Dynamical generation of geometric squeezing in interacting Bose-Einstein condensates

When the rotating frequency of a noninteracting Bose-Einstein condensate (BEC) confined in a weak anisotropic harmonic potential is suddenly quenched to its trapping frequency, the condensate evolves from its ground state to a single-mode squeezed state with exponentially growing quantum fluctuation anisotropy. Such a squeezed state is called the geometrically squeezed state. However, for interacting BECs with two-body collisions, a similar quench only results in quantum fluctuations oscillating periodically without squeezing. In this work, we identify superfluid stability as the key factor behind this nonsqueezing phenomenon, with the periodic oscillations arising from collective excitations of a stable collective excitation mode. By strategically breaking the stability criteria, we propose a dynamical approach for generating squeezing that can exponentially suppress quantum fluctuations in a relatively short time, surpassing the efficiency of existing experimental preparation schemes.