Few-boson system with a single impurity: Universal bound states tied to Efimov trimers

Abstract

Small weakly-bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly-bound $N$-body clusters consisting of $N-1$ identical bosons (denoted by "B") of mass $m$ that interact with a single distinguishable impurity particle (denoted by "X") of mass $M$. The system properties are analyzed as a function of the mass ratio $\kappa$ (values from $\kappa =1$ to $50$ are considered), where $\kappa$ is equal to $m/M$, and the two-body $s$-wave scattering length $a_{\text{BX}}$ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.

arXiv comment14 pages, 7 figures

References in corpus (25)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Vortices in a Bose-Einstein Condensate
• Universality in Few-body Systems with Large Scattering Length
• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• Metastability and Coherence of Repulsive Polarons in a Strongly Interacting Fermi Mixture
• Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Universality in Three- and Four-Body Bound States of Ultracold Atoms
• Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium
• Universal Properties of the Four-Body System with Large Scattering Length
• Impurity in a Bose-Einstein condensate: study of the attractive and repulsive branch using quantum Monte-Carlo methods
• Impurity in a Bose-Einstein condensate and the Efimov effect
• Efimov Resonances in Ultracold Quantum Gases
• Microscopic Origin and Universality Classes of the Efimov Three-Body Parameter
• Physical Origin of the Universal Three-body Parameter in Atomic Efimov Physics
• Efimov physics in bosonic atom-trimer scattering
• The Bose polaron problem: effect of mass imbalance on binding energy
• Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient
• Spectra of helium clusters with up to six atoms using soft core potentials
• Generalized Efimov scenario for heavy-light mixtures
• Shallow Efimov tetramer as inelastic virtual state and resonant enhancement of the atom-trimer relaxation
• Energy and structural properties of $N$-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator
• Positronic complexes with unnatural parity
• Tetramer Bound States in Heteronuclear Systems
• Tetramers of two heavy and two light bosons