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arXiv:2311.10238 · AAPPS bulletin

Thermally stable p-wave repulsive Fermi polaron without a two-body bound state

Hui Hu, Jia Wang, Xia-Ji Liu

Published Nov 16, 2023• 6 citations
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Abstract

Abstract We theoretically investigate the polaron physics of an impurity immersed in a two-dimensional Fermi sea, interacting via a p-wave interaction at finite temperature. In the unitary limit with a divergent scattering area, we find a well-defined repulsive Fermi polaron at short interaction range, which shows a remarkable thermal stability with increasing temperature. The appearance of such a stable repulsive Fermi polaron in the resonantly interacting limit can be attributed to the existence of a quasi-bound dressed molecule state hidden in the two-particle continuum, although there is no bound state in the two-particle limit. We show that the repulsive Fermi polaron disappears when the interaction range increases or when the scattering area is tuned to the weakly interacting regime. The large interaction range and small scattering area instead stabilize attractive Fermi polarons.

DOI
10.1007/s43673-023-00100-8

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Abstract We theoretically investigate the polaron physics of an impurity immersed in a two-dimensional Fermi sea, interacting via a p-wave interaction at finite temperature. In the unitary limit with a divergent scattering area, we find a well-defined repulsive Fermi polaron at short interaction range, which shows a remarkable thermal stability with increasing temperature. The appearance of such a stable repulsive Fermi polaron in the resonantly interacting limit can be attributed to the existence of a quasi-bound dressed molecule state hidden in the two-particle continuum, although there is no bound state in the two-particle limit. We show that the repulsive Fermi polaron disappears when the interaction range increases or when the scattering area is tuned to the weakly interacting regime. The large interaction range and small scattering area instead stabilize attractive Fermi polarons.
Based on the recently developed interaction renormalization for the one-dimensional ppp-wave interaction, we study the problem of a single impurity immersed in a highly polarized Fermi sea. They interact through a narrow ppp-wave Feshbach resonance, so the effective range r0{r}_{0}r0​ naturally appears in the system. We use the variational approach limited to single-particle--hole excitations on top of the unperturbed Fermi sea. The polaron exhibits two branches of solutions, namely, the attractive and repulsive branches, with varying scattering length across the resonance. We calculate the energy spectrum, residue, and effective mass for each of the branches. We compare the polaronic energy with the energy of the dressed molecule and find that the molecular state is energetically favored when increasing the interaction strength. The critical interaction strength for the polaron-to-molecule transition will shift to the BCS side of the ppp-wave resonance as the effective range increases.
Impurities in a Fermi sea, or Fermi polarons, experience a Casimir interaction induced by quantum fluctuations of the medium. When there is short-range attraction between impurities and fermions, also the induced interaction between two impurities is strongly attractive at short distance and oscillates in space for larger distances. We theoretically investigate the scattering properties and compute the scattering phase shifts and scattering lengths between two heavy impurities in an ideal Fermi gas at zero temperature. While the induced interaction between impurities is weakly attractive for weak impurity-medium interactions, we find that impurities strongly and attractively interacting with the medium exhibit resonances in the induced scattering with a sign change of the induced scattering length and even strong repulsion. These resonances occur whenever a three-body Efimov bound state appears at the continuum threshold. At energies above the continuum threshold, we find that the Efimov state in medium can turn into a quasibound state with a finite decay width.
The Fermi polaron, formed by an impurity interacting with a surrounding Fermi sea, exemplifies the canonical quasiparticle concept as a cornerstone in our description of quantum many-body systems across a wide range of energy scales. Experiments on atomic quantum gases have provided profound insights into the universal nature of the Fermi polaron. While most previous studies have focused on the case of zero impurity momentum, finite-momentum properties have remained largely uncharted. Here, we investigate the moving Fermi polaron by combining a novel Raman acceleration scheme with high-precision radio-frequency spectroscopy, exploring the quasiparticle dispersion relation over a wide range of momenta. We compare our measurements of energy shifts and spectral linewidths with a microscopic theory and reach quantitative agreement for all momenta. For low momenta, we find the energy of the moving polaron to be fully consistent with the Fermi liquid picture of a dressed particle with a constant effective mass. At high momenta, the polaron approaches the behavior of a weakly interacting bare particle, featuring small energy shifts and weak broadening. For intermediate momenta, broadening is generally larger and, most strikingly, the behavior differs for attractive and repulsive polarons. While the repulsive polaron exhibits a smooth connection between both regimes along with a monotonic change of the energy shift, the attractive case shows a peculiar non-monotonic behavior. With increasing momentum, the attractive polaron enters a regime where its energy deviates from the constant effective mass expression and broadening suddenly increases. By comparing this observation with theory, we show that this abrupt behavior coincides with the attractive polaron entering a molecule-hole continuum, where it is no longer the ground state. We interpret this as a motion-induced polaron-molecule transition.
We consider a single spin-down impurity atom interacting via an attractive, short-range potential with a spin-up Fermi sea in two dimensions (2D). Similarly to 3D, we show how the impurity can form a metastable state (the "repulsive polaron") with energy greater than that of the non-interacting impurity. Moreover, we find that the repulsive polaron can acquire a finite momentum for sufficiently weak attractive interactions. Even though the energy of the repulsive polaron can become sizeable, we argue that saturated ferromagnetism is unfavorable in 2D because of the polaron's finite lifetime and small quasiparticle weight.
We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron–molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.
The properties of impurities immersed in a large Fermi sea are naturally described in terms of dressed quasiparticles: attractive and repulsive polarons, and dressed molecules. Motivated by recent experiments on narrow Feshbach resonances, we analyze here how the quasiparticle properties are affected by a non-zero resonance range. We find two interesting analytic results. For large range, the ground-state energy close to resonance is shown to become perturbative in the inverse range. In the limit of broad resonance instead, we provide a new Tan's relation linking the impurity ground-state energy E ↓ to the number of atoms in its dressing cloud Δ N . As a corollary, at unitarity one finds Δ N =− E ↓ / F , with F the Fermi energy of the bath.