Synthetic dimensions in ultracold molecules: quantum strings and membranes

TL;DR

This paper explores how ultracold molecules can be used to create synthetic dimensions through their rotational states, enabling the simulation of complex quantum phases like strings and membranes driven by interactions.

Contribution

It introduces a method to use molecular rotational states as synthetic dimensions, allowing for controllable topological and many-body quantum phases in ultracold molecular systems.

Findings

Rotational states can form extensive synthetic lattices with hundreds of sites.

Microwave coupling enables controllable synthetic tunneling and topological band structures.

Dipole interactions induce formation of quantum strings and membranes.

Abstract

Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using measurements of rotational state populations.