# Vortex-hole duality: a unified picture of weak and strong-coupling regimes of bosonic ladders with flux

## TL;DR

This paper reveals a duality in bosonic ladders with flux, connecting weak-coupling vortex superfluids and strong-coupling charge-density waves, with implications for understanding quantum Hall states and experimental realizations.

## Contribution

It introduces a unified framework describing vortex-hole duality across coupling regimes in bosonic ladders with flux, linking different quantum phases.

## Key findings

- Strong-coupling crystalline states near π-flux are independent of particle statistics.
- These states relate to fractional quantum Hall states in the thin-cylinder limit.
- Quantum gases with contact interactions can experimentally explore this duality.

## Abstract

Two-leg bosonic ladders with flux harbor a remarkable vortex-hole duality between the weak-coupling vortex lattice superfluids and strong-coupling charge-density-wave crystals. The strong-coupling crystalline states, which are realized in the vicinity of $\pi$-flux, are independent of particle statistics, and are related with the incompressible fractional quantum Hall states in the thin-cylinder limit. These fully gapped ground states, away of $\pi$-flux, develop nonzero chiral (spin) currents. Contact-interacting quantum gases permit exploration of this vortex-hole duality in experiments.