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arXiv:2207.04742 · SciPost Physics

Self-binding of one-dimensional fermionic mixtures with zero-range interspecies attraction

Jules Givois, Andrea Tononi, Dmitry S. Petrov

Published May 3, 2023• 4 citations
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Abstract

For sufficiently large mass ratios the attractive exchange force caused by a single light atom interacting with a few heavy identical fermions can overcome their Fermi degeneracy pressure and bind them into an N+1 N + 1 cluster. Here, by using a mean-field approach valid for large N N , we find that N+1 N + 1 clusters can attract each other and form a self-bound charge density wave, the properties of which we fully characterize. Our work shows that there are no fundamental obstacles for having self-bound states in fermionic mixtures with zero-range interactions.

DOI
10.21468/scipostphys.14.5.091

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Heavy-light N+1N+1N+1 clusters of two-dimensional fermions
We study binding of N N identical heavy fermions by a light atom in two dimensions assuming zero-range attractive heavy-light interactions. By using the mean-field theory valid for large N N we show that the N+1 N + 1 cluster is bound when the mass ratio exceeds 1.074N^2 1.074 N 2 . The mean-field theory, being scale invariant in two dimensions, predicts only the shapes of the clusters leaving their sizes and energies undefined. By taking into account beyond-mean-field effects we find closed-form expressions for these quantities. We also discuss differences between the Thomas-Fermi and Hartree-Fock approaches for treating the heavy fermions.
We consider the problem of NNN 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 NNN, 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 N3{N}^{3}N3 at large NNN. 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.
We study analytically and numerically the binding properties, in particular the ground state, of the so-called (2+1)(2+1)(2+1)-fermion system, which is a three-dimensional system of two identical fermions interacting with a third particle of different species through a zero-range interaction. We model the system with a specific self-adjoint point interaction Hamiltonian recently constructed in the mathematical literature. First we characterize the internal symmetry of the bound states in the attractive case. Then we show that the system confines in a precise regime of masses and that its ground-state energy stays finite as the mass becomes close to the critical point of the collapse of the system.
Diffusion Monte Carlo calculations on the possibility of having self-bound one-dimensional droplets of SU(6) $\ifmmode\times\else\texttimes\fi{}$ SU(2) ultracold fermionic mixtures are presented. We found that, even though arrangements with attractive interactions with only two spin types are not self-bound, mixtures with at least three kinds of fermions form stable small drops. However, that stabilization decreases for very tight confinements, where a universal behavior is found for Fermi-Fermi and Fermi-Boson clusters including attractive and repulsive interactions.
We study the emergence of universal tetramer and pentamer bound states in the two-dimensional (N+1) system, which consists of N identical heavy fermions interacting with a light atom. We show that the critical heavy-light mass ratio to support a (3+1) tetramer below the trimer threshold is 3.38, and to support a (4+1) pentamer below the tetramer threshold is 5.14. While the ground state tetramer and pentamer are both with zero total angular momentum, they exhibit very different density distributions and correlations in momentum space, due to their distinct angular momentum decompositions in the dimer-fermion frame. These universal bound states can be accessible by a number of Fermi-Fermi mixtures now realized in cold atoms laboratories, which also suggest novel few-body correlations dominant in their corresponding many-body systems.
We study the formation of bound states in a binary mixture of a few bosons in small square optical lattices. Using the exact diagonalization method, we find that bound clusters of all available bosons can form. We provide a comprehensive numerical examination of these bound states for a wide range of repulsive intraspecies and attractive interspecies interactions. In contrast to binary mixtures in one-dimensional chains, we reveal that the binding energy of the clusters shows a nonmonotonic dependence on the interspecies interaction strengths for small tunneling rates, developing a local minimum for intermediate attractive interactions. The findings of this work highlight the difference between the binding mechanisms of binary bosonic mixtures in one- and higher-dimensional lattices.