Abstract
We apply the diagrammatic Monte Carlo approach to three-dimensional Fermi-polaron systems with mass-imbalance, where an impurity interacts resonantly with a noninteracting Fermi sea whose atoms have a different mass. This method allows to go beyond frequently used variational techniques by stochastically summing all relevant impurity Feynman diagrams up to a maximum expansion order limited by the sign problem. Polaron energy and quasiparticle residue can be accurately determined over a broad range of impurity masses. Furthermore, the spectral function of an imbalanced polaron demonstrates the stability of the quasiparticle and allows to locate in addition also the repulsive polaron as an excited state. The quantitative exactness of two-particle-hole wave-functions is investigated, resulting in a relative lowering of polaronic energies in the mass-imbalance phase diagram. Tan's contact coefficient for the mass-balanced polaron system is found in good agreement with variational methods. Mass-imbalanced systems can be studied experimentally by ultracold atom mixtures like $^6$Li-$^{40}$K.
Highlights
One of the most general and successful concepts in physics is the separation of a physical system into a simpler, controlled subsystem that is interacting with a perturbing subsystem
In the case of a noninteracting Fermi gas, this is called Fermi-polaron problem [1]. This theoretical model can help to map out the phase diagram of a strongly population-imbalanced Fermi gas [2], where the quasiparticle energy and effective mass serve as input parameters for Landau-Pomeranchuk Hamiltonians [3,4] helping to quantify zero-temperature phase separation and the ground-state energy of different phases
We show that two-particle-hole wave functions remain essentially exact in three dimensions and demonstrate the implications for the mass-imbalanced phase diagram
Summary
One of the most general and successful concepts in physics is the separation of a physical system into a simpler, controlled subsystem that is interacting with a perturbing subsystem. In the case of a noninteracting Fermi gas, this is called Fermi-polaron problem [1] This theoretical model can help to map out the phase diagram of a strongly population-imbalanced Fermi gas [2], where the quasiparticle energy and effective mass serve as input parameters for Landau-Pomeranchuk Hamiltonians [3,4] helping to quantify zero-temperature phase separation and the ground-state energy of different phases. The method was used [23,24,25] for the extraction of polaron quasiparticle residues and two-dimensional geometries Up to now, these diagMC implementations have only been applied to the special case of equal masses of impurity and bath atoms.
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