Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state

Cooling a mesoscopic mechanical oscillator to its quantum ground state is elementary for the preparation and control of quantum states of mechanical objects. Here, we pre-cool a 70-MHz micromechanical silica oscillator to an occupancy below 200 quanta by thermalizing it with a 600-mK cold ${}^3\mathrm{He}$ gas. Two-level-system induced damping via structural defect states is shown to be strongly reduced and simultaneously serves as a thermometry method to independently quantify excess heating due to the cooling laser. We demonstrate that dynamical back action optical sideband cooling can reduce the average occupancy to $9\pm 1$ quanta, implying that the mechanical oscillator can be found $(10\pm 1)\%$ of the time in its quantum ground state.

Figure 1

Cooling a micromechanical oscillator. (a) High-$Q$ mechanical and optical modes are co-located in a silica microtoroid. The simulated displacement pattern of the mechanical radial breathing mode (RBM) is shown. The optical whispering gallery mode (WGM) is confined to the rim. (b) Thermalization of the RBM to the temperature of the ${}^3\mathrm{He}$ gas, with the lowest achieved temperature corresponding to a mean occupancy of the RBM below 200 quanta. (c) Optical setup used for displacement monitoring of the mechanical mode, based on homodyne analysis of the light re-emerging from the toroid’s WGM (see text for detailed description).

Figure 2

TLS-induced change of the resonance frequency [${\Omega }_{\mathrm{m}}(T)$] (a) and inverse mechanical quality factor [$Q_{\mathrm{m}}^{-1}(T)$] (b) of the radial breathing mode. Measured data (points) agree well with the models (solid lines) described in Eqs. (1) and (2). Subtraction of the temperature-independent clamping damping (line iii) yields the theoretically possible material-limited damping values (squares and line ii). At very low temperatures, damping by resonant interaction with TLS (line iv) would be dominant. ${\Omega }_0$ is the mechanical angular frequency ${\Omega }_{\mathrm{m}}(T)$ measured at the arbitrary temperature $T=620\hspace{0.5em}$mK. The model parameters are given in Appendix .

Figure 3

(a) Effective resonance frequency and (b) linewidth of the RBM when a 2-$\mathrm{mW}$ power laser is tuned through the lower mechanical sideband of the split optical mode (inset). Points are measured data extracted from the recorded spectra of thermally induced mechanical displacement fluctuations, and solid lines are a coupled fit using the model of Eqs. (1, 2, 3, 4, 5, 6), taking into account resonant and off-resonant (stray light) heating, modifying temperature-dependent damping and frequency shift caused by the TLS.

Figure 4

Cooling factor $(T_{\mathrm{cryo}}+\delta T_{\mathrm{stray}})/T_{\mathrm{eff}}$ and phonon occupancy of the RBM vs laser detuning $\mathrm{\Delta ̄}$ for (a) $P_{\mathrm{in}}=2\hspace{0.5em}\mathrm{mW}$ and (b) $P_{\mathrm{in}}=4\hspace{0.5em}\mathrm{mW}$. Points are phonon occupancies derived from the measured noise temperature, while solid lines correspond to the occupancies expected from the dependency of sample temperature and (intrinsic and effective) damping extracted from the detuning series as shown in Fig. 3. A minimum phonon number of $\mathrm{n̄}=9\pm 1$ is obtained. The inset shows a mechanical displacement noise (DN) spectrum at the optimum detuning ($\mathrm{\Delta ̄}={\mathrm{\Delta ̄}}_{\mathrm{opt}}$), illustrating the high signal-to-noise ratio achieved despite the low occupancy for $P_{\mathrm{in}}=2\hspace{0.5em}\mathrm{mW}$.

Figure 5

Double-well potential with relevant levels and naming convention.