Quasi-energies and Floquet states of two weakly coupled Bose-Einstein condensates under periodic driving

TL;DR

This paper studies the quasi-energies and Floquet states of two weakly coupled Bose-Einstein condensates under periodic driving, revealing a triangular structure linked to localization phenomena and comparing mean-field and quantum models.

Contribution

It introduces a detailed comparison of mean-field and second-quantized models for driven BECs, highlighting the triangular quasi-energy structure and localization effects.

Findings

Triangular quasi-energy band structure observed in both models

Localization phenomenon linked to the triangular structure

Quantum quasi-energies agree with semi-classical quantization

Abstract

We investigate the quasi-energies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasi-energies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasi-energy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second quantized model, we find also a triangular structure in the quantum quasi-energy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasi-energies is further explored by a semi-classical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasi-energies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.