Quantum Optomechanics in a Liquid

We measure the quantum fluctuations of a single acoustic mode in a volume of superfluid He that is coupled to an optical cavity. Specifically, we monitor the Stokes and anti-Stokes light scattered by a standing acoustic wave that is confined by the cavity mirrors. The intensity of these signals (and their cross-correlation) exhibits the characteristic features of the acoustic wave’s zero-point motion and the quantum backaction of the intracavity light. While these features are also observed in the vibrations of solid objects and ultracold atomic gases, their observation in superfluid He opens the possibility of exploiting the remarkable properties of this material to access new regimes of quantum optomechanics.

Figure 1

Schematic of the experiment. (a) Top: Illustration of the optomechanical device. The optical fibers (yellow) and ferrules (white) are fixed inside a Cu cell (gray) which is attached to the mixing chamber of a dilution refrigerator (DR, not shown). Liquid He (blue) fills the cell. The fibers enter the cell via epoxy feedthroughs (black). Bottom: Enlarged view of the cavity. Red curve: The intensity profile of an optical mode. Blue shading: The density profile of the acoustic mode that couples to the optical mode. The actual optical and acoustic modes used in this work have, respectively, 91 and 182 half wavelengths along the cavity length. (b) Simplified layout of the measurement setup. Light from a tunable laser (TL) passes through a phase modulation system ($\phi M$) driven by a microwave source (MW). Light is delivered to (and collected from) the DR via a circulator (pink). The reflected light is collected on a photodiode (PD), and the resulting photocurrent is analyzed by a data acquisition system (DAQ). Details are given in the Supplemental Material [31].

Figure 2

Sidebands produced by the acoustic mode’s fluctuations. Inset: Illustration of the measurement scheme. Black curve: Cavity line shape. Colored arrows: Laser tones. Colored curves: Acoustic sidebands. Upper panel: The spectrum of the red and blue motional sidebands ($S_{ii}^{(rr)}$ and $S_{ii}^{(bb)}$) and the real part of their cross-correlation ($\mathrm{Re}[S_{ii}^{(rb)}]$). A frequency-independent background has been subtracted from $S_{ii}^{(rr)}$ and $S_{ii}^{(bb)}$. Lower panel: The imaginary part of the cross-correlation ($\mathrm{Im}[S_{ii}^{(rb)}]$). The data were normalized and fit as described in the text and the Supplemental Material [31]. For this measurement, $T_{\mathrm{MC}}=20\mathrm{mK}$ and $n_{\mathrm{circ}}=400$.

Figure 3

Thermal and quantum fluctuations of the acoustic mode. (a) The mean phonon number $n_{\mathrm{th}}$ associated with the acoustic mode’s bath temperature plotted vs $T_{\mathrm{MC}}$. (b) The same measurements of $n_{\mathrm{th}}$ as in (a) but plotted as a function of $T_{\mathrm{eff}}$, the effective device temperature calculated in the Supplemental Material [31]. The color of each marker encodes $n_{\mathrm{circ}}$, the intracavity photon number. The black points are obtained by averaging data in 15 mK bins. In both (a) and (b), the dashed lines show the expected behavior $n_{\mathrm{th}}=1/(e^{\hslash {\omega }_{\mathrm{ac}}/k_{B}T}-1)$, while the gray area represents the systematic uncertainty resulting from the calibration of the heterodyne signal (Supplemental Material [31]). (c) Three measures of the quantum features plotted as a function of $T_{\mathrm{eff}}$. The dashed line is the prediction of quantum optomechanics theory; the gray area shows the systematic uncertainty resulting from the calibration of the heterodyne signal. Each data point is produced from data and fits similar to Fig. 2 (averaged over 15 mK bins). Error bars indicate the statistical uncertainty in these fits.