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arXiv:1603.06963 · Physical Review A

Dark continuum in the spectral function of the resonant Fermi polaron

Olga Goulko, Andrei S. Mishchenko, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Nov 23, 2016• 52 citations
arXivHTMLPDF

Abstract

We present controlled numerical results for the ground-state spectral function of the resonant Fermi polaron in three dimensions. We establish the existence of a ``dark continuum''---a region of anomalously low spectral weight between the narrow polaron peak and the rest of the spectral continuum. The dark continuum develops when the $s$-wave scattering length is of the order of the inverse Fermi wave vector, $a\ensuremath{\lesssim}1/{k}_{\mathrm{F}}$, i.e., in the absence of a small interaction-related parameter when the spectral weight is not expected to feature a near-perfect gap structure after the polaron peak.

DOI
10.1103/physreva.94.051605

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We present controlled numerical results for the ground-state spectral function of the resonant Fermi polaron in three dimensions. We establish the existence of a ``dark continuum''---a region of anomalously low spectral weight between the narrow polaron peak and the rest of the spectral continuum. The dark continuum develops when the sss-wave scattering length is of the order of the inverse Fermi wave vector, a\ensuremath≲1/kFa\ensuremath{\lesssim}1/{k}_{\mathrm{F}}a\ensuremath≲1/kF​, i.e., in the absence of a small interaction-related parameter when the spectral weight is not expected to feature a near-perfect gap structure after the polaron peak.
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We compute the Holstein polaron spectral function on a one-dimensional ring using the finite-temperature TTT Lanczos method. With increasing TTT additional features in the spectral function emerge even at temperatures below the phonon frequency. We observe a substantial spread of the spectral weight towards lower frequencies and the broadening of the quasiparticle (QP) peak. In the weak-coupling regime the QP peak merges with the continuum in the high-TTT limit. In the strong-coupling regime the main features of the low-TTT spectral function remain detectable up to the highest TTT used in our calculations. The effective polaron mass shows a nonmonotonic behavior as a function of TTT at small phonon frequency but increases with TTT at larger frequencies. The self-energy remains kkk independent even at elevated TTT in the frequency range corresponding to the polaron band, while at higher frequencies it develops a distinguishable kkk dependence. Analytical expressions for the first few frequency moments are derived, and they agree well with those extracted from numerical calculations in a wide-TTT regime.
We develop a general theory of Fermi polarons at nonzero temperature, including particle-hole excitations of the Fermi sea shakeup to arbitrarily high orders. The exact set of equations of the spectral function is derived by using both Chevy ansatz and diagrammatic approach, and their equivalence is clarified to hold in free space only, with an unregularized infinitesimal interaction strength. The correction to the polaron spectral function arising from two-particle-hole excitations is explicitly examined for an exemplary case of Fermi polarons in one-dimensional optical lattices. We find quantitative improvements at low temperatures with the inclusion of two-particle-hole excitations, in both polaron energies and decay rates. Our exact theory of Fermi polarons with arbitrary orders of particle-hole excitations might be used to better understand the intriguing polaron dynamical responses in two or three dimensions, whether in free space or within lattices.
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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.