Non-Markovian quantum feedback from homodyne measurements: The effect of a nonzero feedback delay time

We solve exactly the non-Markovian dynamics of a cavity mode in the presence of a feedback loop based on homodyne measurements, in the case of a nonzero feedback delay time. With an appropriate choice of the feedback parameters, this scheme is able to significantly increase the decoherence time of the cavity mode, even for delay times not much smaller than the decoherence time itself.