# Periodically and Quasi-periodically Driven Dynamics of Bose-Einstein Condensates

### Submission summary

 As Contributors: Pengfei Zhang Arxiv Link: https://arxiv.org/abs/2008.00373v2 (pdf) Date submitted: 2020-08-11 06:12 Submitted by: Zhang, Pengfei Submitted to: SciPost Physics Discipline: Physics Subject area: Atomic, Molecular and Optical Physics - Theory Approach: Theoretical

### Abstract

We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 2008.00373v2 on 11 August 2020

## Reports on this Submission

### Strengths

1. The Authors study BECs for a (quasi-)periodically modulated Bogoliubov scattering length.
2. They motivate the study by arguing that periodic drives can be used for many useful applications, but that the resulting quantum dynamics is difficult to solve.
3. There are some cases where symmetry allows for a large simplification, and they go on to consider such systems.
4. They draw a topological connection by generating a Hofstadter butterfly analogue for the two protocols under investigation.
5. Generally speaking, this appears to be novel, high quality work that adresses an important question.

### Weaknesses

1. The most pressing issue for me is that a seemingly crucial connection is left unexplained.
It is not clear to me why when the system evolves as $n_k(t) \sim e^{\lambda_k t}$ we should consider it to be in a heating phase. That is, the connection between the physical system under study and the formalism has not been made clear.

2. There is a missing reference after 'non-trivial dynamics'

3. Some of the sentences are confusingly worded or gramatically incorrect.

### Report

Overall, I think this work is of a high standard and I would be happy to recommend it for publication in SciPost Physics.

### Requested changes

1. Physical justification for the criteria $n_k \sim e^{\lambda_k t}$ corresponding to the system being in the heating phase.

2. Fixing missig reference

3. Editorial assistance to fix grammar/wording

• validity: high
• significance: high
• originality: high
• clarity: ok
• formatting: good
• grammar: acceptable