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Physical Review A

Classical analog of quantum models in synthetic dimensions

Max Cohen, Max Casebolt, Yutan Zhang, Kaden R. A. Hazzard, Richard T. Scalettar

Published Jan 3, 2024• 6 citations
Publisher

Abstract

The authors introduce a classical spin model motivated by the quantum Hamiltonian for synthetic-dimension systems based on ultracold molecules or Rydberg atoms. The authors use mean-field theory, Monte Carlo methods, and machine-learning approaches to study the phase diagram.
DOI
10.1103/physreva.109.013303

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We introduce a classical analog of quantum matter in ultracold molecule -- or Rydberg atom -- synthetic dimensions, extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying its finite temperature properties. For intermediate values of J1, the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high temperature disordered phase and the low temperature ferromagnetic phase. We also employ machine learning to uncover non-trivial features of the phase diagram using the learning by confusion approach. The key result there is that the method is able to discern several successive phase transitions.
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 VVV, 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 VVV as well as a quantum phase transition---a critical value Vc{V}_{c}Vc​ below which the transition temperature vanishes.
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 by Sundar et al. [Sci. Rep. 8, 3422 (2018); Phys. Rev. A 99, 013624 (2019)], and one is 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 tricritical point on the phase boundary. By examining the dependence of the tricritical 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.