Massive particle interferometry with lattice solitons

1) The interferometric scheme is clearly explained, and the case for such a study well motivated.

2) The results are very well discussed.

1) The role of transverse directions should be addressed.

2) An estimate of the effects of the approximations done in the paper to achieve high sensitivity should be as well addressed (see the report).

My general comment is that the paper is clearly written, on a subject of clear interest, and in my opinion it meets the criteria for publication. However I feel that it is important that the Authors consider the role of transverse directions. To be more precise, the setup described by the Authors is based on two main assumptions (leaving apart the temperature):
- model (2) is obtained for large optical lattices; and
- transverse degrees of freedom have been integrated.
I clearly agree that these effects are (or can be made) fairly small and can be taken into account. So, if this was a paper on soliton splitting, I would say that a further analysis would be not needed. But the Authors, as I see from the introduction, are motivated by quantum sensing and I agree with such a motivation. So, one wants to have high sensitivities, with "the potential to achieve quantum advantage with an
improvement of a device’s sensitivity of a factor of a hundred
with respect to the standard matter-wave solutions". But, do the errors due to Bose-Hubbard approximation and -- more importantly -- due to realistic role of transverse degrees of freedom would prevent from reaching such high sensitivities? To be more explicit, if one has an \omega of tens of Hz, and even an \omega_transverse of tens of kHz (therefore a ratio 10^-3), can one expects to be competitive with other schemes where the relative error of the quantities to be measured is smaller than 10^-3? I am not referring to the instability of the soliton solutions due to transverse degrees of freedom during the dynamics (that it is anyway an issue), but actually on the limit that the unavoidable presence of the transverse directions would put on sensitivity. In other words, if one compares for the numbers given above the full 3D quantum dynamics with the dynamics from the model (2) and finds a relative error 10^-3, that would be excellent - but what about the sensitivity? I do not ask to do a full, systematic study of the impact of approximations on the sensitivity, but I think is important that the issue is mentioned and at least qualitatively discussed.

1) Discuss the effect on the interferometric scheme of the approximations used to write models (2) and (1) (especially the role of transverse degrees of freedom).

1. The paper deals with a proposal of an experimental implementation of an atomic interferometer based on scattering of a Lieb-Liniger-McGuire bright quantum soliton from a sharp potential barrier in the presence of a loose 1D harmonic confinement that provides the recombnation operation. The first strong point of the paper is its sound numerical approach that employs a lattice model.

2. Based on their analysis, the authors come to a very important conclusion that a (partial or full) disintegration of a bright quantum soliton does not prevent the interferometric signal (the number of atoms in a certain half of the harmonic trap) from being seen.

1. However, there is an important issue that has not been properly addressed in the paper, namely, the fluctuations of the number of atoms in a soliton. If we allow for averaging over N fluctuating according, say, to the Poisson law, how strong is the reduction of the interference contrast? I am afraid that the interference fringes on Fig. 2 and 3 will drop well below +/- 1 atom, if we assume the values <N>=5 or 6 as the expectation values for the Poisson distribution (or a Gaussian with a comparable r.m.s.).

2. It is reasonable to try to increase N (which is not possible numerically, but easy in experiment). But then we may encounter another problem: if the typical energy per particle in a Lieb-Liniger-McGuire bound state becomes larger than the radial trapping frequency, the simple 1D physical picture breaks down and we have to take into account radial excitations (i.e., consider a multiband 1D problem). This issue is also not addressed in the paper.

In general, this paper meets the criteria for SciPost Phys. and can be published after the two weak points mentioned above will have been improved.

1. The authors should provide their results averaged over a certain distribution of the atom number N. If the Poisson distribution will yield too bad results, the authors should mention the ways to reduce the variance of N, e.g., by a postselection or by some other method. Do the authors expect the laser culling of atoms [Dudarev, Raizen, Niu, PRL 98, 063001 (2007)] to work for this purpose?

2. The authors should discuss the applicability of the reduction from 3D to 1D in their propoised interferometer or, at least, to give an estimation for the upper limit on N that allows for neglecting radial excitations.