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arXiv:2408.15007 · Physical review. B./Physical review. B

Exact polaron-polaron interactions between heavy impurities in a quantum Hall fluid

Jia Wang, Xia-Ji Liu, Hui Hu

Published Jul 14, 2025• 1 citation
arXivHTMLPDF

Abstract

We present an exact solution for effective polaron-polaron interactions between heavy impurities, mediated by a sea of noninteracting light fermions in the quantum Hall regime with highly degenerate Landau levels. For weak attraction between impurities and fermions, where only the manifold of lowest Landau levels is relevant, we obtain an analytical expression of mediated polaron-polaron interactions. Remarkably, polaron interactions are exactly zero when fermions in the lowest Landau levels outnumber heavy impurities. For strong attraction, different manifolds of higher Landau levels come into play and we derive a set of equations that can be used to numerically solve the mediated polaron interaction potential. We find that the potential vanishes when the distance R between impurities is larger than the magnetic length, but strongly diverges at short range following a Coulomb form − 1 / R . Our exact results of polaron-polaron interactions might be examined in cold-atom setups, where a system of Fermi polarons in the quantum Hall regime is realized with a synthetic gauge field or under fast rotation. Our predictions could also be useful to understand the effective interaction between exciton-polarons in electron-doped semiconductors under strong magnetic field.

DOI
10.1103/hjck-bn6j

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We present an exact solution for effective polaron-polaron interactions between heavy impurities, mediated by a sea of noninteracting light fermions in the quantum Hall regime with highly degenerate Landau levels. For weak attraction between impurities and fermions, where only the manifold of lowest Landau levels is relevant, we obtain an analytical expression of mediated polaron-polaron interactions. Remarkably, polaron interactions are exactly zero when fermions in the lowest Landau levels outnumber heavy impurities. For strong attraction, different manifolds of higher Landau levels come into play and we derive a set of equations that can be used to numerically solve the mediated polaron interaction potential. We find that the potential vanishes when the distance R between impurities is larger than the magnetic length, but strongly diverges at short range following a Coulomb form − 1 / R . Our exact results of polaron-polaron interactions might be examined in cold-atom setups, where a system of Fermi polarons in the quantum Hall regime is realized with a synthetic gauge field or under fast rotation. Our predictions could also be useful to understand the effective interaction between exciton-polarons in electron-doped semiconductors under strong magnetic field.
Abstract The notion of quasi-particles is essential for understanding the behaviour of complex many-body systems. A prototypical example of a quasi-particle is a polaron, formed by an impurity strongly interacting with a surrounding medium. Fermi polarons, created in a Fermi sea, provide a paradigmatic realization of this concept. Importantly, such quasi-particles interact with each other via the modulation of the medium. However, although quantum simulation experiments with ultracold atoms have substantially improved our understanding of individual polarons, the detection of their interactions has so far remained elusive. Here we report the observation of mediated interactions between Fermi polarons consisting of K impurities embedded in a Fermi sea of Li atoms. Our results confirm two predictions of Landau’s Fermi-liquid theory: the shift in polaron energy due to mediated interactions, which is linear in the concentration of impurities; and its sign inversion with impurity quantum statistics. For weak-to-moderate interactions between the impurities and the medium, our results agree with the static predictions of Fermi-liquid theory. For stronger impurity–medium interactions, we show that the observed behaviour at negative energies can be explained by a more refined many-body treatment including retardation and dressed molecule formation.
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.
We investigate the fundamental problem of a small density of bosonic impurities immersed in a dilute Bose gas at zero temperature. Using a rigorous perturbative expansion, we show that the presence of the surrounding medium enhances the repulsion between dressed bosonic impurities (polarons) in the regime of weak interactions. Crucially, this differs from prevailing theories based on Landau quasiparticles, which neglect the possibility of quantum degenerate impurities and predict an exchange-induced attraction. We furthermore show that the polaron-polaron interactions are strongly modified if the medium chemical potential rather than the density is held fixed, such that the medium-induced attraction between thermal impurities becomes twice the expected Landau effective interaction. Our work provides a possible explanation for the differing signs of the polaron-polaron interactions observed in experiments across cold atomic gases and two-dimensional semiconductors, and it has important implications for theories of quasiparticles and quantum mixtures in general.
Mediated interactions between quasiparticles lie at the heart of Landau Fermi-liquid theory, yet their behavior in the strongly correlated regime is not fully understood. Motivated by recent experiments [Nat. Phys. 20, 68--73 (2024)], we investigate mediated interactions between quasiparticles emerging from a Fermi sea---Fermi polarons---using zero-temperature quantum Monte Carlo methods. Our main result is that the Landau interaction between polarons remains repulsive in the strongly interacting regime for any coupling strength in the polaronic branch, in contrast to the downward trend observed experimentally near resonance. Deep in the short-range universal regime, our results are insensitive to the microscopic details of the interaction potential, providing robust evidence for the sign of the ground-state induced interaction. In addition, we determine the real-space interaction between static impurities, recovering a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like behavior at weak coupling and the nonperturbative Born-Oppenheimer result at strong coupling. More broadly, our results establish a microscopic benchmark for how Landau quasiparticle interactions survive beyond the perturbative regime of strongly correlated quantum matter.
Bose polarons, quasiparticles composed of mobile impurities surrounded by cold Bose gas, can experience strong interactions mediated by the many-body environment and form bipolaron bound states. Here we present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a nonperturbative theory and complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings. Our approach is based on a mean-field theory that accounts for deformations of the superfluid by the impurities and in this way minimizes quantum fluctuations. The mean-field equations are solved exactly in the Born-Oppenheimer approximation, leading to an analytic expression for the interaction potential of heavy polarons, which is found to be in excellent agreement with quantum Monte Carlo (QMC) results. In the strong coupling limit, the potential substantially deviates from the exponential form valid for weak coupling and has a linear shape at short distances. Taking into account the leading-order Born-Huang corrections, we calculate bipolaron binding energies for impurity-boson mass ratios as low as 3 and find excellent agreement with QMC results.
We consider the behavior of a small density of mobile impurities (polarons) immersed in a quantum gas, a generic scenario that can be realized in cold atomic gases, liquid helium mixtures, and doped semiconductors. We present a unified theoretical framework for understanding polaron quasiparticles beyond the single-impurity limit, and we identify two key factors that control the polaron-polaron interactions: (i) the statistics of the impurities, including whether or not they are degenerate, and (ii) the constraints on the medium response, i.e., whether the medium density or chemical potential is held fixed. By constructing wave functions for two bosonic, fermionic, or distinguishable impurities immersed in a Bose or Fermi gas, we derive rigorous results for the polaron interactions in the limit of weak impurity-medium coupling. We furthermore obtain an exact relationship between the polaron interactions at fixed medium density and at fixed chemical potential, a result which is valid for arbitrary interaction strength. Our work provides an important guide for understanding experiments, and it acts as a starting point for future strong-coupling theories of polaron interactions that capture all of the effects identified in this work.