Emergence of Crystalline Few-body Correlations in Mass-imbalanced Fermi Polarons

Abstract

Identifying few-body correlations is an efficient tool to solve complex many-body problems. The polarons, interpolating between few-and many-body systems, serve as an ideal platform to achieve the goal. In this work, we reveal various crystalline few-body correlations emergent from a smooth crossover of mass-imbalanced Fermi polarons in two dimension. Here a unified variational approach up to three particle-hole excitations allows us to extract the dominant n-body correlations for n ranging from 2 (dimer), 3 (trimer) to 4 (tetramer). It is found that when the fermion-impurity mass ratio is beyond certain critical value, the Fermi polaron will undergo a smooth polaron-trimer or polarontrimer-tetramer crossover as increasing the fermion-impurity attraction, in contrast to the polaronmolecule transition for the equal mass case. During the crossover, the 3-and 4-body correlations gradually emerge and become dominant, which can manifest themselves in the momentum-space crystallization, i.e., the particle-hole excitations of majority fermions tend to distribute with equal interval near the Fermi surface forming a stable diagonal or triangular structure. Such emergent crystallization can be detected through the density-density correlation of majority fermions. Our results shed light on the intriguing quantum phases in the mass-imbalanced Fermi-Fermi mixtures beyond the pairing superfluid paradigm.