Spectral Theory of the Fermi Polaron

Olga Goulko, Andrei S. Mishchenko, Nikolay V. Prokof'ev +1 more

Hui Hu, Jia Wang, Xia-Ji Liu

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.

Marko Cetina, Michael Jag, Rianne S. Lous +4 more

Hui Hu, Jia Wang, Xia-Ji Liu

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.

F. Marsiglio

Hiroyuki Tajima, Shun Uchino

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 is of significance to depict the many-polaron regime.