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arXiv:quant-ph/0509039 · Physical Review A

Feedback cooling of atomic motion in cavity QED

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

Published Jul 31, 2006• 54 citations
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Abstract

We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.

DOI
10.1103/physreva.74.012322

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We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.
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.
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.
Summary form only given. Atoms in an optical lattice, though very slow, perform a slight random motion that reflects the non-zero temperature of the trapped atoms. We are proposing a way of reducing such random motion using real-time feedback. The method is related to the stochastic cooling used to transversely cool particle beams. Another stochastic cooling method for laser-cooled atoms has been proposed in "Stochastic cooling of atoms using lasers," see Phys. Rev. A, vol. 58, p. 4757 (1998). Our scheme involves a measurement of the coherent redistribution of photons between different laser beams of the optical lattice.