Rapidly rotating quantum gases realize the physics of charged particles in high magnetic fields. We developed a novel protocol, geometric squeezing, that enables to create Bose-Einstein condensates in a single Landau gauge wavefunction of the lowest Landau level. Based on the non-commutativity of guiding center X and Y coordinates, geometric squeezing in a saddle potential is a real space analogue to squeezing in phase space of a one-dimensional particle in an inverted harmonic oscillator potential.
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