Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

Abstract

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.

Many-body quantum dynamics and induced correlations of Bose polarons

“…In this case the Thomas-Fermi radius of the BEC is R TF ≈4.2 and the impurities are in a superposition of their spin components described by equation (2). We mainly analyze the case of two non-interacting (g II =0) impurities and briefly discuss the scenario of two weakly interacting impurity atoms in order to expose the effect of their mutual interaction in the dynamics.…”

“…For a relevant discussion on the lifetime of the above-described spectral features we refer the interested reader to [99]. It is also important to mention that in the weakly interacting impurity-BEC regime where the contrast is finite in the course of the evolution the spectral function A(ω f ) corresponds to the injection spectrum in the framework of the reverse rf spectroscopy [2,26].…”

Theory of excitation of Rydberg polarons in an atomic quantum gas

“…This gives the Ramsey contrast |S(t)|. Changing the phase of the final π rotation, the full signal S(t) = |S(t)|e iϕ(t) can be measured [45,56,57]. In Fig.…”

Critical slowdown of non-equilibrium polaron dynamics

“…Another example is the polaron quasiparticle, which was originally introduced by Landau [6] to describe the interaction of electrons with the atomic crystal of a solid, and has since been employed to understand a broad range of problems in condensed matter physics [7]. Experiments on imbalanced Fermi gases [8][9][10][11][12] provide an ideal quantum simulation platform for the Fermi polaron [13][14][15]. At the same time, the possibility to realize so-called Bose polarons in atomic Bose-Einstein condensates (BECs) [16,17] has raised further questions and ushered in new theoretical investigations [18][19][20][21][22][23][24][25][26][27][28][29][30], expanding our understanding of quantum impurity physics.…”