Multimode optomechanical system in the quantum regime

Abstract

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10⁷) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.

Keywords: multimode; optomechanics; quantum correlations.

Fig. 1.

Multimode optomechanical system. (A) Optical setup, in which a low-noise Ti:S laser with modulation sidebands from an electro-optic modulator (EOM) pumps a Fabry–Perot resonator held in a cryostat. The resonator contains the sample chip (M) with the nanomechanical membrane and two spacer chips (S). (B) Tuning of optical resonator linewidth and frequency with membrane position with respect to the wavelength, which was changed in this experiment (varied around 810 nm). Solid lines are theoretical TMM predictions (SI Appendix). (C) Dark-field images of two mechanical modes.

Fig. 2.

(Top) Response of the sample frame (orange) and the sample center containing the membrane (red) to an acoustic excitation of the sample frame, showing broadband suppression of phonon propagation down to the measurement background (gray). (Bottom) Resulting membrane mode $Q$ factors (light and dark blue circles), showing consistently $Q\gtrsim {10}^7$ in the protected 1- to 3-MHz frequency region—also for low-index modes with $i\vee j<3$ (light blue)—but not outside. Inset shows photograph of the actual sample.

Fig. 3.

(Top) Multimode OMIT in the cavity response, with expected frequencies ${\mathrm{\Omega }}_{\mathrm{m}}^{(i,j)}$ indicated by red lines (for clarity, $i\ge j$), labeled with the mode index. Inset shows the extracted location of the optical beam within one quadrant of the membrane, with color-coded normalized probability density. Contours of equal displacement of the (3,2) mode are also shown, with the membrane’s clamped edges indicated in orange. (Bottom) Strong simultaneous light squeezing from six mechanical modes. Blue traces are the recorded cavity output spectra, and orange is the shot noise level. The solid blue line shows the single-mechanical mode model, and the dashed blue line shows the two near-generate mechanical modes model. Differences are discussed in SI Appendix.

Fig. 4.

The strongest squeezing trace, close to the (3, 2) mode, in comparison with vacuum noise (orange). The bright blue line is a zero-free parameter model for a single mechanical mode. Slight adjustments of cavity outcoupling and mirror noise yield better-fitting model traces (dark blue), both in a single-mode (solid line) and a dual-mode (dashed line) model.