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arXiv:2309.07019 · SciPost Physics

Polaron spectroscopy of interacting Fermi systems: Insights from exact diagonalization

Ivan Amelio, Nathan Goldman

Published Feb 26, 2024• 14 citations
arXivHTMLPDF

Abstract

Immersing a mobile impurity into a many-body quantum system represents a theoretically intriguing and experimentally effective way of probing its properties. In this work, we study the polaron spectral function in various environments, within the framework of Fermi-Hubbard models. Inspired by possible realizations in cold atoms and semiconductor heterostructures, we consider different configurations for the background Fermi gas, including charge density waves, multiple Fermi seas and pair superfluids. While our calculations are performed using an exact-diagonalization approach, hence limiting our analysis to systems of few interacting Fermi particles, we identify robust spectral features supported by theoretical results. Our work provides a benchmark for computations based on mean-field approaches and reveal surprising features of polaron spectra, inspiring new theoretical investigations.

DOI
10.21468/scipostphys.16.2.056

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Immersing a mobile impurity into a many-body quantum system represents a theoretically intriguing and experimentally effective way of probing its properties. In this work, we study the polaron spectral function in various environments, within the framework of Fermi-Hubbard models. Inspired by possible realizations in cold atoms and semiconductor heterostructures, we consider different configurations for the background Fermi gas, including charge density waves, multiple Fermi seas and pair superfluids. While our calculations are performed using an exact-diagonalization approach, hence limiting our analysis to systems of few interacting Fermi particles, we identify robust spectral features supported by theoretical results. Our work provides a benchmark for computations based on mean-field approaches and reveal surprising features of polaron spectra, inspiring new theoretical investigations.
A mobile impurity immersed in a noninteracting Fermi sea is dressed by the gapless particle-hole excitations of the fermionic medium. This conventional Fermi-polaron setting is well described by the so-called ladder approximation, which consists of neglecting impurity-hole scattering processes. In this work, we analyze polaron formation in the context of insulating states of matter, considering increasing levels of correlation in the medium: band insulators originating from external periodic potentials, spontaneously formed charge density waves, and a Fermi-Hubbard system undergoing a metal-Mott insulator transition. The polaron spectral function is shown to exhibit striking signatures of the underlying fermionic background, such as the single-particle band gap, particle-hole symmetry and the transition to the Mott state. These signatures are identified within the framework of the Chevy ansatz, i.e., upon restricting the Hilbert space to single particle-hole excitations. Interestingly, we find that the ladder approximation is inaccurate in these band systems, due to the fact that the particle and hole scattering phase spaces are comparable. Our results provide a step forward in the understanding of polaron formation in correlated many-body media, which are relevant to both cold-atom and semiconductor experiments. Published by the American Physical Society 2024
In this work we provide a comprehensive review of theoretical and experimental studies of the properties of polarons formed by mobile impurities strongly interacting with quantum many-body systems. We present a unified perspective on the universal concepts and theoretical techniques used to characterize polarons in two distinct platforms, ultracold atomic gases and atomically-thin transition metal dichalcogenides, which are linked by many deep parallels. We review polarons in both fermionic and bosonic environments, highlighting their similarities and differences including the intricate interplay between few- and many-body physics. Various kinds of polarons with long-range interactions or in magnetic backgrounds are discussed, and the theoretical and experimental progress towards understanding interactions between polarons is described. We outline how polaron physics, regarded as the low density limit of quantum mixtures, provides fundamental insights regarding the phase diagram of complex condensed matter systems. Furthermore, we describe how polarons may serve as quantum sensors of many-body physics in complex environments. Our work highlights the open problems, identifies new research directions and provides a comprehensive framework for this rapidly evolving research field.
The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.
We study the ground state and excitations of a one-dimensional trapped polarized Fermi gas interacting with a single impurity. First, we study the tunneling dynamics of the impurity through a potential barrier, such as one effectively created by a double-well trap. To this end, we perform an exact diagonalization of the full few-body Hamiltonian and analyze the results in a local-density approximation. Off-diagonal and one-particle correlation matrices are studied and are shown to be useful for discerning between different symmetries of the states. Second, we consider a radio-frequency spectroscopy of our system and the resulting spectral function. These calculations can motivate future experiments, which can provide further insight into the physics of a Fermi polaron.
The remarkable single-particle control of individual ions combined with the versatility of ultracold atomic gases makes hybrid ion-atom systems an exciting new platform for quantum simulation of few- and many-body quantum physics. Here, we study theoretically the properties of a mobile ion immersed in a quantum degenerate gas of fermionic atoms. Using an effective low-energy atom-ion interaction together with a well-established approach that includes exactly two-body correlations, we calculate the full spectral response of the ion and demonstrate the existence of several quasiparticle branches, which are charged analogs of the Fermi polaron observed in neutral atomic gases. Due to the long-range nature of the atom-ion interaction, these ionic Fermi polarons have several properties distinct from their neutral counterparts such as the simultaneous presence of several stable states and smooth transitions from repulsive to attractive polarons with increasing interaction strength. Surprisingly, the residue of the ionic polaron is shown to increase with the Fermi density for fixed interaction strength, which is in marked contrast with the neutral polaron. The properties of the ionic polaron approach that of the neutral polaron only in the low-density limit where the average interparticle spacing is larger than the characteristic length of the atom-ion interaction. We finally analyze the effects of the Fermi gas on the molecular ions, which are bound atom-dimer states.
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.