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arXiv:1805.00241 · Physical Review A

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

Christian Sames, Christoph Hamsen, Haytham Chibani, P. A. Altin, Tatjana Wilk, Gerhard Rempe

Published May 8, 2018• 5 citations

Abstract

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 $\ensuremath{\sim}5$-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 $\ensuremath{\sim}500$-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.

DOI: 10.1103/physreva.97.053404

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•Jan 1, 2003•1 citation

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

\ensuremath{\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

\ensuremath{\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.

Recent realizations of single-atom trapping and tracking in cavity QED open the door for feedback schemes which actively stabilize the motion of a single atom in real time. We present feedback algorithms for cooling the radial component of motion for a single atom trapped by strong coupling to single-photon fields in an optical cavity. Performance of various algorithms is studied through simulations of single-atom trajectories, with full dynamical and measurement noise included. Closed loop feedback algorithms compare favorably to open-loop "switching" analogs, demonstrating the importance of applying actual position information in real time. The high optical information rate in current experiments enables real-time tracking that approaches the standard quantum limit for broadband position measurements, suggesting that realistic active feedback schemes may reach a regime where measurement backaction appreciably alters the motional dynamics.

Real-time feedback control of quantum systems is often limited by partial observations, nonlinear dynamics and measurement noise, which make accurate model-based controllers difficult to design. Here we show that deep reinforcement learning can cool the motion of a single neutral atom coupled to a high-finesse optical cavity using only the continuously monitored cavity transmission. We first train the controller in simulation and then transfer it to the experiment, where online fine-tuning adapts it to unmodeled experimental dynamics. The learned policy damps the atom's motion in real time and achieves a cooling time constant of 388 +/- 14 microseconds, corresponding to only two motional periods in the trap. It also outperforms a standard linear differentiator controller in cooling speed while maintaining comparable atom retention over a broad range of operating conditions. These results establish reinforcement learning as a practical strategy for feedback control in quantum-limited experiments where compact analytical models are incomplete.

Recent realizations of single-atom trapping and tracking in cavity QED open the door for feedback schemes which actively stabilize the motion of a single atom in real time. We present feedback algorithms for cooling the radial component of motion for a single atom trapped by strong coupling to single-photon fields in an optical cavity. Performance of various algorithms is studied through simulations of single-atom trajectories, with full dynamical and measurement noise included. Closed loop feedback algorithms compare favorably to open-loop "switching" analogs, demonstrating the importance of applying actual position information in real time. The high optical information rate in current experiments enables real-time tracking that approaches the standard quantum limit for broadband position measurements, suggesting that realistic active feedback schemes may reach a regime where measurement backaction appreciably alters the motional dynamics.

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 μK. 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.

An experiment is described where slow laser-cooled atoms are injected into a high-finesse optical cavity. Single atoms are trapped in the cavity light field and observed by measuring the light intensity transmitted through the cavity. Feedback-based methods are realized to extend the time the atom stays in the cavity. The influence of atoms on the cavity transmission and the light force on atoms in a cavity are also analyzed theoretically. This allows to study the motion of an atom in the cavity and to interpret the experimental transmission signals. The current limitations for the storage time are identified and a strategy to overcome them is suggested. Apart from that, a method is proposed which allows a two-dimensional position measurement of atoms in the cavity.