Two-dimensional optomechanical crystal resonator in gallium arsenide

In the field of quantum computation and communication, there is a compelling need for quantum coherent frequency conversion between microwave electronics and infrared optics. A promising platform for this is an optomechanical crystal resonator that uses simultaneous photonic and phononic crystals to create a colocalized cavity coupling an electromagnetic mode to an acoustic mode, which then via electromechanical interactions can undergo direct transduction to electronics. The majority of the work in this area has been on one-dimensional nanobeam resonators, which provide strong optomechanical couplings but, due to their geometry, suffer from an inability to dissipate heat produced by the laser pumping required for operation. Recently, a quasi-two-dimensional optomechanical crystal cavity has been developed in silicon, exhibiting similarly strong coupling with better thermalization but at a mechanical frequency above optimal qubit operating frequencies. Here, we adapt this design to gallium arsenide, a natural thin-film single-crystal piezoelectric that can incorporate electromechanical interactions, obtaining a mechanical resonant mode at $f_{\mathrm{m}}\approx 4.5\mathrm{GHz}$ that is ideal for superconducting qubits and demonstrating optomechanical coupling of $g_{\mathrm{om}}/(2\pi )\approx 650\mathrm{kHz}$.

Figure 1

(a) The layout and geometric parametrization of the optomechanical crystal resonator. The crystal (mirror) unit cell is highlighted. The parameter values in the gradient section between the defect and crystal unit cells are scaled with a ${\mathrm{SmoothStep}}_1$ function plotted by the purple line below. (b) The acoustic dispersion relations from finite-element-model simulations of the mirror unit cell. Band gaps for $\stackrel{+}{y}\stackrel{+}{z}$ symmetric modes are highlighted by yellow bands. (c) The electromagnetic dispersion relations from finite-element-model simulations of the mirror unit cell. Band gaps for $\stackrel{+}{z}$ symmetric modes are highlighted in yellow and cover our infrared frequency of interest, $194\mathrm{THz}$, marked with a dashed red line. (d) Simulation of the displacement field, $Q_y$, for the paddle breathing mode at $4.63\mathrm{GHz}$. Displacements in paddles neighboring the defect are too small to make out but are plotted above on a log scale. (e) Simulations of the electric field for an electromagnetic resonance at $197\mathrm{THz}$. The specific dimensions used for the simulations are given in the Supplemental Material [29].

Figure 2

(a) A scanning-electron-microscope image, taken at ${45}^{\circ }$, of a device similar to the one measured here. Two large suspended-grating coupler pads deflect light in and out of plane to couple to overhead optical fibers. The optomechanical crystal plate is suspended in the middle with large serpentine tethers to relieve tension during the release process. (b) An enlarged image of the optomechanical plate from (a), taken top down, showing the vertebrae resonator. Proximity-effect correction during electron-beam lithography is essential for uniform snowflakes. (c) A simplified diagram of the optical measurement setup, showing only elements discussed in the text. The phase modulator is driven by a microwave-frequency signal generator and provides a calibration of the power measured by the spectrum analyzer. The V-groove assembly holds the fiber optics above the device. A portion of the output signal is used in a dither-locking system, utilizing a lock-in amplifier and a proportional-integral-derivative (PID) controller, that adjusts the laser's output frequency. The detection chain consists of an erbium-doped fiber amplifier (EDFA) followed by a filter to cut out amplified spontaneous emission and then a microwave-frequency bandwidth photodetector.

Figure 3

(a) The full system optical transmission (orange) and reflection (cyan) with color-coded probing regions covered by the dither lock. The transmission includes the waveguide, the grating coupler, the fiber-optic components, and the detector efficiencies. (b) The thermal mechanical spectrum imprinted on the optical signal when probed at the optical resonance and inflection points (color coded accordingly). Each trace is the average of 100 scans with a 100-point moving average and a statistical uncertainty of $\pm 1$ standard deviation is depicted in light shading about the trace. (c) Scans of the thermal mechanical spectrum with different input powers, referenced to the V-groove assembly. The inset shows the fitted spectrum amplitude $\mathcal{A}$ as a function of the input power over the linear operating regime of our photodetector, with $P^2$ fit curves.