We consider the decoherence of a pseudo-spin ensemble under collective random rotations, and study, both theoretically and experimentally, how a nondestructive measurement combined with real-time feedback correction can protect the state against such
a decoherence process. We theoretically characterize the feedback efficiency with different parameters --- coherence, entropy, fidelity --- and show that a maximum efficiency is reached in the weak measurement regime, when the projection of the state induced by the measurement is negligible. This article presents in detail the experimental results published in [Phys. Rev. Lett. textbf{110}, 210503 (2013)], where the feedback scheme stabilizes coherent spin states of trapped ultra-cold atoms, and nondestructively probed with a dispersive optical detection. In addition, we study the influence of several parameters, such as atom number and rotation angle, on the performance of the method. We analyze the various decoherence sources limiting the feedback efficiency and propose how to mitigate their effect. The results demonstrate the potential of the method for the real-time coherent control of atom interferometers.
We report the relative frequency stabilization of a distributed feedback erbium-doped fiber laser on an optical cavity by serrodyne frequency shifting. A correction bandwidth of 2.3 MHz and a dynamic range of 220 MHz are achieved, which leads to a st
rong robustness against large disturbances up to high frequencies. We demonstrate that serrodyne frequency shifting reaches a higher correction bandwidth and lower relative frequency noise level compared to a standard acousto-optical modulator based scheme. Our results allow to consider promising applications in the absolute frequency stabilization of lasers on optical cavities.
