# Rotons and Bose condensation in Rydberg-dressed Bose Gases

## TL;DR

This paper explores the ground-state properties and excitations of Rydberg-dressed bosons, revealing a transition from a superfluid to droplet crystal phase, with significant correlation effects beyond mean-field theory.

## Contribution

It introduces a combined theoretical and simulation approach to analyze phase transitions and correlations in Rydberg-dressed Bose gases, highlighting the formation of droplet crystals.

## Key findings

- Homogeneous system becomes unstable towards droplet crystal formation at strong couplings.
- Correlation energy significantly affects the ground-state energy at intermediate couplings.
- First-order phase transition from superfluid to droplet phase with cubic symmetry predicted.

## Abstract

We investigate the ground-state properties and excitations of Rydberg-dressed bosons in both three and two dimensions, using the hypernetted-chain Euler-Lagrange approximation, which accounts for correlations and thus goes beyond the mean field approximation. The short-range behavior of the pair distribution function signals the instability of the homogeneous system towards the formation of droplet crystals at strong couplings and large soft-core radius. This tendency to spatial density modulation coexists with off-diagonal long-range order. The contribution of the correlation energy to the ground-state energy is significant at large coupling strengths and intermediate values of the soft-core radius while for a larger soft-core radius the ground-state energy is dominated by the mean-field (Hartree) energy. We have also performed path integral Monte Carlo simulations to verify the performance of our hypernetted-chain Euler-Lagrange results in three dimensions. In the homogeneous phase, the two approaches are in very good agreement. Moreover, Monte Carlo simulations predict a first-order quantum phase transition from a homogeneous superfluid phase to the quantum droplet phase with face-centered cubic symmetry for Rydberg-dressed bosons in three dimensions.