Figure 1

Schematic of the experiment. (a) An ensemble of 4000 ultracold ${}^{87}\mathrm{Rb}$ atoms is trapped in three to five adjacent potential minima of an optical standing wave, within a high-finesse optical cavity. The ensemble’s center-of-mass motion coherently scatters light from cavity probe light, detected using a balanced heterodyne receiver. Acousto-optic modulators (AOs) are used to lock the probe with respect to cavity resonance and to shift the probe’s frequency with respect to the heterodyne detector’s local oscillator. (b) Probe spectrum in the cavity. A strong resonant tone (solid green peak) applies backaction to and acquires sidebands from the collective atomic motion. A weak detuned tone (dashed gray peak) is used for locking the probe frequency with respect to the cavity and does not significantly affect the oscillator, neither via incoherent backaction nor via dynamical cooling. (c) A harmonic oscillator in its ground state can only extract energy from the optical field, leading to an asymmetry in the resonant probe’s Raman sidebands, indicative of the mean phonon occupation number $\overline{\nu }$.Reuse & Permissions

Figure 2

Asymmetric optical scattering from quantum collective motion. (a) Photon spectra of light exiting the cavity, scattered by collective atomic motion. Shown are the measured Stokes sidebands [left panels, (red) circles] and anti-Stokes sidebands [right panels, (blue) circles] at various cooperativities (from top to bottom, $C_{\mathrm{om}}=9.6,1.9,0.4$), together with the prediction (solid lines) of Eq. (1), plotted vs cyclic frequency $f=\omega /2\pi$. The mechanical linewidths and resonance frequencies are fit to the data, but the peak heights are theoretically determined. The predicted peak areas agree with the measured areas of the photon spectra, which form a calibration-dependent measure of the phonon occupation. (b) Measured phonon occupation vs cooperativity. The collective mode occupation, determined by the green circles, increases by $C_{\mathrm{om}}/2$, according to the zero-free-parameter measurement-backaction theory [solid (red) line; the shaded region indicates a $68\%$ systematic confidence interval]. In contrast, the rms single-atom axial occupation, measured using time-of-flight thermometry of the gas (yellow diamonds, measured at 1 ms of probing), remains near its initial value during the measurement (the gray line indicates theoretical prediction).Reuse & Permissions

Figure 3

Energy exchange between light and motion. (a) Energy-exchange spectral densities for various probe cooperativities (from top to bottom, $C_{\mathrm{om}}=9.6,3.2,1.6$). Traces are vertically offset for clarity (by $12,2,0\times {10}^{-27}\mathrm{W}/\mathrm{Hz}$). (b) Heating rate due to the resonant probe (magenta squares), the weak locking tone (gray circles), and the summed heating from both tones (green diamonds), together with zero-free-parameter measurement-backaction theory (solid gray line), plotted as a function of the collective coupling rate $4\overline{n}{g}_{\mathrm{om}}^2/\kappa ={\Gamma }_m{C}_{\mathrm{om}}$. (c) Temperature of the atomic gas vs the product of the collective coupling rate and the total interrogation time (yellow diamonds at 5 ms, cyan circles at 9 ms). Also shown is the theoretical increase in the bath temperature (solid gray line).Reuse & Permissions