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arXiv:2312.05318 · Physical Review A

Momentum-dependent quasiparticle properties of the Fermi polaron from the functional renormalization group

Jonas von Milczewski, Richard Schmidt

Published Sep 9, 2024• 4 citations
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Abstract

We study theoretically the lifetimes of attractive and repulsive Fermi polarons, as well as the molecule at finite momentum in three dimensions. To this end, we develop a technique that allows for the computation of Green's functions in the whole complex frequency plane using exact analytical continuation within the functional renormalization group. The improved numerical stability and reduced computational cost of this method yield access to previously inaccessible momentum-dependent quasiparticle properties of low-lying excited states. While conventional approaches like the non-self-consistent T -matrix approximation method cannot determine these lifetimes, we are able to find the momentum-dependent lifetime at different interaction strengths of both the attractive and repulsive polaron as well as the molecule. At weak coupling our results confirm predictions made from effective Fermi liquid theory regarding the decay of the attractive polaron, and we demonstrate that Fermi liquidlike behavior extends far into the strong-coupling regime where the attractive polaron and molecule exhibit a p 4 momentum scaling in their decay widths. Our results offer an intriguing insight into the momentum-dependent quasiparticle properties of the Fermi polaron problem, which can be measured using techniques such as Raman transfer and Ramsey interferometry. Published by the American Physical Society 2024

DOI
10.1103/physreva.110.033309

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We study theoretically the lifetimes of attractive and repulsive Fermi polarons, as well as the molecule at finite momentum in three dimensions. To this end, we develop a technique that allows for the computation of Green's functions in the whole complex frequency plane using exact analytical continuation within the functional renormalization group. The improved numerical stability and reduced computational cost of this method yield access to previously inaccessible momentum-dependent quasiparticle properties of low-lying excited states. While conventional approaches like the non-self-consistent T -matrix approximation method cannot determine these lifetimes, we are able to find the momentum-dependent lifetime at different interaction strengths of both the attractive and repulsive polaron as well as the molecule. At weak coupling our results confirm predictions made from effective Fermi liquid theory regarding the decay of the attractive polaron, and we demonstrate that Fermi liquidlike behavior extends far into the strong-coupling regime where the attractive polaron and molecule exhibit a p 4 momentum scaling in their decay widths. Our results offer an intriguing insight into the momentum-dependent quasiparticle properties of the Fermi polaron problem, which can be measured using techniques such as Raman transfer and Ramsey interferometry. Published by the American Physical Society 2024
We present a systematic study of a mobile impurity immersed in a three-dimensional Fermi sea of fermions at finite temperature, by using the standard non-self-consistent many-body TTT-matrix theory that is equivalent to a finite-temperature variational approach with the inclusion of one-particle-hole excitation. The impurity spectral function is determined in the real-frequency domain, avoiding any potential errors due to the numerical analytic continuation in previous TTT-matrix calculations and the small spectral broadening parameter used in variational calculations. In the weak-coupling limit, we find that the quasiparticle decay rate of both attractive and repulsive polarons does not increase significantly with increasing temperature, and therefore Fermi polarons may remain well defined far above Fermi degeneracy. In contrast, near the unitary limit with strong coupling, the decay rate of Fermi polarons rapidly increases and the quasiparticle picture breaks down close to the Fermi temperature. We analyze in detail the recent ejection and injection radio-frequency (rf) spectroscopy measurements, performed at Massachusetts Institute of Technology (MIT) and at the European Laboratory for Non-Linear Spectroscopy (LENS), respectively. We show that the momentum average of the spectral function, which is necessary to account for the observed rf spectroscopy, has a sizable contribution to the width of the quasiparticle peak in spectroscopy. As a result, the measured decay rate of Fermi polarons could be significantly larger than the calculated quasiparticle decay rate at zero momentum. By taking this crucial contribution into account, we find that there is a reasonable agreement between theory and experiment for the lifetime of Fermi polarons in the strong-coupling regime, as long as they remain well defined.
We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi oscillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes to the lower-lying attractive branch. Thus, the theory-experiment agreement demonstrates that the quasiparticle lifetime is dominated by many-body dephasing within the upper repulsive branch rather than by relaxation from the upper branch itself. Our findings shed light on recent experimental observations of persistent repulsive correlations, and have important consequences for the nature and stability of the strongly repulsive Fermi gas.
The Fermi polaron, formed by an impurity interacting with a surrounding Fermi sea, exemplifies the canonical quasiparticle concept as a cornerstone in our description of quantum many-body systems across a wide range of energy scales. Experiments on atomic quantum gases have provided profound insights into the universal nature of the Fermi polaron. While most previous studies have focused on the case of zero impurity momentum, finite-momentum properties have remained largely uncharted. Here, we investigate the moving Fermi polaron by combining a novel Raman acceleration scheme with high-precision radio-frequency spectroscopy, exploring the quasiparticle dispersion relation over a wide range of momenta. We compare our measurements of energy shifts and spectral linewidths with a microscopic theory and reach quantitative agreement for all momenta. For low momenta, we find the energy of the moving polaron to be fully consistent with the Fermi liquid picture of a dressed particle with a constant effective mass. At high momenta, the polaron approaches the behavior of a weakly interacting bare particle, featuring small energy shifts and weak broadening. For intermediate momenta, broadening is generally larger and, most strikingly, the behavior differs for attractive and repulsive polarons. While the repulsive polaron exhibits a smooth connection between both regimes along with a monotonic change of the energy shift, the attractive case shows a peculiar non-monotonic behavior. With increasing momentum, the attractive polaron enters a regime where its energy deviates from the constant effective mass expression and broadening suddenly increases. By comparing this observation with theory, we show that this abrupt behavior coincides with the attractive polaron entering a molecule-hole continuum, where it is no longer the ground state. We interpret this as a motion-induced polaron-molecule transition.
A light impurity in a Fermi sea undergoes a transition from a polaron to a molecule for increasing interaction. We develop a method to compute the spectral functions of the polaron and molecule in a unified framework based on the functional renormalization group with full self-energy feedback. We discuss the energy spectra and decay widths of the attractive and repulsive polaron branches as well as the molecular bound state, and confirm the scaling of the excited-state decay rate near the transition. The quasiparticle weight of the polaron shifts from the attractive to the repulsive branch across the transition, while the molecular bound state has a very small residue characteristic for a composite particle. We propose an experimental procedure to measure the repulsive branch in a 6Li^{6}\mathrm{Li}6Li Fermi gas using rf spectroscopy and calculate the corresponding spectra.
We develop a non-Gaussian variational approach that enables us to study both equilibrium and far-from-equilibrium physics of the two-dimensional Fermi polaron. This method provides an unbiased analysis of the polaron-to-molecule phase transition without relying on truncations in the total number of particle-hole excitations. Our results—which include the ground-state energy and quasiparticle residue—are in qualitative agreement with the known Monte Carlo calculations. The main advantage of the non-Gaussian states compared to conventional numerical methods is that they enable us to explore long-time polaron evolution and, in particular, study various spectral properties accessible to both solid-state and ultracold atom experiments. We design two types of radiofrequency spectroscopies to measure polaronic and molecular spectral functions. Depending on the parameter regime, we find that these spectral functions and fermionic density profiles near the impurity either display long-lived oscillations between the repulsive and attractive polaron branches or exhibit fast relaxational dynamics to the molecular state.
How a polaron loses its quasiparticle coherence with increasing temperature is a long-standing open problem. Holstein addressed it in 1959 only in the extreme antiadiabatic, strong-coupling limit, while more recent numerically exact approaches are largely restricted to one dimension. Here we solve this problem on square and simple cubic lattices across the weak-, intermediate-, and strong-coupling regimes. We show that the polaron effective mass m∗m^*m∗ and inverse lifetime 1/τ1/τ1/τ increase monotonically with temperature until, at T∼0.5 ΩT \sim 0.5\,ΩT∼0.5Ω, the quasiparticle peak dissolves into a broad incoherent thermal continuum. The phonon frequency ΩΩΩ therefore defines a universal coherence scale, independent of dimensionality and coupling strength, validating Holstein's prediction far beyond the regime in which it was derived. These results follow from a finite-temperature generalization of the Momentum Average (MA) approximation, yielding a closed-form, diagrammatically derived self-energy that is asymptotically exact in the strong-coupling limit at all temperatures. Benchmark comparisons demonstrate excellent quantitative agreement of the resulting 1D spectral functions with the numerically exact Variational Exact Diagonalization-Finite-Temperature Lanczos Method (VED-FTLM) and finite-TTT Density Matrix Renormalization Group (DMRG).