Three-Mode Optoacoustic Parametric Amplifier: A Tool for Macroscopic Quantum Experiments

We introduce the three-mode optoacoustic parametric amplifier (OAPA), a close analog of the optical parametric amplifier, for macroscopic quantum mechanics experiments. The radiation pressure reaction of light on the reflective surface of an acoustic resonator provides a nonlinearity similar to the Kerr effect in the optical parametric amplifier. The OAPA can be tuned to operate in a positive gain regime where acoustic signals are amplified or in a negative gain regime where acoustic modes are cooled. Compared with conventional optoacoustic devices, (i) the OAPA incorporates two transverse cavity modes such that the carrier and sideband fields simultaneously resonate, and (ii) it is less susceptible to the laser phase and amplitude noise. These two features significantly ease the experimental requirements for cooling of acoustic modes to their quantum-ground state and creating entangled pairs of phonons and photons.

Figure 1

Experimental demonstration of three-mode optoacoustic parametric interaction. (a) The schematic setup of the experiment. A thermal tuning plate was used to vary the cavity $g$ factor to tune the frequency difference between ${\mathrm{TEM}}_{01}$ and ${\mathrm{TEM}}_{00}$ modes. The resonant scattering of the ${\mathrm{TEM}}_{01}$ mode is detected by a quadrant photodiode (QPD). (b) Experimental results fitted by a Lorentzian curve. The first peak corresponds to three-mode interactions with an acoustic mode at 160.0 kHz and the second one at 84.8 kHz. As the suspended cavity $g$ factor approaches unity, the cavity becomes extremely sensitive to angular fluctuations and unstable. Finally, it loses lock, and the data collection is ceased.

Figure 2

Proposed experimental setup. A tuning cavity serves as an add-on to the main cavity to tune the frequency difference between ${\mathrm{TEM}}_{00}$ and ${\mathrm{TEM}}_{01}$ modes. An ordinary photodiode (PD), QPD, and a capacitive readout allow detections of the ${\mathrm{TEM}}_{00}$, ${\mathrm{TEM}}_{01}$, and acoustic modes independently. The ${\mathrm{TEM}}_{01}$ mode injection is not required in the cooling experiment and only necessary for generating tripartite quantum entanglement. An acousto-optic modulator (AOM) and a phase mask (PM) create the right frequency and wave front for the ${\mathrm{TEM}}_{01}$ mode.

Figure 3

Resonator design. (a) A silicon torsional mode resonator of dimensions $\sim 1\mathrm{mm}\times 0.8\mathrm{mm}\times 0.5\mathrm{mm}$ and mass $\sim 1\mathrm{mg}$ with resonant frequency $\sim 1\mathrm{MHz}$. The contours show the strain amplitude, which is concentrated in the spindle ends and minimum at the center where the ${\mathrm{TEM}}_{01}$ mode interacts. (b) Displacement distribution of the surface of the resonator torsional mode, showing a simple torsional displacement gradient along a central vertical axis. (c) The optical ${\mathrm{TEM}}_{01}$ mode amplitude distribution which has good overlap with the acoustic mode.