Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1507.08116 · New Journal of Physics

Three-body bound states of two bosonic impurities immersed in a Fermi sea in 2D

F F Bellotti, T. Frederico, M T Yamashita, D V Fedorov, A S Jensen, Nikolaj Thomas Zinner

Published Apr 18, 2016• 10 citations
arXivHTMLPDF

Abstract

We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials and the problem is solved in momentum space. The two impurities can attach to a fermion from the sea and form three-body bound states. The energy of these states increase as function of the Fermi momentum k F , leading to three-body bound states below the Fermi energy. The fate of the states depends highly on two- and three-body thresholds and we find evidence of medium-induced Borromean-like states in 2D. The corrections due to particle-hole fluctuations in the Fermi sea are considered in the three-body calculations and we show that in spite of the fact that they strongly affect both the two- and three-body systems, the correction to the point at which the three-body states cease to exist is small.

DOI
10.1088/1367-2630/18/4/043023

Related papers

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

Orest Hryhorchak, V. G. Pastukhov

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.

arXiv:2607.20075•Jul 22, 2026•0 citations

Three-body bound states of two bosons and one impurity in one dimension

Yanxia Liu, Yi-Cong Yu, Shu Chen

We investigate one-dimensional three-body systems composed of two identical bosons and one mass-imbalanced atom (impurity) with attractive two-body and three-body zero-range interactions. In the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio and the ratio of intra- and intercomponent interaction strength via direct calculation of Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is different from other two identical particles. We obtain the binding energies together with the corresponding wave functions. When the mass of impurity atom is very large, there are at most three three-body bound states. In the presence of three-body zero-range interaction, we reveal that weak three-body interaction will not always induce one more three-body bound state. At some special parameter points, arbitrary small three-body interaction can generate one more three-body bound state. This corresponds to the transition of the number of three-body bound states induced only by two-body attractive interaction.

arXiv:2104.14111•Physical Review A•Sep 2, 2021•6 citations

Scattering of two heavy Fermi polarons: Resonances and quasibound states

Tilman Enss, Binh Tran, M. Rautenberg +6 more

Impurities in a Fermi sea, or Fermi polarons, experience a Casimir interaction induced by quantum fluctuations of the medium. When there is short-range attraction between impurities and fermions, also the induced interaction between two impurities is strongly attractive at short distance and oscillates in space for larger distances. We theoretically investigate the scattering properties and compute the scattering phase shifts and scattering lengths between two heavy impurities in an ideal Fermi gas at zero temperature. While the induced interaction between impurities is weakly attractive for weak impurity-medium interactions, we find that impurities strongly and attractively interacting with the medium exhibit resonances in the induced scattering with a sign change of the induced scattering length and even strong repulsion. These resonances occur whenever a three-body Efimov bound state appears at the continuum threshold. At energies above the continuum threshold, we find that the Efimov state in medium can turn into a quasibound state with a finite decay width.

arXiv:2009.03029•Physical Review A•Dec 17, 2020•26 citations

Ground state of a tightly bound composite dimer immersed in a Fermi sea

Christophe Mora, Frédéric Chevy

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 $a$. Working up to order ${a}^{3}$, 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.

arXiv:0908.0608•Physical Review A•Sep 10, 2009•99 citations

Multi three-body bound states in one dimensional Bose gases

Yanxia Liu, Yi-Cong Yu, Shu Chen

We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio via the direct calculation of the Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is not equal to another two identical particles. We can obtain not only the binding energies but also the corresponding wave functions. When the mass of impurity atom is vary large, there are at most three three-body bound states. We then study the effect of three-body zero-range interaction and unveil that it can induces one more three-body bound state at a certain region of coupling strength ratio under a fixed mass ratio.

•Apr 29, 2021•0 citations

Scaling and universality in two dimensions: three-body bound states with short-ranged interactions

F F Bellotti, T. Frederico, M T Yamashita +3 more

The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle and the two different two-body subsystems are characterized by two-body energies and masses. The three-body energy in units of one of the two-body energies is a universal function of the other two-body energy and the mass ratio. We derive convenient analytical formulae for calculations of the three-body energy as a function of these two independent parameters and exhibit the results as universal curves. In particular, we show that the three-body system can have any number of stable bound states. When the mass ratio of the distinct to identical particles is greater than 0.22, we find that at most two stable bound states exist, while for two heavy and one light mass an increasing number of bound states is possible. The specific number of stable bound states depends on the ratio of two-body bound state energies and on the mass ratio, and we map out an energy–mass phase diagram of the number of stable bound states. Realizable systems of both fermions and bosons are discussed in this framework.

arXiv:1107.3017•Journal of Physics B Atomic Molecular and Optical Physics•Sep 26, 2011•29 citations
We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials and the problem is solved in momentum space. The two impurities can attach to a fermion from the sea and form three-body bound states. The energy of these states increase as function of the Fermi momentum k F , leading to three-body bound states below the Fermi energy. The fate of the states depends highly on two- and three-body thresholds and we find evidence of medium-induced Borromean-like states in 2D. The corrections due to particle-hole fluctuations in the Fermi sea are considered in the three-body calculations and we show that in spite of the fact that they strongly affect both the two- and three-body systems, the correction to the point at which the three-body states cease to exist is small.
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.
We investigate one-dimensional three-body systems composed of two identical bosons and one mass-imbalanced atom (impurity) with attractive two-body and three-body zero-range interactions. In the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio and the ratio of intra- and intercomponent interaction strength via direct calculation of Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is different from other two identical particles. We obtain the binding energies together with the corresponding wave functions. When the mass of impurity atom is very large, there are at most three three-body bound states. In the presence of three-body zero-range interaction, we reveal that weak three-body interaction will not always induce one more three-body bound state. At some special parameter points, arbitrary small three-body interaction can generate one more three-body bound state. This corresponds to the transition of the number of three-body bound states induced only by two-body attractive interaction.
Impurities in a Fermi sea, or Fermi polarons, experience a Casimir interaction induced by quantum fluctuations of the medium. When there is short-range attraction between impurities and fermions, also the induced interaction between two impurities is strongly attractive at short distance and oscillates in space for larger distances. We theoretically investigate the scattering properties and compute the scattering phase shifts and scattering lengths between two heavy impurities in an ideal Fermi gas at zero temperature. While the induced interaction between impurities is weakly attractive for weak impurity-medium interactions, we find that impurities strongly and attractively interacting with the medium exhibit resonances in the induced scattering with a sign change of the induced scattering length and even strong repulsion. These resonances occur whenever a three-body Efimov bound state appears at the continuum threshold. At energies above the continuum threshold, we find that the Efimov state in medium can turn into a quasibound state with a finite decay width.
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 investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio via the direct calculation of the Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is not equal to another two identical particles. We can obtain not only the binding energies but also the corresponding wave functions. When the mass of impurity atom is vary large, there are at most three three-body bound states. We then study the effect of three-body zero-range interaction and unveil that it can induces one more three-body bound state at a certain region of coupling strength ratio under a fixed mass ratio.
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle and the two different two-body subsystems are characterized by two-body energies and masses. The three-body energy in units of one of the two-body energies is a universal function of the other two-body energy and the mass ratio. We derive convenient analytical formulae for calculations of the three-body energy as a function of these two independent parameters and exhibit the results as universal curves. In particular, we show that the three-body system can have any number of stable bound states. When the mass ratio of the distinct to identical particles is greater than 0.22, we find that at most two stable bound states exist, while for two heavy and one light mass an increasing number of bound states is possible. The specific number of stable bound states depends on the ratio of two-body bound state energies and on the mass ratio, and we map out an energy–mass phase diagram of the number of stable bound states. Realizable systems of both fermions and bosons are discussed in this framework.