Pulsed Excitation Dynamics of an Optomechanical Crystal Resonator near Its Quantum Ground State of Motion

Using pulsed optical excitation and read-out along with single-phonon-counting techniques, we measure the transient backaction, heating, and damping dynamics of a nanoscale silicon optomechanical crystal cavity mounted in a dilution refrigerator at a base temperature of $T_f\approx 11\mathrm{mK}$. In addition to observing a slow (approximately 740-ns) turn-on time for the optical-absorption-induced hot-phonon bath, we measure for the 5.6-GHz “breathing” acoustic mode of the cavity an initial phonon occupancy as low as $⟨n⟩=0.021\pm 0.007$ (mode temperature $T_{\min }\approx 70\mathrm{mK}$) and an intrinsic mechanical decay rate of ${\gamma }_0=328\pm 14\mathrm{Hz}$ ($Q_m\approx 1.7\times {10}^7$). These measurements demonstrate the feasibility of using short pulsed measurements for a variety of quantum optomechanical applications despite the presence of steady-state optical heating.

Popular Summary

Beyond the usual paradigm of cavity optomechanics in which mechanical motion is confined to single objects such as movable end mirrors and intracavity membranes, optomechanical crystals (OMCs) can be fashioned into planar circuits for photons and phonons, and arrays of optomechanical elements can be interconnected via optical and acoustic waveguides. Such coupled OMC arrays have been proposed as a way to realize quantum optomechanical memories, nanomechanical circuits for continuous variable quantum information processing and phononic quantum networks, and as a platform for engineering and studying quantum many-body physics of optomechanical metamaterials. The realization of optomechanical systems in the quantum regime is predicated on limiting thermal noise in the mechanics while simultaneously introducing large coherent coupling between optical and mechanical degrees of freedom. Here, we provide measurements of OMC devices in which the mechanical motion is thermalized in the quantum ground state of motion at millikelvin temperatures.

Using pulsed optical excitation along with sensitive photon counting, we study the transient dynamics of the optical backaction, absorption heating, and mechanical damping in these devices. These studies indicate that the 5.6-GHz mechanical resonance of the structure cools to an occupancy as small as 0.02 phonons (98% of the time in the quantum ground state) and exhibits a thermal decoherence time of up to $450\mu \mathrm{s}$ with no light applied (corresponding to a mechanical $Q$ factor of 17 million). Crucially, the absorption-induced hot phonon bath that heats and damps the mechanical mode of interest does not develop instantaneously but, rather, slowly builds over a few microseconds to its steady-state value.

Our analysis based on these observations indicates that the current OMC devices should be suitable for implementing a wide range of quantum state engineering tasks, such as Fock-state generation and entanglement of disparate mechanical elements.

Figure 1

(a) Pulsed pump light at frequency ${\omega }_l$ (red arrows) is directed to an OMC cavity inside a dilution fridge via an optical circulator. The cavity reflection is then filtered at the cavity frequency ${\omega }_c$ (black arrows) and directed to a SPD. (b) SEM image of the silicon OMC cavity studied in this work. (c) Finite-element-method simulation of the localized acoustic resonance at 5.6 GHz of the OMC cavity. Deformation of the beam structure is exaggerated to highlight the mechanical motion, with color indicating the regions of high (red) and low (blue) displacement magnitude. The inset shows the three processes affecting the mode occupancy: (i) detuned pump light at ${\omega }_l$ (red arrow) exchanges energy with the acoustic mode at rate ${\gamma }_{\mathrm{OM}}$, generating scattered photons at ${\omega }_c$ (black arrow) in the process; (ii) pump light drives excitation of electronic defect states in the silicon device layer, subsequently exciting a hot-phonon bath that heats the localized acoustic resonance at rate ${\gamma }_p$; and (iii) phonons escape the cavity volume via the acoustic shield at intrinsic decay rate ${\gamma }_0$, coupling the localized resonance to the fridge bath. (d) Noise-equivalent phonon number $n_{\mathrm{NEP}}$ (gray squares) and phonon occupancy $⟨n⟩$ (red circles) for red-detuned ($\mathrm{\Delta }={\omega }_m$) CW pumping versus intracavity photon number $n_c$. The dashed red line indicates the expected $n_{\mathrm{NEP}}$ contribution from SPD dark counts. The vertical dashed line at $n_c\approx 45$ $(4.5\times 10^{-5})$ indicates the photon number during the on state (off state) of the pulse. Solid green and purple lines show fits to the CW heating model for fridge bath temperatures of $T_f=70$ and 10 mK, respectively.

Figure 2

(a) Total photon-count rate versus time $t$ for a red-detuned (red circles, $\mathrm{\Delta }={\omega }_m$) and blue-detuned (blue squares, $\mathrm{\Delta }=-{\omega }_m$) probe. For both data sets, $n_{c,\text{on}}\approx 45$ and $T_{\mathrm{per}}=5\mathrm{ms}$. Vertical dashed lines indicate the start and stop times of the pulses. (b) Asymmetry $\xi$ versus time within the pulse $t$. The dashed green line shows the theoretically expected $\xi (t)$ when backaction effects are neglected and a single time-dependent phonon occupancy is assumed for both detunings. The dash-dotted orange line shows $\xi (t)$, including the effects of backaction, neglecting optical heating and assuming $\xi (0)=0$. Error bars show one standard deviation (s.d.) determined from the measured count rates, assuming Poissonian counting statistics. (c) Calibrated phonon occupancy $⟨n⟩$ versus $t$ for $\mathrm{\Delta }={\omega }_m$ (red circles) and $\mathrm{\Delta }=-{\omega }_m$ (blue squares). The solid black lines show fits to a model including a slow exponential turn-on of the hot-phonon bath. The inset shows detail for $0<t<750\mathrm{ns}$ on a linear scale for $\mathrm{\Delta }={\omega }_m$. Error bars show one s.d. determined from the measured count rates, assuming Poissonian counting statistics. For the blue-detuned data, the error bars are smaller than the data markers.

Figure 3

Ratio of initial to final phonon number $⟨n{⟩}_i/⟨n{⟩}_f$ versus pulse period $T_{\mathrm{per}}$. The solid red curve shows a fit to exponential decay. Error bars show one s.d. determined from the measured count rates, assuming Poissonian counting statistics. The inset shows $⟨n⟩$ versus $t$ for the different values of $T_{\mathrm{per}}$.

Figure 4

(a) Maximum phonon occupancy during a pulse $⟨n{⟩}_{\max }$ versus pulse period $T_{\mathrm{per}}$ and pulse width $T_{\text{pulse}}$. The white contour delineates the region where the effective cooperativity $C_{\mathrm{eff}}\ge 1$ throughout the pulse. (b) $C_{\mathrm{eff}}$ versus time $t$ within the pulse for $T_{\mathrm{per}}=5\mathrm{ms}$ and $T_{\text{pulse}}=3\mu \mathrm{s}$.

Figure 5

(a) Fidelity $F$ of the generation of a single-phonon Fock state versus pulse width $T_{\text{pulse}}$ (pulse period $T_{\mathrm{per}}=1\mathrm{ms}$). (b) Average time required to herald a Fock state $T_{\text{Fock}}$ versus pulse width $T_{\text{pulse}}$. The solid line is calculated using the total detection efficiency measured in this work, while the dashed line uses the estimated ideal detection efficiency.