A new excitation mode has been predicted to exist in the unitary Fermi gas. It has a form of a spin-polarized impurity, which was dubbed as ferron. It is characterized by a closed nodal surface of the pairing field surrounding a partially spin-polarized superfluid region, where the phase differs by
π. In this paper, we discuss the effect of temperature on the generation of the ferron and the adiabaticity of the spin-polarizing potential together with ferron's ground state properties.
We investigate the highly polarized limit of a two-dimensional Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer, or even larger clusters. Similarly to three dimensions, we find that the Fermi sea favors the trimer state so that it exists for ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario that corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (${m}_{\ensuremath{\uparrow}}={m}_{\ensuremath{\downarrow}}$), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.
An impurity atom immersed in an ultracold atomic Fermi gas can form a quasiparticle, so-called Fermi polaron, due to impurity-fermion interaction. We consider a three-dimensional homogeneous dipolar Fermi gas as a medium, where the interatomic dipole-dipole interaction (DDI) makes the Fermi surface deformed into a spheroidal shape, and, using a Chevy-type variational method, investigate the ground-state properties of the Fermi polaron: the effective mass, the momentum distribution of a particle-hole excitation, the drag parameter, and the medium-density modification around the impurity. These quantities are shown to exhibit spatial anisotropies in such a way as to reflect the momentum anisotropy of the background dipolar Fermi gas. We also give numerical results for the polaron properties at the unitarity limit of the impurity-fermion interaction in the case in which the impurity and fermion masses are equal. It has been found that the transverse effective mass and the transverse momentum drag parameter of the polaron both tend to decrease by $\ensuremath{\sim}10%$ when the DDI strength is raised from 0 up to around its critical value, while the longitudinal ones exhibit a very weak dependence on the DDI.
We analyze when a repulsively interacting two-component Fermi gas becomes thermodynamically unstable against phase separation. We focus on the strongly polarized limit, where the free energy of the homogeneous mixture can be calculated accurately in terms of well-defined quasiparticles, the repulsive polarons. Phase diagrams as a function of polarization, temperature, mass imbalance, and repulsive polaron energy, as well as scattering length and range parameter, are provided. We show that the lifetime of the repulsive polaron increases significantly with the interaction range and the mass of the minority atoms, raising the prospects of detecting the transition to the elusive itinerant ferromagnetic state with ultracold atoms.
One of the salient features of ultracold atomic systems is that they are intrinsically clean. Nevertheless, artificial impurities can be engineered in atomic systems, which allows one to investigate their effects. In this talk, I will discuss our recent work on the effects of a localized impurity potential on atomic Fermi gases. Such an impurity can be used to manipulate or probe exotic quantum phases of fermionic superfluids. For example, it can be exploited to create the FFLO state in a controlled manner or to realize Majorana edge state in a topological Ferm gas with Rashba spin-orbit coupling.
We study in three dimensions the problem of a spatially homogeneous zero-temperature ideal Fermi gas of spin-polarized particles of mass
m perturbed by the presence of a single distinguishable impurity of mass
M. The interaction between the impurity and the fermions involves only the partial
s wave through the scattering length
a and has negligible range
b compared to the inverse Fermi wave number
1/kF of the gas. Through the interactions with the Fermi gas the impurity gives birth to a quasiparticle, which will be here a Fermi polaron (or more precisely a monomeron). We consider the general case of an impurity moving with wave vector $\mathbf{K}\ensuremath{\ne}\mathbf{0}$: Then the quasiparticle acquires a finite lifetime in its initial momentum channel because it can radiate particle-hole pairs in the Fermi sea. A description of the system using a variational approach, based on a finite number of particle-hole excitations of the Fermi sea, then becomes inappropriate around
K=0. We rely thus upon perturbation theory, where the small and negative parameter ${k}_{\mathrm{F}}a\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ excludes any branches other than the monomeronic one in the ground state (as, e.g., the dimeronic one), and allows us a systematic study of the system. We calculate the impurity self-energy ${\ensuremath{\Sigma}}^{(2)}(\mathbf{K},\ensuremath{\omega})$ up to second order included in
a. Remarkably, we obtain an analytical explicit expression for ${\ensuremath{\Sigma}}^{(2)}(\mathbf{K},\ensuremath{\omega})$, allowing us to study its derivatives in the plane $(K,\ensuremath{\omega})$. These present interesting singularities, which in general appear in the third-order derivatives ${\ensuremath{\partial}}^{3}{\ensuremath{\Sigma}}^{(2)}(\mathbf{K},\ensuremath{\omega})$. In the special case of equal masses,
M=m, singularities appear already in the physically more accessible second-order derivatives ${\ensuremath{\partial}}^{2}{\ensuremath{\Sigma}}^{(2)}(\mathbf{K},\ensuremath{\omega})$; using a self-consistent heuristic approach based on ${\ensuremath{\Sigma}}^{(2)}$ we then regularize the divergence of the second-order derivative ${\ensuremath{\partial}}_{K}^{2}\ensuremath{\Delta}E(\mathbf{K})$ of the complex energy of the quasiparticle found in Trefzger and Castin [Europhys. Lett. 104, 50005 (2013)] at
K=kF, and we predict an interesting scaling law in the neighborhood of
K=kF. As a by product of our theory we have access to all moments of the momentum of the particle-hole pair emitted by the impurity while damping its motion in the Fermi sea at the level of Fermi's golden rule.