Topological dynamics of adiabatic cat states

The topic is timely. The conclusions are based on thorough derivations and detailed arguments.

The paper ends up very heavy to read since it focuses much on technical details. For the final results -- utilizing a quantized version of a topological pumping one can prepare cat states -- it seems unmotivated to fill 33 pages consisting much of derivations (cat states are pretty general in physical models). The specific model considered seems unnecessarily complicated if the goal is to prepare cat states.

In the manuscript "Topological dynamics of adiabatic cat states", Luneau et al. consider a qubit coupled to two boson modes. In particular, the setup with two quantized modes driving the qubit generalizes a model of topological pumping with two classical fields. Using analytical arguments and derivations, accompanied by numerical simulations, it is shown how the evolution results in cat states characterized by a superposition of states well separated in phase space.

The paper provides a thorough analysis of the system at hand, their arguments are exhaustive and detailed. The objective of the paper, analyzing how the topological pumping mechanism is modified by replacing the classical fields with quantized ones, feels relevant. The conclusions are backed up by a solid analysis. Nonetheless, personally, I find this paper very hard to read, not due to the complexity of the problem, but because I drown in technical details. While refereeing I had to split the reading between several occasions in order to appreciate all arguments. Often, while reading all the technical analyzes I had to return to the beginning of the paper to remind myself what was actually the purpose of the paper; instead of following a logic line with clear goals I got stuck in derivations (one minor reason for this was that some notations were not what I am used to, but that varies from communities and personal taste). I had the feeling that many of the technical derivations could be included as appendices, but then I noticed that there were already nine appendices. I understand that this is a very personal opinion, and some others might appreciate all the technical parts, but my feeling is that to get the message through one does not need all this. After all, the main conclusion that a qubit interacting with two quantized modes results in cat states is not very new, but rather general. In fact, two boson modes initially in coherent states and interacting with a qubit via a Jaynes-Cummings interaction will also result in an entangled cat. Apart from the above general comment about the structure I have some more specific comments:

1) I lack a discussion about the relevance of the results. The light-matter interaction defined in eq. (2) involves the phase operators, and seems very particular. The meaning of phase states has a long history in quantum optics; both in terms of how to define and interpret a conjugate variable to the number operator, and how phase states can be prepared. Typically, the phase operators when expressed in terms of Fock states involve infinitely large Fock states, and I do not know how realistic the interaction of eq (2) is for real experiments. How could it be realized? As said above, it seems that cat states can be prepared by much simpler means.

2) The authors stress how the topological pumping with quantized fields leads to the build-up of entanglement between the qubit and the fields. Of course, this is a general statement and does not depend on topology. Indeed, others have asked similar questions in the past; what if we replace the classical field with a quantum one? The authors cite a few works already, and another one is Rev. Lett. 89, 220404 (2002).

3) The link to Bloch oscillations is mentioned. It brings to mind a recent work of Bloch oscillations in state space Rev. A 98, 053820 (2018).

Some specific suggestions are mentioned in my report.

- Thorough analytic and numerical study

- Phenomenon described in the paper already discovered

The manuscript “Topological dynamics of adiabatic cat states” studies the generation of cat states in a 2-level system (a spin) coupled to 2 driving modes. The cat states are generated using the mechanism of topological frequency conversion from Ref 14, where an adiabatically 2-tone driven spin acts as a medium for energy transfer between the tones at a universal rate; the direction of energy transfer is determined by the alignment of the spin with the instantaneous net field acting on the modes. When aligning the spin perpendicular to the initial field (Ie in an equal superposition of alignment and anti-alignment), the “photon numbers” of the individual modes change in time at opposite rates for the aligned and anti-aligned components. This paper studies how this principle can be used to generate a cat state which is in an equal superposition of two states with highly distinct photon numbers.
The idea put forward in the paper, i.e., of using topological frequency conversion to generate cat states, has been proposed and studied previously in the literature, namely in Refs. [22] (and also in [24]). It is therefore not clear what constitutes the new discovery in the present manuscript. The present paper does provide a thorough analytic/numerical characterization of the cat states; however, I currently do not see a clear motivation for this analysis that would justify publication based on this characterization alone.
Therefore, I unfortunately do not see how the manuscript meets any of SciPost’s 4 expectations (listed under acceptance criteria). I would reconsider the manuscript if (1) the authors clearly explain what constitutes their new discovery, in particular how it contrasts to, e.g., Refs. 22 and 24., and (2) how this discovery meets the acceptance criteria of Scipost.
As a more physics-related question, I am a little unsure of how ``cattiness’’ manifests itself physically. As I understand, the operators n_1 and n_2 (which distinguish the two halves of the cat state) do not directly correspond to physical observables, but are mathematical constructs introduced to conveniently describe multi-tone driven quantum systems. The authors do mention that they for instance emerge when treating the drives as quantized modes and working in the large-n limit. However, I think the manuscript would benefit greatly if the authors made the physical meaning of these observables more clear, and, even better, proposed ways to detect the cattiness.