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arXiv:2311.11554 · Physical Review A

Spectral function of Fermi polarons at finite temperature from a self-consistent many-body T -matrix approach in real frequency

Hui Hu, Xia-Ji Liu

Published Jun 6, 2024• 2 citations
arXivHTMLPDF

Abstract

We theoretically examine the finite-temperature spectral function of Fermi polarons in three dimensions by using a self-consistent many-body $T$-matrix theory in real frequency. In comparison with the previous results from a non-self-consistent many-body $T$-matrix approach, we show that the treatment of self-consistency in the impurity Green's function leads to notable changes in almost all the dynamical quantities, including the vertex function, impurity self-energy, and spectral function. Eventually, it gives rise to quantitatively different predictions for the measurable radio-frequency spectrum and Raman spectrum at finite temperature. Using the recent spectroscopic measurements as a benchmark, we find that the self-consistent many-body $T$-matrix theory somehow provides a better explanation for the experimental data. The notable difference in the predictions from the non-self-consistent and self-consistent theories suggests that more accurate theoretical descriptions are needed in order to fully account for the current spectroscopic observations on Fermi polarons.

DOI
10.1103/physreva.109.063313

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We theoretically examine the finite-temperature spectral function of Fermi polarons in three dimensions by using a self-consistent many-body TTT-matrix theory in real frequency. In comparison with the previous results from a non-self-consistent many-body TTT-matrix approach, we show that the treatment of self-consistency in the impurity Green's function leads to notable changes in almost all the dynamical quantities, including the vertex function, impurity self-energy, and spectral function. Eventually, it gives rise to quantitatively different predictions for the measurable radio-frequency spectrum and Raman spectrum at finite temperature. Using the recent spectroscopic measurements as a benchmark, we find that the self-consistent many-body TTT-matrix theory somehow provides a better explanation for the experimental data. The notable difference in the predictions from the non-self-consistent and self-consistent theories suggests that more accurate theoretical descriptions are needed in order to fully account for the current spectroscopic observations on Fermi polarons.
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.
By using a non-self-consistent many-body TTT-matrix theory, we calculate the finite-temperature Raman spectroscopy of a mobile impurity immersed in a Fermi bath in three dimensions. The dependencies of the Raman spectrum on the transferred momentum, temperature, and impurity-bath interaction are discussed in detail. We confirm that the peak in the Raman spectrum shows a weaker dependence on the impurity concentration than that in the radio-frequency spectroscopy due to the nonzero transferred momentum, as anticipated. We compare our theoretical prediction with the recent measurement by Gal Ness et al. [G. Ness, C. Shkedrov, Y. Florshaim, O. K. Diessel, J. von Milczewski, R. Schmidt, and Y. Sagi, Phys. Rev. X 10, 041019 (2020)] without any adjustable parameters. At weak coupling, we find a good quantitative agreement. However, close to the Feshbach resonance the agreement becomes worse. At strong coupling, we find that an unrealistic Fermi bath temperature might be needed to account for the experimental data.
Abstract By using both diagrammatic theory and Chevy ansatz approach, we derive an exact set of equations, which determines the spectral function of Fermi polarons with multiple particle-hole excitations at nonzero temperature. In the diagrammatic theory, we find out the complete series of Feynman diagrams for the multi-particle vertex functions, when the unregularized contact interaction strength becomes infinitesimal, a typical situation occurring in two- or three-dimensional free space. The latter Chevy ansatz approach is more widely applicable, allowing a nonzero interaction strength. We clarify the equivalence of the two approaches for an infinitesimal interaction strength and show that the variational coefficients in the Chevy ansatz are precisely the on-shell multi-particle vertex functions divided by an excitation energy. Truncated to a particular order of particle-hole excitations, the set of equations can be used to approximately calculate the finite-temperature polaron spectral function, once the numerical singularities in the equations are appropriately treated. As a concrete example, we calculate the finite-temperature spectral function of Fermi polarons in one-dimensional lattices, taking into account all the two-particle-hole excitations. We show that the inclusion of two-particle-hole excitations quantitatively improve the predictions on the polaron spectral function. Our results provide a useful way to solve the challenge problem of accurately predicting the finite-temperature spectral function of Fermi polarons in three-dimensional free space. In addition, our clarification of the complete set of Feynman diagrams for the multi-particle polaron vertex functions may inspire the development of more accurate diagrammatic theories of population-imbalanced strongly interacting Fermi gases, beyond the conventional many-body T-matrix approximation.
We theoretically investigate how quasiparticle properties of an attractive Fermi polaron are affected by nonzero temperature and finite impurity concentration in three dimensions and in free space. By applying both non-self-consistent and self-consistent many-body TTT-matrix theories, we calculate the polaron energy (including decay rate), effective mass, and residue, as functions of temperature and impurity concentration. The temperature and concentration dependencies are weak on the BCS side with a negative impurity-medium scattering length. Toward the strong attraction regime across the unitary limit, we find sizable dependencies. In particular, with increasing temperature the effective mass quickly approaches the bare mass and the residue is significantly enhanced. At temperature $T\ensuremath{\sim}0.1{T}_{F}$, where TF{T}_{F}TF​ is the Fermi temperature of the background Fermi sea, the residual polaron-polaron interaction seems to become attractive. This leads to a notable down-shift in the polaron energy. We show that, by taking into account the temperature and impurity concentration effects, the measured polaron energy in the first Fermi polaron experiment [Schirotzek , Phys. Rev. Lett. 102, 230402 (2009)] could be better theoretically explained.
We consider a spin impurity with multiple energy levels moving in a noninteracting Fermi sea and theoretically solve this Fermi-spin-polaron problem at nonzero temperature by using a non-self-consistent many-body TTT-matrix theory. We focus on the simplest case with spin 12\frac{1}{2}21​, where the two energy states of the impurity are coupled by a Rabi flip term. At small Rabi coupling, the impurity exhibits damped Rabi oscillations, where the decoherence is caused by the interaction with the Fermi sea, as recently reported in Fermi-polaron experiments with ultracold atoms. We investigate the dependence of Rabi oscillations on the Rabi coupling strength and examine the additional nonlinear damping due to large Rabi coupling. At finite temperature and nonzero impurity concentration, the impurity can acquire a pronounced momentum distribution. We show that the momentum or thermal average can sizably reduce the visibility of Rabi oscillations. We compare our theoretical predictions to recent experimental data and find good agreement without any adjustable parameters.
An extremely polarized mixture of an ultracold Fermi gas is expected to reduce to a Fermi polaron system, which consists of a single impurity immersed in the Fermi sea of majority atoms. By developing a many-body T -matrix theory, we investigate spectral properties of the polarized mixture in experimentally relevant regimes in which the system of finite impurity concentration at nonzero temperature is concerned. We explicitly demonstrate presence of polaron physics in the polarized limit and discuss effects of many polarons in an intermediate regime in a selfconsistent manner. By analyzing the spectral function at finite impurity concentration, we extract the attractive and repulsive polaron energies. We find that a renormalization of majority atoms via an interaction with minority atoms and a thermal depletion of the impurity chemical potential are of significance to depict the many-polaron regime.