Fermi polarons at finite temperature: Spectral function and rf-spectroscopy

Abstract

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 $T$-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 $T$-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 increase 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 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 take 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.

arXiv comment16 pages and 14 figures

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• Thermally stable p-wave repulsive Fermi polaron without a two-body bound state
• Theory of the spectral function of Fermi polarons at finite temperature
• Polaronic Proton and Diproton Clustering in Neutron-Rich Matter
• Raman spectroscopy of Fermi polarons
• Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices
• Fermi spin polaron and dissipative Fermi-polaron Rabi dynamics
• Spectral properties and observables in ultracold Fermi gases
• Momentum-dependent quasiparticle properties of the Fermi polaron from the functional renormalization group
• Peaks and widths of radio-frequency spectra: An analysis of the phase diagram of ultra-cold Fermi gases
• Exact spectral properties of Fermi polarons in one-dimensional lattices: Anomalous Fermi singularities and polaron quasiparticles
• Microscopic many-body theory of two-dimensional coherent spectroscopy of excitons and trions in atomically thin transition metal dichalcogenides
• Spectral function of Fermi polarons at finite temperature from a self-consistent many-body $T$-matrix approach in real frequency
• Repulsive Fermi and Bose Polarons in Quantum Gases
• Super Fermi polaron and Nagaoka ferromagnetism in a two-dimesnional square lattice
• The normal state of attractive Fermi gases from coupled-cluster theory