Quantized Transport of Gap Solitons in the Harper-Hofstadter Model

@misc{ashfield2026quantized,
  title = {{Quantized Transport of Gap Solitons in the Harper-Hofstadter Model}},
  author = {Oliver Ashfield and Henry Davenport and Tom Sheppard and David G. Reid and Holly A. J. Middleton-Spencer and A. C. Berceanu and Frank Schindler and Iacopo Carusotto and Hannah M. Price},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21917},
  eprint = {2609.21917},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21917},
}

TY  - UNPB
TI  - Quantized Transport of Gap Solitons in the Harper-Hofstadter Model
AU  - Oliver Ashfield
AU  - Henry Davenport
AU  - Tom Sheppard
AU  - David G. Reid
AU  - Holly A. J. Middleton-Spencer
AU  - A. C. Berceanu
AU  - Frank Schindler
AU  - Iacopo Carusotto
AU  - Hannah M. Price
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21917
UR  - https://arxiv.org/abs/2609.21917
AB  - We investigate the dynamics of gap solitons found in the Harper-Hofstadter model with an additional cubic nonlinearity, such as that describing weakly-interacting cold atoms or a Kerr nonlinearity in an optical platform. We find that certain solitons with frequencies deep in the band gap travel with a robust, quantized velocity perpendicular to the applied force and maintain their spatial profile over long timescales. Crucially, this velocity is linearly proportional to the applied force, allowing for arbitrary steering of the nonlinear wavepacket, without breakdown, using only a tunable external force. This quantized transport persists despite a highly non-uniform occupation of the linear Bloch states, and contrasts with solitons near the band edge, which deform and delocalize under the same force. These results point to a robust and highly controllable mechanism for steering nonlinear solitons in experimentally accessible platforms.
ER  -