Binding of heavy fermions by a single light atom in one dimension

Abstract

We consider the problem of $N$ identical fermions interacting via a zero-range attractive potential with a lighter atom in one dimension. Using the few-body approach based on the Skorniakov and Ter-Martirosian equation, we determine the energies and the critical mass ratios for the emergence of the tetramer, pentamer, and hexamer. For large $N$, we solve the problem analytically by using the mean-field theory based on the Thomas-Fermi approximation. The system becomes bound when the heavy-to-light mass ratio exceeds a critical value which grows as $N^3$ at large $N$. We also employ a more sophisticated Hartree-Fock approach, which turns out to be equivalent to the Thomas-Fermi approximation for determining the energies, but provides a better description of the microscopic structure of the clusters.

6 pages, 2 figures

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Cited by in corpus (10)

• Quartet Superfluid in Two-dimensional Mass-imbalanced Fermi Mixtures
• Emergence of Crystalline Few-body Correlations in Mass-imbalanced Fermi Polarons
• Competing few-body correlations in ultracold Fermi polarons
• Self-binding of one-dimensional fermionic mixtures with zero-range interspecies attraction
• Heavy-light $N+1$ clusters of two-dimensional fermions
• From spontaneous to explicit symmetry breaking in a finite-sized system: Bosonic bound states of an impurity
• Effective theory for strongly attractive one-dimensional fermions
• Universal clusters in quasi-two-dimensional ultracold Fermi mixtures
• Several fermions strongly interacting with a heavy mobile impurity in a one-dimensional harmonic trap
• Absence of binding of heavy fermions by two light atoms in two dimensions