Optomechanical crystal in light-resilient quantum ground state

TL;DR

The paper presents release-free silicon optomechanical crystal cavities that address thermal noise from optical absorption by improving thermal anchoring without suspension. It demonstrates dramatic thermo-optic robustness at cryogenic temperatures, achieving near-unit mechanical occupancy at substantially higher intracavity powers than suspended counterparts, and characterizes heat exchange with hot and cold baths using pulsed and CW thermometry. The work reports quantitative bath-coupling parameters, fast rethermalization dynamics, and non-exponential noise decay linked to residual reservoirs and possible TLS. These results establish a practical, chip-scale platform for low-noise, high-power electro-optomechanics with potential for GHz phonon-based interfaces and on-chip microwave–optical transduction.

Abstract

Interaction between light and high-frequency sound is a key area in integrated photonics, quantum and nonlinear optics, and quantum science. However, the typical suspended optomechanical structures suffer from poor thermal anchoring, making them susceptible to thermal noise arising from optical absorption. Here, we demonstrate a chip-scale, release-free silicon optomechanical crystal cavity (OMC) operating cryogenically with improved resilience to laser light. Relative to a suspended nanobeam OMC, we observe an 18 dB suppression of the thermo-optic effect, and the device sustains near-unity phonon occupation at 35 dB higher intracavity optical energy. Time-resolved measurements further reveal rapid initial thermalization governed by the mechanical decay time. With further material and design improvements in sight, these results bolster release-free systems on a chip as a path for low-noise and high-power classical and quantum electro-optomechanics, such as for frequency converters between microwave and optical photons.

Figures (13)

• Figure 1: Release-free optomechanical crystal for improved thermal anchoring. (a) Top-down view of simulated mechanical and optical mode profiles showing normalized displacement $\vec{u}$ and electrical $\vec{E}$ fields respectively. The OMC consists of a defect region with 31 unit cells between two adiabatically tapered mirror regions kolvik_clamped_2023. (b) The bottom side of the silicon nanobeam is fully attached to the underlying substrate, opening up a channel through which heat can decay. The mechanical mode of interest is protected from leakage by total internal reflection. (c) Simplified phonon-counting setup and a scanning electron micrograph of two release-free OMCs adjacent to an optical bus waveguide. We place the devices in a dilution refrigerator at temperature $T_\mathrm{f}$ and study them using a near-infrared laser with a wavelength around 1550. Using acousto-optic modulation (AOM), we send both continuous-wave and pulsed signals to the devices via a circulator. Finally, we measure the reflected light with a photodiode (PD) or through single-photon detection (SPD). The SPD arm singles out optomechanical sidebands by removing pump light with two filter cavities with 13.2 bandwidth. (d) Phenomenological model describing the mechanical environment under optical pumping. The optical mode $\hat{a}$ is populated through an input waveguide with rate $\kappa_\mathrm{e}$ and decays to the environment through internal losses $\kappa_\mathrm{i}$. Pumping the optical mode gives rise to the optomechanical interaction that allows phonon-photon exchange at rate $\gamma_\mathrm{om} = 4g_\mathrm{om}^2n_\mathrm{c}/\kappa$ where $\kappa =\kappa_\mathrm{i} + \kappa_\mathrm{e}$ and $n_\mathrm{c}$ is the number of intracavity pump photons. The mechanical mode $\hat{b}$ is coupled to the hot (cold) thermal bath at rates $\gamma_\mathrm{p}$ ($\gamma_\mathrm{0}$) where the cold bath is thermalized to $T_\mathrm{f}$ and the hot bath to an elevated temperature $T_\mathrm{p}$ due to optical absorption in $\hat{a}$ and the input waveguide. Enhanced thermal anchoring opens a direct channel for hot bath phonon decay into the cold bath, reducing the thermal load on the mechanical mode.
• Figure 2: Suppressed thermo-optic nonlinearity in a release-free optomechanical crystal. (a) Normalized optical reflection recorded at 10 mK where release-free and suspended data is horizontally offset for visual clarity. We record the data while sweeping the laser frequency in a sawtooth pattern with direction indicated by the black arrow. For each optical power we calculate the intracavity photon number $n_\mathrm{c}$ achieved at resonant pumping. (b) Optical frequency shift $\Delta\omega$ as function of temperature and intracavity photons $n_\mathrm{c}$. At each power, we extract the optical resonance frequency shift. Bold data points correspond to the curves presented in (a).
• Figure 3: Thermal noise dynamics of resonantly-driven release-free and suspended OMCs. (a) Simplified schematic of the experimental setup used for pulsed phonon-counting. We illuminate the device under test (DUT) with high extinction ratio optical pulses generated through AOM. Next, we use a set of Fabry--Pérot filters to single out the anti-Stokes sideband at frequency $+\omega_{\rm m}$ relative to the pump. We handle timing between optical pulsing and SPD using a pulse sequencer. (b) The pulse sequence: We drive and read out with resonant pulses of duration $T_\text{0}$ and delay $T_\text{d}$. Using Eq. \ref{['eq:thermal_noise_dynamics']}, we extract initial $(n_\mathrm{i})$ and final $(n_\mathrm{f})$ phonon occupation during the optical illumination. (c) Total mechanical linewidth for the release-free device as function of $n_\mathrm{c}$. We study the dynamics of the scattered optomechanical sideband when illuminating the device with $T_0 = \qty{2}{\micro\second}$. For each optical power of the experiment, we fit the collected SPD data (see inset) with Eq. \ref{['eq:thermal_noise_dynamics']} while accounting for filter dispersion to extract the total linewidth with least squares standard deviation. The estimated linewidth agrees with the dark ($n_\mathrm{c} = 0$) ringdown result in (d) (black dashed line). Lastly, we fit the linewidth data with a power law (orange dashed line) $\gamma_\mathrm{m}(n_\mathrm{c}) = \gamma_\mathrm{0} + \gamma_\mathrm{p}(n_\mathrm{c}),$ where $\gamma_\mathrm{p}(n_\mathrm{c}) = a(n_\mathrm{c})^b$. (d) Normalized initial phonon occupation versus delay time $T_\text{d}$ with 95% credibility intervals. We measure exponential decay for both devices, revealing light-off decay rates $\gamma_\mathrm{0}/(2\pi) = \qty{660}{\kilo\hertz}$$(\qty{528}{\hertz})$ for the release-free (suspended) device.
• Figure 4: Single-phonon operation at high continuous-wave optical power at 10 mK. Average mechanical occupation under continuous-wave optical illumination in release-free and suspended OMCs for red, blue and resonant pumping. Data is given with one standard deviation assuming Poissonian statistics for single-photon-counting. To the resonant data, we fit power laws of the form $n_\mathrm{m}(n_\mathrm{c}) = \alpha \cdot(n_\mathrm{c})^\beta$, where the different exponents are highlighted in the figure.
• Figure 5: Off-resonant pulsed noise dynamics of release-free OMC. (a,c,e) Pulse train with 100 ns pulses at $n_\mathrm{c} = 128$ for varying repetition rates ($R$). (b,d,f) Pump-probe experiment for varying probe delay times ($T_\mathrm{d}$) with repetition rate $R = \qty{70}{\kilo\hertz}$, 2 pulse durations and $n_\mathrm{c}=48$. (a,b) Pulse schemes. $n_\mathrm{i}$ ($n_\mathrm{f}$) is the initial (final) occupation as defined in Eq. \ref{['eq:thermal_noise_dynamics']} whereas $n_\mathrm{coh}$ is the occupation reached on coherent driving. (c,d) Measured filtered mechanical occupation ($n_\mathrm{m}^*(t)$) with fits to Eq. \ref{['eq:thermal_noise_dynamics']} with applied filter transfer function. (e) Best fit parameters $[n_\mathrm{i},n_\mathrm{f}]$ from (c) together with calculated average phonon occupation $n_\mathrm{avg}$ with 95% credibility intervals (data points). We include lifetime-limited theory curves (dashed lines) showing the expected noise performance when $n_\mathrm{i}$ decays exponentially in between pulses with time constant from Fig. \ref{['fig:pulse_exp']}d. For this calculation we first fit $n_\mathrm{f}(R)=(R/R_0)^\theta$ where $R_0 = \qty{52}{\kilo\hertz}$ and $\theta=0.114$. Next we calculate $n_\mathrm{i}(T_\mathrm{d}) = n_\mathrm{f}\exp(-\gamma_\mathrm{0} T_\mathrm{d}) + n_0$ where $T_\mathrm{d} = R^{-1} - T_\mathrm{0}$ and $n_0$ is the dilution fridge occupation at $T_\mathrm{f}=\qty{50}{\milli\kelvin}$. (f) Best fit parameters $[n_\mathrm{i},n_\mathrm{f}]$ from (d) with 95% credibility intervals (data points). We fit the initial occupation to $n_\mathrm{i}(T_\mathrm{d}) = n_\mathrm{coh}\exp(-\gamma_\mathrm{coh}T_\mathrm{d}) + n_\mathrm{res}$ with $n_\mathrm{coh} = 64$, $\gamma_\mathrm{coh}/(2\pi)=\qty{607}{\kilo\hertz}$ and $n_\mathrm{res} = 0.81$ (blue line). The individual terms of $n_\mathrm{i}(T_\mathrm{d})$ are shown as dashed purple lines.