The coherence time for the many-particle Bloch oscillating state is in fact very hard to calculate (mainly because even the coherent part is time-dependent rather than stationary). It can, however, be estimated and so we have added in the following sentences on p3:“\textcolor{red}{The coherence time is particularly hard to calculate in the Bloch oscillating case \cite{Ven13} due to the time dependence introduced by the Bloch oscillations, especially in the presence of many particles, but it can be roughly estimated to be $\tau=\tau_{\mathrm{sp}}/(1+C)$ \cite{Ven09} at cavity resonance, where$\tau_{\mathrm{sp}}^{-1}=2 \gamma \vert \alpha \vert^2 \Omega_{0}^2/\Delta_{a}^2$ is the spontaneous emission rate at an antinode. The factors $\vert \alpha \vert^2$ and$\Delta_{a}$ are the mean number of cavity photons and the detuning of the laser from atomic resonance, respectively, and will be properly defined in the next section. The numerical value of $\tau$ for the parameters considered in this paper will be given in Section \ref{sec:metrology}. Of course, Bose-Einstein condensates can be continuously measured and used for sensingwithout a cavity, e.g.\ \cite{Ruostekoski98,Dalvit02,Saba05,Lee12,Java13}, but the cavity case is particularly interesting because it allows for a strong atom-light interaction even in the quantum regime.} “In addition, in Section 6 (paragraph 4, Pg 18) we have provided further details required to estimate the coherence time for the parameters used in the paper. We find thatcoherence times of up to a couple of seconds (many thousands of Bloch oscillation periods) are possible
In particular for the blue detuned case not only the average momentum but also the momentum spread will grow.