Continuous parametric feedback cooling of a single atom in an optical cavity

We demonstrate a feedback algorithm to cool a single neutral atom trapped inside a standing-wave optical cavity. The algorithm is based on parametric modulation of the confining potential at twice the natural oscillation frequency of the atom, in combination with fast and repetitive atomic position measurements. The latter serve to continuously adjust the modulation phase to a value for which parametric excitation of the atomic motion is avoided. Cooling is limited by the measurement backaction which decoheres the atomic motion after only a few oscillations. Nonetheless, applying this feedback scheme to an $\sim 5$-kHz oscillation mode increases the average storage time of a single atom in the cavity by a factor of 60 to more than 2 s. In contrast to previous feedback schemes, our algorithm is also capable of cooling a much faster $\sim 500$-kHz oscillation mode within just microseconds. This demonstrates that parametric cooling is a powerful technique that can be applied in all experiments where optical access is limited.

Figure 1

Experimental setup. A single atom is trapped inside the optical cavity by a red-detuned dipole trap. This system is probed with a resonant beam that is detected by avalanche photodiodes (APDs) in photon counting mode and demodulated in real time at a preset frequency $f_{\text{pfb}}$ on a field-programmable gate array (FPGA) shown in the green box. The amplitude and phase are extracted and used to feedback to the atom via a sinusoidal intensity modulation of the dipole trap. The parameter ${\varphi }_{\text{pfb}}$ advances the phase of the feedback with respect to the atom's oscillation to enable cooling.

Figure 2

Observing the atomic motion. (a) Transmission for a typical atom storage event; low transmission indicates the presence of an atom. The zoomed-in section shows how the FPGA locks to the atomic oscillation. The black solid trace is the measured cavity transmission, the red dotted trace is related to the inferred atomic oscillation amplitude (see the text), and the green dashed trace is the local oscillator phase locked to the measured atomic oscillation. Below, the blue solid trace shows the measured phase difference between the local oscillator and the atomic motion. (b) Fourier transform of measured transmission. The peak appears below the expected frequency of $2{\omega }_{\rho }/2\pi$ due to the nonlinear dependence of cavity transmission on radial position. It is broadened due to the measurement backaction, reflecting decoherence of the atomic oscillation by the probing laser beam. A fit incorporating the nonlinear transmission function, which connects the atomic position to the transmitted intensity, yields a $Q$ factor of 2.8 (see the text for details).

Figure 3

Radial parametric feedback. Average storage time of an atom in the cavity as a function of phase advance ${\varphi }_{\text{pfb}}$ for various feedback frequencies. The phase advance which gives optimal cooling decreases as the feedback frequency increases. Error bars represent the standard error in the mean for the storage time. The lines are fits of a periodic Gaussian that is used to determine the ideal phase advance. The dashed horizontal line shows the average storage time without feedback.

Figure 4

Radial parametric feedback versus feedback frequency. Measured average storage time (solid line with circles) and optimal phase advance (dotted line with squares) as a function of feedback frequency $f_{\text{pfb}}$. The error bars represent the standard error in the mean for the storage time and the fitting error in the determination of optimal phase.

Figure 5

Axial parametric feedback. Performance of axial feedback cooling at $f_{\text{pfb}}=625\mathrm{kHz}$, corresponding to twice the natural oscillation frequency of the atom along the axis of the standing-wave dipole trap. The data points represent experimental measurements of storage time averaged over at least 100 runs per point and the solid line is a sinusoidal fit to the data. Error bars represent the standard error in the mean for the storage time.