Optomechanical Cavity Cooling of an Atomic Ensemble

We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number $⟨n{⟩}_{\min }={2.0}_{-0.3}^{+0.9}$. Both $⟨n{⟩}_{\min }$ and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.

Figure 1

Ensemble cavity cooling. A probe laser (solid red lines) is placed at red detuning from cavity resonance to enhance anti-Stokes scattering into the cavity (dotted blue lines), which cools a single collective mode $\mathcal{C}$ (solid green oval) at a cooperatively enhanced rate ${\gamma }_c$. Single-particle modes can only be cooled by mixing (at rate ${\gamma }_{\mathrm{m}}$) with $\mathcal{C}$. This differs from ordinary laser cooling (inset), where free-space emission causes the atoms to be cooled independently.

Figure 2

Mean occupation number $⟨n⟩$ of mode $\mathcal{C}$ vs time during cavity cooling at ${\Gamma }_{\mathrm{sc}}=1.1\times {10}^5{\mathrm{s}}^{-1}$ (gray squares), $2.3\times {10}^5{\mathrm{s}}^{-1}$ (green circles), $3.4\times {10}^5{\mathrm{s}}^{-1}$ (gold triangles), and $6.4\times {10}^5{\mathrm{s}}^{-1}$ (red diamonds). Each data set is obtained by averaging variances from 10 traces. Inset: single trace of cavity transmission during cavity heating ($t<0$, blue background) followed by cooling ($t>0$, red background).

Figure 3

Collective cooling rates. (a) Energy decay rate ${\gamma }_{\exp }$ vs scattering rate ${\Gamma }_{\mathrm{sc}}$ for: $N=8000(700)$, $\Delta /(2\pi )=270\mathrm{MHz}$ (solid black squares); $N=2800(400)$, $\Delta /(2\pi )=140\mathrm{MHz}$ (open red circles); $N=700(200)$, $\Delta /(2\pi )=70\mathrm{MHz}$ (solid blue triangles). Lines are fits to data. (b) $N$ dependence of cooling rate normalized to single-atom scattering rate into cavity.

Figure 4

Spectra of fractional transmission fluctuations $S_I/{\overline{I}}^2$ taken with (a) $N=230(50)$ atoms and (b) $N=450(90)$ atoms during cavity cooling at $\delta =-\kappa /2$ [lower (red) traces, left axis] or heating at $\delta =+\kappa /2$ [upper (blue) traces, right axis]. Black curves are fits; subtraction of the background level $S_{\mathrm{bg}}$ (gray curves) yields collective-mode occupation $⟨n{⟩}^{\pm }$ at $\delta =\pm \kappa /2$: (a) $⟨n{⟩}^{+}=4.4\pm 0.7$, $⟨n{⟩}^{-}={2.3}_{-0.3}^{+0.7}$; (b) $⟨n{⟩}^{+}=7\pm 1$, $⟨n{⟩}^{-}={2.0}_{-0.3}^{+0.9}$.