Validity of the Lowest Landau Level Approximation for Rotating Bose Gases

TL;DR

This study evaluates the validity of the Lowest Landau Level approximation in rotating Bose gases by exact calculations of energy spectra, revealing conditions under which various quantum states are stabilized.

Contribution

It provides a detailed analysis of Landau level occupation and the validity of the LLL approximation for different quantum states in rotating Bose gases.

Findings

LLL approximation valid only for decreasing interaction strength with particle number for vortex states

Strongly correlated states can tolerate increasing interaction strength while remaining in the LLL

Pfaffian and Laughlin states may be stabilized at sub-centrifugal rotation frequencies in large systems

Abstract

The energy spectrum for an ultracold rotating Bose gas in a harmonic trap is calculated exactly for small systems, allowing the atoms to occupy several Landau levels. Two vortex-like states and two strongly correlated states (the Pfaffian and Laughlin) are considered in detail. In particular, their critical rotation frequencies and energy gaps are determined as a function of particle number, interaction strength, and the number of Landau levels occupied (up to three). For the vortex-like states, the Lowest Landau level (LLL) approximation is justified only if the interaction strength decreases with the number of particles; nevertheless, the constant of proportionality increases rapidly with the angular momentum per particle. For the strongly correlated states, however, the interaction strength can increase with particle number without violating the LLL condition. The results suggest that in large systems, the Pfaffian and Laughlin states might be stabilized at rotation frequencies below the centrifugal limit for sufficiently large interaction strengths, with energy gaps a significant fraction of the trap energy.