) as a function of pressure. The solid black curve shows a linear fit with constant offset ${\mathrm{\Gamma }}_{\mathrm{res}}$ (dashed line). The dotted line indicates the contribution of the gas to the heating rate. The red solid line shows the theoretical prediction for the radiation torque shot noise heating rate ${\mathrm{\Gamma }}_{\mathrm{sn}}$. See the Supplemental Material [33] for details on the model and error estimates.

Figure 4

Heating rate as a function of relative intensity noise (RIN) at $2{\mathrm{\Omega }}_{\mathrm{l}}$ at $1.1(1)\times {10}^{-8}\mathrm{mbar}$ (blue circles). An effect on the heating rate is observable only for RIN values exceeding $-125\mathrm{dBc}/\mathrm{Hz}$.