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arXiv:2607.20075

Two- and three-body bound states in one-dimensional Fermi bipolaron with three-body interaction

Orest Hryhorchak, V. G. Pastukhov

Published Jul 22, 2026• 0 citations
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Abstract

We discuss the ground-state properties of two bosonic (or spin-1/2 fermionic in a singlet spin state) impurities immersed in a one-dimensional ideal Fermi gas with only the three-body contact interaction accounted for. Despite its simplicity, the considered model is found to demonstrate a variety of medium-induced few-body bound states. Particularly, using variational calculations with trial wave functions that correctly take into account one particle-hole excitation, we predict the emergence of a dimer state and several trimer states over a wide range of the three-body coupling parameter.

DOI
10.48550/arxiv.2607.20075

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Bipolaron in one-dimensional SU(3)SU(3)SU(3) fermions with three-body interaction
The properties of the one-dimensional SU(3)SU(3)SU(3) population-imbalanced fermions are discussed. The system is assumed to be in the two-body resonance where all two-body scattering lengths diverge, and the only interaction between fermions that is taken into account is the short-range three-body one. In particular, we consider the situation when only one `flavor' of fermions is macroscopically occupied, and there are exactly two atoms of two others. This system supports the trimer and the medium-induced dimer states studied here in detail and shows evidence of color superfluidity.
We investigate numerically the problem of few (one or two) noninteracting spin-1/21/21/2 fermions in a shallow harmonic trap coupled via contact repulsive interactions to a uniform one-dimensional bath of lattice bosons, described by the Bose-Hubbard model. Through extensive density-matrix renormalization group calculations, we extract the binding energy and the effective mass of quasiparticles, including dressed impurities (polarons) and their two-body bound states (bipolarons), emerging from the effective nonlocal Casimir interaction between the impurities. We show that the mixture exhibits rather different pairing behaviors depending on the singlet vs triplet spin state configurations of the two fermions. For opposite spin states, bipolarons are found for any finite value of the impurity-bath coupling. In particular, in the strong-coupling regime their binding energy reduces to that of a single polaron, provided the boson-boson repulsion is not too weak. For equal spin states, we show that bipolarons emerge only beyond a critical strength of the Bose-Fermi interaction and their effective mass grows rapidly approaching the strong-coupling regime.
In this paper, we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length aaa. Working up to order a3{a}^{3}a3, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.
We briefly review some current theoretical and experimental aspects of the problem of a single spinless impurity in a 3D polarised atomic Fermi gas at zero temperature where the interactions can be tuned using a wide Feshbach resonance. We show that various few-body states in vacuum composed of the impurity and background gas atoms (single impurity, dimer, trimer, tetramer) give rise to corresponding dressed states ({\em polaron}, {\em dimeron}, {\em trimeron}, {\em tetrameron}) in the gas and inherit many of their characteristics. We study the ground state focussing on the choice of wave function and its properties. We raise a few unsolved problems: whether the polaron and dimeron are really separate branches, what other few-body states might exist, the nature of the groundstate for large numbers of particle-hole pairs and why is the polaron ansatz so good. We then turn to the excited states, and to the calculation of the effective mass. We examine the bounds on the effective mass and raise a conjecture about that of composite quasiparticle states.
We solve the three-boson problem with contact two-and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies.Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions.Combining these results with our three-body analytics, we extract the three-dimer scattering length close to the dimer-dimer zero crossing.In both considered cases the three-dimer interaction turns out to be repulsive.Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.