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arXiv:1708.00134 · Physical Review A

Repulsive Fermi polarons with negative effective mass

Wenliang Li, Xiaoling Cui

Published Nov 7, 2017• 12 citations
arXivHTMLPDF

Abstract

A recent experiment at the European Laboratory for Non-Linear Spectroscopy (LENS) on a three-dimensional (3D) Fermi gas has reported a negative effective mass (${m}^{*}<0$) for Fermi polarons in the strongly repulsive regime. There naturally arises a question of whether the negative ${m}^{*}$ is a precursor of the instability towards phase separation (or itinerant ferromagnetism). In this paper, we make use of the exact solutions to study the ground state and excitation properties of repulsive Fermi polarons in one dimension, which also can exhibit a negative ${m}^{*}$ in the super-Tonks-Girardeau regime. By analyzing the total spin, quasimomentum distribution, and pair correlations, we conclude that the negative ${m}^{*}$ is irrelevant to the instability towards ferromagnetism or phase separation but rather an intrinsic feature of collective excitations for fermions in the strongly repulsive regime. Surprisingly, for large and negative ${m}^{*}$, such an excitation is accompanied with a spin-density modulation when the majority fermions move closer to the impurity rather than being repelled far away, contrary to the picture of phase separation. These results shed light on the recent observation of negative ${m}^{*}$ in the 3D repulsive Fermi polarons.

DOI
10.1103/physreva.96.053609

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A recent experiment at the European Laboratory for Non-Linear Spectroscopy (LENS) on a three-dimensional (3D) Fermi gas has reported a negative effective mass (m∗<0{m}^{*}<0m∗<0) for Fermi polarons in the strongly repulsive regime. There naturally arises a question of whether the negative m∗{m}^{*}m∗ is a precursor of the instability towards phase separation (or itinerant ferromagnetism). In this paper, we make use of the exact solutions to study the ground state and excitation properties of repulsive Fermi polarons in one dimension, which also can exhibit a negative m∗{m}^{*}m∗ in the super-Tonks-Girardeau regime. By analyzing the total spin, quasimomentum distribution, and pair correlations, we conclude that the negative m∗{m}^{*}m∗ is irrelevant to the instability towards ferromagnetism or phase separation but rather an intrinsic feature of collective excitations for fermions in the strongly repulsive regime. Surprisingly, for large and negative m∗{m}^{*}m∗, such an excitation is accompanied with a spin-density modulation when the majority fermions move closer to the impurity rather than being repelled far away, contrary to the picture of phase separation. These results shed light on the recent observation of negative m∗{m}^{*}m∗ in the 3D repulsive Fermi polarons.
Abstract Using the variational method, we study the properties of a spin-down impurity immersed in a one-dimensional (1D) spin-up Fermi sea. With repulsive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. We clearly calculate the binding energy, effective mass, momentum distribution, Tan contact, and pair correlation. Even in strong repulsive regimes, the results can agree with the exact Bethe Ansatz results. The repulsive polaron energy E + is below Fermi energy E F and no negative effective masses are found in whole interaction regimes, unequal masses polarons are also calculated. We show a clear momentum distribution and calculate the Tan contact from three different aspects. Furthermore, we explore the particle-hole excitation and find that the hole terms in Fermi sea have a great influence on the polaron energy and contact in repulsive regime. These results show that the variational method can still be used effectively in 1D repulsive polaron system .
We revisit the polaron-molecule transition in three-dimensional (3D) fermion systems using the well-established variational approach. The molecule is found to be intrinsically unstable against lowest-order particle-hole excitations, and it can only approximate the ground state of impurity systems with a finite total momentum in the strong-coupling regime. The polaron-molecule transition can therefore be reinterpreted as a first-order transition between single impurity systems with different total momenta. Within a certain interaction window near their transition, both states appear as local minima in the dispersion curve, indicating they can coexist in a realistic system. We have further confirmed the polaron-molecule coexistence in the presence of a finite impurity concentration and at low temperature, which directly leads to a smooth polaron-molecule transition as observed in recent experiments of 3D ultracold Fermi gases. Our results have provided an unambiguous physical picture for the competition and conversion between a polaron and molecule, and also shed light on Fermi polaron properties in low dimensions.
We characterize properties of the so-called repulsive polaron across the recently discovered orbital Feshbach resonance in alkaline-earth-metal-like atoms. Being a metastable quasiparticle excitation at the positive energy, the repulsive polaron is induced by the interaction between an impurity atom and a Fermi sea. By analyzing in detail the energy, the polaron residue, the effective mass, and the decay rate of the repulsive polaron, we reveal interesting features that are intimately related to the two-channel nature of the orbital Feshbach resonance. In particular, we find that the lifetime of the repulsive polaron is nonmonotonic in the Zeeman-field detuning between the two channels, and has a maximum on the BEC-side of the resonance. Further, by considering the stability of a mixture of the impurity and the majority atoms against phase separation, we show that the itinerant ferromagnetism may exist near the orbital Feshbach resonance at appropriate densities. Our results can be readily probed experimentally, and have interesting implications for the observation of itinerant ferromagnetism near an orbital Feshbach resonance.
We calculate the exact spectral function of a single impurity repulsively interacting with a bath of fermions in one-dimensional lattices, by deriving the explicit expression of the form factor for both regular Bethe states and the irregular spin-flip state and η-pairing state, based on the exactly solvable one-dimensional Hubbard model. While at low impurity momentum Q∼0 the spectral function is dominated by two power-law Fermi singularities, at large momentum we observe that the two singularities develop into two-sided distributions and eventually become anomalous Fermi singularities at the boundary of the Brillouin zone (i.e., Q=±π), with the power-law tails extending toward low energy. Near the quarter filling of the Fermi bath, we also find two broad polaron peaks at large impurity momentum, collectively contributed by many excited many-body states with non-negligible form factors. Our exact results of those distinct features in one-dimensional Fermi polarons, which have no correspondences in two and three dimensions, could be readily probed in cold-atom laboratories by trapping highly imbalanced two-component fermionic atoms into one-dimensional optical lattices.
We consider the Fermi polaron problem of an impurity hopping around a two-dimensional square lattice and interacting with a sea of fermions at given filling factor. When the interaction is attractive, we find standard Fermi polaron quasiparticles, categorized as attractive polarons and repulsive polarons. When the interaction becomes repulsive, interestingly, we observe an unconventional highly excited polaron quasiparticle, sharply peaked at the corner of the first Brillouin zone with momentum $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$. This super Fermi polaron branch arises from the dressing of the impurity's motion with holes, instead of particles of fermions. We show that super Fermi polarons become increasingly well defined with increasing impurity-fermion repulsions and might be considered as a precursor of Nagaoka ferromagnetism, which would appear at sufficiently large repulsions and at large filling factors. We also investigate the temperature dependence of super Fermi polarons and find that they are thermally robust against the significant increase in temperature.
We show that phase separation must occur in a mixture of fermions with repulsive interaction if their mass difference is sufficiently large. This phenomenon is highly dimension dependent. Consequently, the density profiles of phase separated 3D mixtures are very different from those in 1D. Noting that the ferromagnetic transition of a spin-1/2 repulsive Fermi gas is the equal mass limit of the phase separation in mixtures, we show from the Bethe ansatz solution that a ferromagnetic transition will take place in the scattering states when the interaction passes through the strongly repulsive regime and becomes attractive.