# Phase transition of ultracold atoms immersed in a BEC vortex lattice

## TL;DR

This paper explores the quantum phases of ultracold atoms in a vortex lattice, revealing how vortex dynamics induce long-range interactions that alter the phase diagram, with implications for experimental realization.

## Contribution

It introduces an extended Bose-Hubbard model incorporating vortex-induced phonon interactions and analyzes its phase diagram using variational and Monte Carlo methods.

## Key findings

- Long-range attraction shifts Mott-insulator regions
- Vortex dynamics modify quantum phase boundaries
- Feasibility discussed for experimental implementation

## Abstract

We investigate the quantum phases of ultracold atoms trapped in a vortex lattice using a mixture of two bosonic species (A and B), in the presence of an artificial gauge field. Heavy atoms of species B are confined in the array of vortices generated in species A, and they are described through a Bose-Hubbard model. In contrast to the optical-lattice setups, the vortex lattice has an intrinsic dynamics, given by its Tkachenko modes. Including these quantum fluctuations in the effective model for B atoms yields an extended Bose-Hubbard model, with an additional "phonon"-mediated long-range attraction. The ground-state phase diagram of this model is computed through a variational ansatz and the quantum Monte Carlo technique. When compared with the ordinary Bose-Hubbard case, the long-range interatomic attraction causes a shift and resizing of the Mott-insulator regions. Finally, we discuss the experimental feasibility of the proposed scheme, which relies on the proper choice of the atomic species and on a large control of physical parameters, like the scattering lengths and the vorticity.