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arXiv:2609.03656

Finite-temperature mass gap and quench dynamics of mobile impurities in a Fermi gas

Baihua Gong

Published Sep 3, 2026• 0 citations
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Abstract

Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation $Δ(T)=2U_F\tanh[Δ(T)/4k_B T]$, with $U_F=k_F^2/2M$ and $M$ the impurity mass. This equation admits a nonzero solution below the characteristic temperature $T^*=U_F/(2k_B)$ and closes as $(T^*-T)^{1/2}$. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response $S(t)$ after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above $T^*$. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.

DOI
10.48550/arxiv.2609.03656

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Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation Δ(T)=2UFtanh⁡[Δ(T)/4kBT]Δ(T)=2U_F\tanh[Δ(T)/4k_B T]Δ(T)=2UF​tanh[Δ(T)/4kB​T], with UF=kF2/2MU_F=k_F^2/2MUF​=kF2​/2M and MMM the impurity mass. This equation admits a nonzero solution below the characteristic temperature T∗=UF/(2kB)T^*=U_F/(2k_B)T∗=UF​/(2kB​) and closes as (T∗−T)1/2(T^*-T)^{1/2}(T∗−T)1/2. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response S(t)S(t)S(t) after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above T∗T^*T∗. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.
We present a unified theory that connects the quasiparticle picture of Fermi polarons for mobile impurities to the Anderson orthogonality catastrophe for static impurities. By operator reordering of the underlying many-body Hamiltonian, we obtain a modified fermionic dispersion relation that features a recoil-induced energy gap, which we call the "mass gap." We show that the resulting mean-field Hamiltonian exhibits an in-gap state for finite impurity mass, which takes a key role in Fermi polaron and molecule formation. We identify the mass gap as the microscopic origin of the quasiparticle weight of Fermi polarons and derive a power-law scaling of the weight with the impurity-to-fermion mass ratio. The associated in-gap state is shown to give rise to the emergence of the polaron-to-molecule transition away from the limiting case of the Anderson orthogonality catastrophe in which the transition is absent.
We extend the functional determinant approach (FDA), previously restricted to static impurities, to the case of finite-mass impurities by using the mass-gap description of Fermi polarons [Phys. Rev. Lett. 135, 193401 (2025)]. The quadratic structure of the mass-gap model enables the exact evaluation of many-body spectra and Ramsey dynamics for mobile impurities. We show that this mass-gap FDA smoothly interpolates between the Fermi-edge singularity for infinitely heavy impurities and the emergence of quasiparticle weight for finite impurity mass. Our results demonstrate that the mass-gap FDA provides a transparent and computationally efficient framework to describe the quantum dynamics of mobile impurities.
In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by [Formula: see text]. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures [Formula: see text] where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid [Formula: see text]He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.
Mobile impurities in cold atomic gases constitute a new platform for investigating polaron physics. Here we show that when impurity atoms interact with a two-dimensional Fermi gas with quadratic band touching, the polaron picture may either hold or break down depending on the particle-hole asymmetry of the band structure. If the hole band has a smaller effective mass than the particle band, the quasiparticle is stable and its diffusion coefficient varies with temperature as $D(T)\ensuremath{\propto}{ln}^{2}T$. If the hole band has larger mass, the quasiparticle weight vanishes at low energies due to an emergent orthogonality catastrophe. In this case we map the problem onto a set of one-dimensional channels and use conformal field theory techniques to obtain $D(T)\ensuremath{\propto}{T}^{\ensuremath{\nu}}$ with an interaction-dependent exponent $\ensuremath{\nu}$. The different regimes can be detected in the nonequilibrium expansion dynamics of an initially confined impurity.
We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using the exact functional determinant approach. We describe the Fermi superfluid through the conventional Bardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap on quasiparticle properties revealed by the two spectroscopies. The energy cost for pair breaking prevents Anderson's orthogonality catastrophe that occurs in a noninteracting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity limit. Hence, we rigorously confirm the remarkable features such as dark continuum, molecule-hole continuum, and repulsive polaron. For a magnetic impurity scattering at finite temperature, we predict additional resonances related to the subgap Yu-Shiba-Rusinov bound state, whose positions can be used to measure the superfluid pairing gap. For a nonmagnetic scattering at zero temperature, we surprisingly find undamped repulsive polarons. These exact results might be readily observed in quantum gas experiments with Bose-Fermi mixtures that have a large-mass ratio.
We study the problem of a mobile impurity of mass MMM interacting {\sl via} a s-wave broad or narrow Feshbach resonance with a Fermi sea of particles of mass mmm. Truncating the Hilbert space to at most one pair of particle-hole excitations of the Fermi sea, we determine ground state properties of the polaronic branch other than its energy, namely the polaron quasiparticle residue ZZZ, and the impurity-to-fermion pair correlation function G(x)G(x)G(x). We show that G(x)G(x)G(x) deviates from unity at large distances as −(A_4+B_4cos⁡2k_Fx)/(k_Fx)4-(A\_4+B\_4 \cos 2 k\_F x)/(k\_F x)^4−(A_4+B_4cos2k_Fx)/(k_Fx)4, where k_Fk\_Fk_F is the Fermi momentum; since A_4>0A\_4>0A_4>0 and B_4>0B\_4>0B_4>0, the polaron has a diverging rms radius and exhibits Friedel-like oscillations. In the weakly attractive limit, we obtain analytical results, that in particular detect the failure of the Hilbert space truncation for a diverging mass impurity, as expected from Anderson orthogonality catastrophe; at distances between ∼1/k_F\sim 1/k\_F∼1/k_F and the asymptotic distance where the 1/x41/x^41/x4 law applies, they reveal that G(x)G(x)G(x) exhibits an intriguing multiscale structure.