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arXiv:1905.01643 · Physical Review A

Rotons and Bose condensation in Rydberg-dressed Bose gases

Iran Seydi, Saeed H. Abedinpour, Robert E. Zillich, Reza Asgari, B. Tanatar

Published Jan 22, 2020• 15 citations
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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 with respect to 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 at selected system parameters 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.

DOI
10.1103/physreva.101.013628

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We investigate the effects of many-body correlations on the ground-state properties of a single-component ultracold Rydberg-dressed Fermi liquid with purely repulsive interparticle interactions in both three and two spatial dimensions. We employed the Fermi-hypernetted-chain Euler-Lagrange approximation and observed that the contribution of the correlation energy on the ground-state energy becomes significant at intermediate values of the soft-core radius and large coupling strengths. For small and large soft-core radii, the correlation energy is negligible and the ground-state energy approaches the Hartree-Fock value. The positions of the main peaks in static structure factor and pair distribution function in the homogeneous fluid phase signal the formation of quantum droplet crystals with several particles confined inside each droplet.
In this paper, we study Bose-Einstein condensation of Rydberg-dressed atoms considering finite range interactions. We use Hartree-Fock-Bogoliubov approximation based on Mean-Field approach. Moreover, within this approximation modified by the finite-range character of the two-body interaction we shall obtain analytical expressions for thermodynamic quantities of Rydberg-dressed Bose gas. The imaginary part of the quasiparticle spectrum of a BEC signals the instability of the roton mode with respect to the formation of supersolid state. Our theory predicts a second-order quantum phase transition from BEC to supersolid phase for Rydberg-dressed bosons in three dimensions.
We explore phases of two-component Rydberg-dressed Bose-Einstein condensates in three spatial dimensions. The competition between the effective ranges of inter- and intra-component soft-core interactions leads to a rich variety of ground states. These include states resembling ionic compounds with face-centered cubic or simple cubic lattice structure. Upon increasing the scattering length, the dimensionality of the symmetry-breaking is lower due to the suppression of large densities, leading to segregated planar or tubular density profiles. We also show that these states are not only stable ground states, but can also emerge dynamically upon time evolution.
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Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter K>1K>1K>1 to hard-rod-like behavior with K<1K<1K<1, with a quasi-supersolid phase emerging for K<1/2K < 1/2K<1/2. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.
Ground-state properties of a two-dimensional fluid of bosons with repulsive dipole-dipole interactions are studied by means of the Euler-Lagrange hypernetted-chain approximation. We present a self-consistent semianalytical theory of the pair distribution function g(r)g(r)g(r) and ground-state energy of this system. Our approach is based on the solution of a zero-energy scattering Schr\"odinger equation for the ``pair amplitude'' g(r)\sqrt{g(r)}g(r)​ with an effective potential from Jastrow-Feenberg correlations. We find excellent agreement with quantum Monte Carlo results over a wide range of coupling strength, nearly up to the critical coupling for the liquid-to-crystal quantum phase transition. We also calculate the one-body density matrix and related quantities, such as the momentum distribution function and the condensate fraction.