# Strings of ultracold molecules in a synthetic dimension

## TL;DR

This paper explores how ultracold polar molecules in a one-dimensional chain can form a string-like phase in a combined real and synthetic dimension space, revealing a phase transition driven by dipole interactions.

## Contribution

It introduces a two-dimensional lattice model combining real and synthetic dimensions and characterizes the phase transition to a string phase using numerical and analytical methods.

## Key findings

- Identification of a phase transition from a gas to a string phase with increasing dipole strength.
- Analytic and numerical characterization of the string phase and its excitations.
- Discovery of emergent particles on the string, enriching the understanding of synthetic dimension systems.

## Abstract

We consider ultracold polar molecules trapped in a unit-filled one-dimensional chain in real space created with an optical lattice or a tweezer array and illuminated by microwaves that resonantly drive transitions within a chain of rotational states. We describe the system by a two-dimensional lattice model, with the first dimension being a lattice in real space and the second dimension being a lattice in a synthetic direction composed of rotational states. We calculate this system's ground-state phase diagram. We show that as the dipole interaction strength is increased, the molecules undergo a phase transition from a two-dimensional gas to a phase in which the molecules bind together and form a string that resembles a one-dimensional object living in the two-dimensional (i.e, one real and one synthetic dimensional) space. We demonstrate this with two complementary techniques: numerical calculations using matrix product state techniques and an analytic solution in the limit of infinitely strong dipole interaction. Our calculations reveal that the string phase at infinite interaction is effectively described by emergent particles living on the string and that this leads to a rich spectrum with excitations missed in earlier mean-field treatments.