Feedback Cooling of a Single Neutral Atom

We demonstrate feedback cooling of the motion of a single rubidium atom trapped in a high-finesse optical resonator to a temperature of about $160\mu \mathrm{K}$. Time-dependent transmission and intensity-correlation measurements prove the reduction of the atomic position uncertainty. The feedback increases the $1/e$ storage time into the 1 s regime, 30 times longer than without feedback. Feedback cooling therefore rivals state-of-the-art laser cooling, but with the advantages that it requires less optical access and exhibits less optical pumping.

Figure 1

(a) Evolution of the probability of an atom to remain trapped without feedback (▵) and with feedback for 25% (▪), 50% (•), and 100% (▴) signal. The $1/e$ storage times are 35 ms, 160 ms, 400 ms, and 1100 ms, respectively. For clarity, error bars are only shown for one curve. (b) Storage time with (▴) and without (▵) feedback versus probe power in units of empty cavity photon number. The error bars obtained from the fit are smaller than the symbols.

Figure 2

(a) Typical transmission signal (red) from an atom that escapes while the dipole trap (black) is ramped down. (b) Reconstructed energy distribution of the atom. Fitting a Boltzmann distribution yields a temperature of $160\pm 5\mu \mathrm{K}$ with feedback and $400\pm 50\mu \mathrm{K}$ without feedback.

Figure 3

Averaged time-dependent transmission (relative to empty cavity) in two successive intervals in which the feedback is enabled (▴) and disabled (▵), respectively. When the feedback is enabled, an exponential drop in transmission with a $1/e$ time constant of 1.2 ms is observed, proving cooling of the atomic motion. Without feedback the average transmission increases linearly due to heating.

Figure 4

Time-dependent intensity-correlation function without feedback in the shallow [a), black line] and deep [b), green line] trap, and with feedback using an integration time of the feedback algorithm of $32\mu \mathrm{s}$ [c), blue line] and $16\mu \mathrm{s}$ [d), red line]. Without feedback the radial oscillations cause a characteristic bump at one-half of the oscillation period. This bump disappears when the feedback is enabled.