Geometric squeezing into the lowest Landau level

TL;DR

This paper demonstrates the dynamic creation of a Bose-Einstein condensate in the lowest Landau level by exploiting geometric squeezing of non-commuting variables, revealing new pathways for studying strongly correlated quantum states.

Contribution

It introduces a method to squeeze non-commuting spatial variables to generate a condensate in the lowest Landau level, enabling exploration of quantum Hall physics.

Findings

Achieved geometric squeezing of guiding centers by over 7 dB below quantum limit.

Produced a condensate with angular momentum exceeding 1000 ħ per particle.

Resolved the size of cyclotron orbits and their zero-point fluctuations.

Abstract

The equivalence between neutral particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. In their quantum descriptions, translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. Here, we exploit the ability to squeeze non-commuting variables to dynamically create a Bose-Einstein condensate occupying a single Landau gauge wavefunction in the lowest Landau level. We directly resolve the extent of the zero-point cyclotron orbits, and demonstrate geometric squeezing of the orbits' guiding centers by more than ${7}~$dB below the standard quantum limit. The condensate attains an angular momentum of more than ${1000}\,{\hbar}$ per particle, and an interatomic distance comparable to the size of the cyclotron orbits. This offers a new route towards strongly correlated fluids and bosonic quantum Hall states.