Cavity Sideband Cooling of a Single Trapped Ion

We report a demonstration and quantitative characterization of one-dimensional cavity cooling of a single trapped ${}^{88}\mathrm{Sr}^{+}$ ion in the resolved-sideband regime. We measure the spectrum of cavity transitions, the rates of cavity heating and cooling, and the steady-state cooling limit. The cavity cooling dynamics and cooling limit of 22.5(3) motional quanta, limited by the moderate coupling between the ion and the cavity, are consistent with a simple model [Phys. Rev. A 64, 033405 (2001)] without any free parameters, validating the rate equation model for cavity cooling.

Figure 1

Schematic of the experimental setup. A single ${}^{88}\mathrm{Sr}^{+}$ ion is confined in the center of a linear RF Paul trap and coupled to an optical resonator oriented along the trap axis. The inset shows the ion energy levels (solid lines) and the cavity resonance (dashed line).

Figure 2

Photon scattering rate ${\Gamma }_c$ into the resonant cavity (${\delta }_{\mathrm{lc}}=0$) as a function of the scattering rate into free-space ${\Gamma }_{\mathrm{sc}}$ for several values of cavity-ion detuning ${\delta }_{\mathrm{ci}}$. Each data point is measured by preparing the ion at fixed temperature by Doppler cooling for $200\mu \mathrm{s}$, then measuring the photon scattering rates for $50\mu \mathrm{s}$. The line is a fit to the form ${\Gamma }_c=\eta {\Gamma }_{\mathrm{sc}}/(1+{\Gamma }_{\mathrm{sc}}/{\Gamma }_{\mathrm{sat}})$ with fit parameters $\eta =0.018(4)$ and ${\Gamma }_{\mathrm{sat}}=8(2)\times {10}^6\mathrm{\text{photons}}/\mathrm{s}$.

Figure 3

Photon scattering rate into the cavity as a function of laser-cavity detuning ${\delta }_{\mathrm{lc}}$ with the ion located at a cavity standing-wave antinode (a), halfway between a node and an antinode (b), and at a node (c). Each data point is measured by preparing the ion at fixed temperature by Doppler cooling for $200\mu \mathrm{s}$, then measuring the rate of scattering photons from the cavity cooling beam into the cavity for $50\mu \mathrm{s}$ with ${\delta }_{\mathrm{ci}}/(2\pi )=-60\mathrm{MHz}$ and ${\Gamma }_{\mathrm{sc}}=1.2\times {10}^7\mathrm{\text{photons}}/\mathrm{s}$. The solid, dashed, and dotted vertical lines are at the carrier, first-order motional sideband, and second-order motional sideband transition frequencies, respectively. The curves are Lorentzian fits with linewidths consistent with the combined linewidth of the cavity and laser.

Figure 4

Cavity cooling dynamics. The ion is sideband cooled to the three-dimensional motional ground state; a cavity cooling pulse with detuning ${\delta }_{\mathrm{lc}}=0$ (carrier), ${\delta }_{\mathrm{lc}}=-{\omega }_z$ (red axial sideband), or ${\delta }_{\mathrm{lc}}=+{\omega }_z$ (blue axial sideband) is applied; and the mean number of motional quanta in the $z$ mode is measured. The three lines are a simultaneous fit to the model described in the supplementary information [23] with fit parameters $n_0=0.30(6)$, ${\Gamma }_{\mathrm{sc}}=2.87(2)\times {10}^6\mathrm{\text{photons}}/\mathrm{s}$, and $\eta =0.0148(2)$. The reduced ${\chi }^2$ of the fit is 1.7.