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arXiv:quant-ph/0310153 · Physical Review Letters

Quantum Feedback Control of Atomic Motion in an Optical Cavity

D. Steck, Kurt A. Jacobs, Hideo Mabuchi, Tanmoy Bhattacharya A, Salman Habib

Published Jun 4, 2004• 117 citations
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Abstract

We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies.

DOI
10.1103/physrevlett.92.223004

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We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies.
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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 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.
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