Quantum membrane phases in synthetic lattices of cold molecules or Rydberg atoms

Abstract

We calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semisynthetic three-dimensional configuration---one synthetic dimension plus a two-dimensional real-space optical lattice or periodic microtrap array---using the stochastic Green's function quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite-size scalings, we show that there is a second-order transition to a low-temperature phase in which two-dimensional ``sheets'' form in the synthetic dimension of internal rotational or electronic states of the molecules or Rydberg atoms, respectively. Simulations for different values of the interaction $V$, which acts between atoms or molecules that are adjacent both in real and synthetic space, allow us to compute a phase diagram. We find a finite-temperature transition at sufficiently large $V$ as well as a quantum phase transition---a critical value ${V}_{c}$ below which the transition temperature vanishes.