Squeezed-Light Interferometry on a Cryogenically Cooled Micromechanical Membrane

Squeezed states of light reduce the signal-normalized photon counting noise of measurements without increasing the light power and enable fundamental research on quantum entanglement in hybrid systems of light and matter. Squeezed states of light have high potential to complement cryogenically cooled sensors, whose thermal noise is suppressed below the quantum noise of light by operation at low temperature. They allow us to reduce the optical heat load on cooled devices by lowering the light power without losing measurement precision. Here, we demonstrate the squeezed-light position sensing of a cryo-cooled micromechanical membrane. The sensing precision is improved by up to 4.8 dB below photon counting noise, limited by optical loss, at a membrane temperature of about 20 K. We prove that realizing a high interference contrast in a cryogenic Michelson interferometer is feasible. Our setup is the first conceptual demonstration towards the envisioned European gravitational-wave detector, the “Einstein telescope,” which is planned to use squeezed states of light together with cryo-cooled mirror test masses.

Figure 1

Schematic of the experimental setup. A SiN membrane is part of Michelson-Sagnac interferometer whose solid spacer is attached to a cryo cooler. Similar to the Michelson interferometers used for the observation of gravitational waves, a quasimonochromatic beam of light carrying coherent states is matched to the overlapping Michelson mode (reflected off the membrane) and Sagnac mode (transmitted through the membrane) through one port and a squeezed vacuum field is matched to the same modes through the other port. Second harmonic generation (SHG); (Cavity enhanced) parametric down-conversion (PDC); Faraday isolator (FI).

Figure 2

Photograph of the Michelson-Sagnac interferometer. It contains the SiN membrane and was cooled to about 20 K by a Gifford-McMahon cryo cooler. Beam splitter and two adjustable steering mirrors were attached to a gold-coated Invar spacer. Membrane position along the optical axis as well as pitch and yaw angles were adjustable (not visible here).

Figure 3

Measured spectra of the same fundamental mode of the thermally excited membrane oscillation at about 400 kHz at (a) room temperature, (b) about 100 K and (c) about 20 K. Thermal excitation was reduced with temperature. The dashed lines correspond to fits according to Eq. (3). From the fit we infer an effective mass of the membrane of $80\pm 10$ ng and a mechanical linewidth of $4\pm 2\mathrm{Hz}$ (changing only slightly with temperature). We were able to maintain the high interferometer fringe contrast of $>98\%$ for the Michelson mode during the cooling process, which is proven by a constant squeeze factor of about ($4.8\pm 0.1$) dB. In (b), we show additionally the antisqueezed noise, increased by $12.9\pm 0.1\mathrm{dB}$ relative to the shot noise. The measurements of squeezing and antisqueezing allow to compute [6] the total optical loss of 31%. Each trace is an average of 100 experiment runs acquired with resolution bandwidth of 1 Hz and video bandwidth of 1 Hz.