Optomechanical disk resonator in the quantum ground state of motion

TL;DR

This work demonstrates a GaAs optomechanical disk resonator prepared near its quantum ground state, achieving a mean phonon occupancy of $\langle n_b\rangle=0.66\pm0.20$ at $T\approx11$ mK. Ground-state cooling is inferred via Brillouin sideband thermometry using evanescent coupling to a WGM and single-photon counting, with a measured single-photon coupling rate $g_0/2\pi=212\pm14$ kHz. The study reveals laser-induced heating as a fundamental limitation, showing fast intracavity heating ($<100$ ns) and slow extracavity heating ($>20$ μs) that depend on the average optical power and duty cycle. These results establish optomechanical disk resonators as viable quantum devices and highlight practical considerations for achieving deeper cooling and high-sensitivity sensing on-chip.

Abstract

Although they have enabled several advances in the field of optomechanics, optomechanical disk resonators have not yet been operated in the quantum regime. We present the first experimental demonstration of an optomechanical disk resonator prepared in the quantum ground state. With a gigahertz frequency, the mechanical breathing mode of the investigated semiconductor disk reaches a level of excitation below a single phonon when cooled in a dilution refrigerator. We quantify the phonon occupancy of the mechanical mode by performing Brillouin sideband spectroscopy: a conical optical fiber is evanescently coupled to the disk optical whispering-gallery mode, and Stokes and anti-Stokes photons scattered by phonon emission and absorption are counted on a single-photon detector. We measure a suppression of the absorption process corresponding to a phonon occupancy of $0.66\pm0.20$. We experimentally investigate the mechanisms ruling laser-induced heating, which limits the lowest measurable phonon occupancy, and notably witness an extra-cavity heating effect.

Figures (11)

• Figure 1: (a) Scanning electron microscope image of an optomechanical GaAs disk resonator. (b) Radial component of the electric field of the optical WGM with azimuthal number $m=22$ and radial number $p=1$. (c) Norm of the displacement field of the fundamental mechanical RBM. (d) Doublet optical spectrum borselli_beyond_2005 measured in reflection through the input fiber and (e) mechanical spectrum measured at room temperature around the RBM resonance frequency $\Omega_m/2\pi = 1.085$ GHz. Solid black lines and dashed red lines in (d) and (e) correspond to measured signals and Lorentzian fits, respectively.
• Figure 2: (a) Sketch of the experimental setup. A sequence of laser pulses, alternately red- and blue-detuned with respect to the optical mode resonance, probe the disk resonator placed in the dilution refrigerator. Brillouin-scattered single photons at the optical resonance frequency, resulting from the optomechanical interaction, are detected with a SPD, while the probe photons are spectrally rejected. (b) Eigenenergies of the system $\ket{n_a,n_b}$, not to scale ($n_a$ and $n_b$ the photon and phonon numbers, respectively). Photons spectrally detuned by one quantum of vibration from the optical resonance can drive Stokes/anti-Stokes processes (blue/red arrows), resulting in single photons scattered at the optical resonance (green arrows) at probabilities proportional to $n_b+1$ (Stokes) or $n_b$ (anti-Stokes).
• Figure 3: Measurements at 4K temperature. (a) Brillouin-scattered single-photon count rates as a function of the optical probe detuning to the optical resonance frequency, under pulse-on input optical power $P$=7.6 $\mu$W. (b) Amplitudes of the mean value of Stokes and anti-Stokes sideband count rates when $\delta_L=\pm\Omega_m/2\pi$, as function of optical power $P$, for two different datasets, showing a close-to-linear behaviour. The inferred single-photon optomechanical coupling rate is $g_0/2\pi=212\pm14$ kHz. For both panels, we subtracted the dark count rate.
• Figure 4: Measurements at millikelvin temperatures. (a) Brillouin-scattered single-photon count rates under blue- and red-detuned driving at $\delta_L=\pm\Omega_m/2\pi$ at low (8.5 nW) and high (7.7 $\mu$W) optical mean power. (b) Stokes and anti-Stokes sideband amplitudes. (c) Inferred mechanical occupancy and corresponding effective modal temperature as a function of the probe pulse-on optical power $P$. (d) Inferred mechanical occupancy and modal temperature as a function of the duty cycle $DC$ with constant $\langle n_a\rangle$. For (a) and (b) panels, we subtracted the dark count rate.
• Figure 5: (Not to scale) Representation of the GaAs disks fabrication process. a. Cleaned wafer; b. spin coating of HSQ resist; c. electron beam lithography in the Scanning Electron Microscope (SEM); d. development of the resist to remove the unexposed HSQ; e. vertical dry etching with the ICP; f. spin coating of S1828 resist; g. UV photolithography; h. development of the resist to remove the exposed S1828; i. mesa wet etching with $\text{H}_3\text{PO}_4$; i. hot bath of SVC14 to remove unexposed S1828; k. HF underetching; l. fabricated devices with conical fibers for coupling light to the disks.