Yes we agree that there will be extra noise due to the open nature of the cavity, and we already refer to this on p3 of the Introduction: “The disadvantage of working in a cavity is that quantum measurement backaction, in the form of random fluctuations in the cavity field due to photons spontaneously leaking out of the cavity, heats up the cold atoms and limits the coherence time of the measurement \cite{Ven13}.” where the cited paper is one of ours [Prasanna Venkatesh, B.; O’Dell, D. H. J.; Bloch oscillations of cold atoms in a cavity: Effects of quantum noise. Phys. Rev. A 2013, 88, 013848] where we directlycalculated the heating effect for Bloch oscillating atoms in a cavity within the Bogoliubov approximation. Following the referee’s suggestion we have added the reference to Mekhov’s paper.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
(b) There will be heating limiting the available measurement time. as the time scale can be faster than om_recoil, it could limit the measurement time to a fairly short period. Some rough estimate on the time scales should be added. In particular for the blue detuned case not only the average momentum but also the momentum spread will grow.