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arXiv:2507.01625 · Physical Review A

Impurity immersed in a two-component few-fermion mixture in a one-dimensional harmonic trap

Marek Teske, Tomasz Sowiński

Published Dec 10, 2025• 0 citations
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Abstract

We investigate a one-dimensional three-component few-fermion mixture confined in a parabolic external trap, where one component contains a single particle acting as an impurity. Focusing on the many-body ground state, we analyze how the interactions between the impurity and the other components influence the system's structure. For fixed interaction strengths within the mixture, we identify a critical interaction strength with the impurity for which the system undergoes a structural transition characterized by a substantial change in its spatial features. We explore this transition from the point of view of correlations and ground-state susceptibility. We remarkably find that this transition exhibits unique universality features not previously observed in other systems, highlighting novel many-body properties existing in multi-component fermionic mixtures.

DOI
10.1103/wgrg-q22s

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We investigate a one-dimensional three-component few-fermion mixture confined in a parabolic external trap, where one component contains a single particle acting as an impurity. Focusing on the many-body ground state, we analyze how the interactions between the impurity and the other components influence the system's structure. For fixed interaction strengths within the mixture, we identify a critical interaction strength with the impurity for which the system undergoes a structural transition characterized by a substantial change in its spatial features. We explore this transition from the point of view of correlations and ground-state susceptibility. We remarkably find that this transition exhibits unique universality features not previously observed in other systems, highlighting novel many-body properties existing in multi-component fermionic mixtures.
Ground-state properties of a few attractively interacting ultracold atoms of different mass confined in a one-dimensional harmonic trap are studied. The analysis is performed in terms of the noise correlation, which captures the two-particle correlations induced by the mutual interactions. Depending on the mass ratio between the components' atoms, the interparticle correlations change their properties significantly from a strong pairlike correlation to an almost uncorrelated phase. This change is accompanied by a simultaneous change in the structure of the many-body ground state. A crucial role of the quantum statistics is emphasized by comparing properties of the Fermi-Fermi mixture with a corresponding Fermi-Bose system.
We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [I. Brouzos and P. Schmelcher, Phys. Rev. Lett. 108, 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [G. Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012)].
The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external confinement, different scenarios of the spatial separation between components manifested by specific shapes of the density profiles can be obtained in the strong interaction limit. We find that the ground-state of the system undergoes a specific transition between orderings when the confinement is changed adiabatically from a uniform box to a harmonic oscillator shape. We study the properties of this transition in the framework of the finite-size scaling method adopted to few-body systems.
We present a numerical analysis of spin-1/2 fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an s-wave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity “breaks” a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.
We explore the ground-state properties of a single impurity immersed in a one-dimensional quantum droplet medium formed by a two-component Bose mixture. Relying on ab initio simulations, we demonstrate that tuning the impurity-droplet interactions allows to controllably reshape the droplets' density profiles and associated correlation patterns. For attractive impurity-medium couplings, the impurity becomes localized within the droplet, which exhibits a density hump at the vicinity of the impurity, while repulsive interactions facilitate phase separation. Comparing our many-body results with the appropriate extended Gross-Pitaevskii description, we find adequate agreement for the droplet density profiles, with the effective field approach systematically overestimating impurity localization. Following a release of the external trap, we unveil that the sign and magnitude of the interactions between the impurity and the droplet hosts dictate the response of the three-component setting, which experiences expansion unless strongly attractive intercomponent couplings are present. These results corroborate the role and presence of correlations in impurity-droplet mixtures and inspire future investigations on impurity physics for probing droplet configurations.
We study the ground-state properties of a two-component fermionic mixture effectively confined in a one-dimensional harmonic trap. We consider scenarios when numbers of particles in components are the same but particles have different masses. We examine whether it is possible to detect signatures of an unconventional pairing between opposite-spin fermions in the presence of attractive interactions. For this purpose, we perform the exact diagonalization of the many-body Hamiltonian and study the two-particle reduced density matrix. In agreement with expectations, we confirm that the many-body ground state is dominated by conventional pairs with a negligible total momentum for a small mass imbalance. Furthermore, we show that for sufficiently large mass ratios the domination of fundamentally different pairs is established and the Fulde-Ferrell-Larkin-Ovchinnikov phase is supported. Finally, we argue that the two mechanisms can coexist in the regime of moderate mass ratios. Due to the current experimental progress in obtaining ultracold fermionic systems in a few-body regime, our predictions may have some importance for the upcoming experiments.