| Abstract: |
| Constructing and manipulating quantum states in fast-rotating Bose-Einstein condensates (BECs) has long stood as a significant challenge as the rotating speed approached a critical velocity. Although a recent experiment [R. J. Fletcher {\it et al.}, Science {\bf 372}, 1318 (2021)] has realized the geometrically squeezed state of the guiding-center mode, the remaining degree of freedom, the cyclotron mode, remains unsqueezed due to the large energy gap of the Landau levels. To overcome this limitation, we propose a Floquet-based state-preparation protocol by periodically driving an anisotropic potential. Through both analytical and numerical calculations, we demonstrate that this protocol not only facilitates single-cyclotron-mode squeezing, but also enables two-mode squeezing. Such two-mode squeezing offers a richer set of dynamics compared to single-mode squeezing and can achieve a wave-packet width well below the lowest-Landau-level limit. Our work provides a highly controllable knob for realizing diverse geometrically squeezed states in ultracold quantum gases within the quantum Hall regime. |
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