Laser Cooling of a Nanomechanical Oscillator to Its Zero-Point Energy

Optomechanical systems in the well-resolved-sideband regime are ideal for studying a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and nonclassical states generation. For these experiments, the mechanical oscillator should be prepared in its ground state, i.e., exhibit negligible residual excess motion compared to its zero-point motion. This can be achieved using the radiation pressure of laser light in the cavity by selectively driving the lower motional sideband, leading to sideband cooling. To date, the preparation of sideband-resolved optical systems to their zero-point energy has eluded laser cooling because of strong optical absorption heating. The alternative method of passive cooling suffers from the same problem, as the requisite milliKelvin environment is incompatible with the strong optical driving needed by many quantum protocols. Here, we employ a highly sideband-resolved silicon optomechanical crystal in a ${}^3\mathrm{He}$ buffer-gas environment at $\sim 2\mathrm{K}$ to demonstrate laser sideband cooling to a mean thermal phonon occupancy of ${0.09}_{-0.01}^{+0.02}$ quantum (self-calibrated using motional sideband asymmetry), which is $-7.4\mathrm{dB}$ of the oscillator’s zero-point energy and corresponds to 92% ground state probability. Achieving such low occupancy by laser cooling opens the door to a wide range of quantum-optomechanical experiments in the optical domain.

Figure 1

Optomechanical crystal and experimental scheme. (a) False-color SEM image of the silicon OMC with a waveguide for input coupling of light. The path of the tapered fiber is indicated by the red dashed line. The inset shows the simulated mechanical breathing mode and optical mode. (b) SEM image of the central portion of the silicon OMC. (c) Measurement scheme using a cooling tone for sideband cooling and a blue probe for motional sideband asymmetry measurement. The local oscillator (LO) is used for detection and is not sent to the cavity.

Figure 2

Power dependence of sideband cooling. (a) Pumping scheme for the power sweep with a cooling tone at a fixed detuning of $-{\mathrm{\Omega }}_m$ relative to the cavity resonance and an additional blue probe for sideband asymmetry calibration, as indicated in the dashed green box. The frequency separation between the cooling tone and blue probe is fixed at $2({\mathrm{\Omega }}_m+\delta )$. (b) Measured effective mechanical linewidth ${\mathrm{\Gamma }}_{\mathrm{eff}}$ from the noise power spectral density vs cooling tone intracavity photon number ${\overline{n}}_c$ (red full circles) in single-tone measurements with a theoretical plot with experimental values (blue curve). (c) and (d) Single-sided noise spectra from balanced heterodyne detection normalized to the shot noise floor from two-tone and single-tone measurements, respectively, with corresponding fit curves, for various intracavity photon numbers. (e) Final phonon occupancy vs intracavity photon number of the cooling tone in single tone measurements. Purple full circles are anchored to the cryostat thermometer temperature at the lowest values of ${\overline{n}}_c$. Green full circles utilize the averaged calibration coefficient obtained from the ancillary two-tone sideband-asymmetry measurements, where the error bars are given by both the errors in the Lorentzian fit and in the calibration coefficient. The inset shows an expanded view at the highest cooling powers. The horizontal red dashed line corresponds to ${\overline{n}}_f=1/2$.

Figure 3

Detuning dependence of the sideband cooling. (a) Pumping scheme for the detuning sweep where the detuning ${\mathrm{\Delta }}_c$ of the cooling tone relative to the cavity resonance is varied. An additional blue probe is used for ancillary sideband asymmetry calibration, as indicated in the dashed green box. Frequency separation between the cooling tone and blue probe is fixed at $2({\mathrm{\Omega }}_m+\delta )$. (b) and (c) Single-sided noise spectra from the balanced heterodyne detection normalized to the shot noise floor from two-tone and single-tone measurements, respectively, with corresponding fit curves, for various detunings. (d) The fitted mechanical linewidth (red full circles, left axis) and optical spring effect (blue full circles, right axis), with corresponding theoretical plots based on experimental optomechanical parameters. (e) Final phonon occupancy vs ${\mathrm{\Delta }}_c$ in single-tone measurements. Green full circles show calibration using the ancillary two-tone quantum thermometry. Dashed green curve shows a theoretical plot calculated from experimental optomechanical parameters assuming ideal thermalization. Blue curve shows a fitting curve incorporating excess optical heating. Error bars are given by the errors in the Lorentzian fits and in the calibration coefficient in two-tone sideband asymmetry. Purple full circles are anchored with cryostat thermometer at ${\mathrm{\Delta }}_c/2\pi \simeq -7.18\mathrm{GHz}$. (f) Signal-to-noise ratio (SNR) vs ${\mathrm{\Delta }}_c$, with the fitting curve to a theoretical model which includes optical heating, with excess heating rate and overall detection efficiency as free fitting parameters.