Finite-Temperature Quantum Matter with Rydberg or Molecule Synthetic Dimensions

TL;DR

This paper investigates the phase diagram of ultracold atoms or molecules with Rydberg or rotational states as a synthetic dimension, revealing multiple ordered phases and complex thermal phase transitions, including tri-critical points, using mean-field theory.

Contribution

It provides the first detailed phase diagram of a many-body system with a synthetic dimension, including finite-temperature effects and the nature of phase transitions.

Findings

Identified three ordered phases, including two localized and one delocalized.

Discovered that thermal phase transitions can be first or second order, with a tri-critical point.

Analyzed how phase boundary features depend on the size of the synthetic dimension.

Abstract

Synthetic dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases - two are localized in the synthetic dimension, predicted as zero-temperature ground states in Refs. [Sci. Rep., 8, 1 (2018) and Phys. Rev. A 99, 013624 (2019)], and a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength, for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tri-critical point on the phase boundary. By examining the dependence of the tri-critical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.