We study the behaviour of weakly bound clusters and their relation to the well-known three-body Efimov states. We adopt a model to describe the universal behaviour of strongly interacting bosonic systems, and we test its validity by reproducing predictions of three- and four-body universal states. Then, we extend our study to larger systems and identify a series of universal cluster states that can be qualitatively interpreted as adding one particle at a time to an Efimov trimer. The properties of these cluster states and their experimental signatures are discussed.We study the behaviour of weakly bound clusters and their relation to the well-known three-body Efimov states. We adopt a model to describe the universal behaviour of strongly interacting bosonic systems, and we test its validity by reproducing predictions of three- and four-body universal states. Then, we extend our study to larger systems and identify a series of universal cluster states that can be qualitatively interpreted as adding one particle at a time to an Efimov trimer. The properties of these cluster states and their experimental signatures are discussed.

arXiv:0909.4056Journal of Physics B Atomic Molecular and Optical PhysicsMay 6, 2010111 citations

Five- and Six-Body Resonances Tied to an Efimov Trimer

Javier von Stecher

We explore the properties of weakly bound bosonic states in the strongly interacting regime. Combining a correlated-Gaussian basis set expansion with a complex-scaling method, we extract the energies and structural properties of bosonic cluster states with N ≤ 6 for different two-body potentials. The identification of five- and six-body resonances attached to the first-excited-Efimov trimer provides strong support to the premise of Efimov universality in bosonic systems. Our study also reveals a rich structure of bosonic cluster states. Besides the lowest cluster states that behave as bosonic droplets, we identify cluster states weakly bound to one or two atoms forming effective cluster-atom dimers and cluster-atom-atom "trimers." The experimental signatures of these cluster states are discussed.We explore the properties of weakly bound bosonic states in the strongly interacting regime. Combining a correlated-Gaussian basis set expansion with a complex-scaling method, we extract the energies and structural properties of bosonic cluster states with N ≤ 6 for different two-body potentials. The identification of five- and six-body resonances attached to the first-excited-Efimov trimer provides strong support to the premise of Efimov universality in bosonic systems. Our study also reveals a rich structure of bosonic cluster states. Besides the lowest cluster states that behave as bosonic droplets, we identify cluster states weakly bound to one or two atoms forming effective cluster-atom dimers and cluster-atom-atom "trimers." The experimental signatures of these cluster states are discussed.

arXiv:1106.2319Physical Review LettersNov 11, 201165 citations

Many-body clusters in boson systems

R. A. Smith

Physics Letters BAug 1, 197619 citations

Energetics and structural properties of bosonic three-dimensional clusters near threshold

D. Blume, Gabriel Hanna

Bulletin of the American Physical SocietyMay 19, 20060 citations

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

D. Blume

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 $N\ensuremath{-}1$ 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 $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ 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.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 $N\ensuremath{-}1$ 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 $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ 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:1901.03542Physical Review AJan 16, 201912 citations

N

-body clusters consisting of $N\ensuremath{-}1$ 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 $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ 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.