A one dimensional Fermi mixture with delta--interaction is investigated in the limit of extreme imbalance. In particular we consider the cases of only one or two minority Fermions which interact with the Fermi-sea of the majority Fermions. We calculate dispersion relation and polaron mass for the minority Fermions as well as equal time density-density correlators. Within a cluster expansion we derive an expression for the effective interaction potential between minority Fermions. For our calculations we use a reformulation of the exact wave functions, originally obtained by Yang and Gaudin by a nested Bethe ansatz, in terms of determinants.
We study numerically a one-dimensional mixture of spin-$\tfrac{1}{2}$ fermions and scalar bosons in the hard-core limit. Considering repulsive fermion-fermion and boson-fermion interactions, we find superfluid and insulator states whose phase diagram is calculated. We determine that given a fermionic density $ρ_F$, the insulator states are located at the bosonic densities $ρ_B=1-ρ_F$ and $ρ_B=1-\tfrac{1}{2}ρ_F$, and emerge even in the absence of fermion-fermion coupling. In addition, the boson-fermion repulsion drives quantum phase transitions inside the insulator lobes with $ρ_B=1/2$. Our pre…
We examine the effect of boson-fermion interaction in a one-dimensional Bose-Fermi mixture by using the density matrix renormalization group method. We show that the boson superfluidity is enhanced by fermions for a weak boson-fermion coupling at an approximate integer boson filling factor (e.g., $0.935\le ρ_b \le 1.0$), and this enhancement is produced both in a fermion metallic state and in a fermion insulating state. A metal-insulator phase transition of fermions induced by boson-fermion interaction is observed even though there is no fermion-fermion interaction in the parent Hamiltonian. F…
Repulsive Bose-Einstein condensate, where the short-range interaction is included up to the third order by the interaction radius, demonstrates existence of a bright soliton in a narrow interval of parameters. This soliton is studied here for the boson-fermion mixture, where spin-1/2 fermions are consider in the regime of full spin polarization. Influence of fermions via the boson-fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered by hydrodynamic model including the pressure evolution equation. Interaction between fermions is c…
We study the formation of quantum droplets in the mixture of a single-component Bose-Einstein condensate (BEC), and a two-species Fermi superfluid across a wide Feshbach resonance. With repulsive boson-boson and attractive boson-fermion interactions, we show that quantum droplets can be stabilized by attractive fermion-fermion interactions in the Bardeen-Cooper-Schieffer (BCS) side of the resonance, and can also exist in deep BEC regime under weak boson-fermion interactions. We map out the phase diagram for stable droplets with respect to the boson-boson and boson-fermion interactions, and dis…
We report the results of the computation of the order $(k_{\rm F}a_0)^2$ correction, where $k_{\rm F}=3π^2ρ$ is the Fermi wave vector and $a_0$ the $s$-wave scattering length of the repulsive interaction, to the ground-state energy of a mixture of oppositely polarized $N_a$ spin $1/2$ fermions $a$ of masses $m_a$ and $N_b$ spin $1/2$ fermions $b$ of masses $m_b$ ($ρ=N/V$, $N=N_a+N_b$). It is shown that the results of the paper \cite{FraPil} in which the same correction has been computed entirely numerically, using a more traditional approach, can be easily and semianalytically reproduced using…
Atom-dimer scattering amplitude for fermionic mixtures with different masses: s-wave and p-wave contributions
研究了费什巴赫共振附近两种费米子混合物中费米子-二聚体散射振幅随质量比的变化。当质量相等时，物理情况是很简单的。我们表明，当质量比增加，情况变得更加复杂。对于s波的贡献，我们得到了一个解析解的渐近极限非常大的质量比。在这种情况下，s波散射振幅显示出大量的零，基本上与在这种情况下费米子-二聚体散射长度的已知大值有关。我们发现，通过精确的数值计算，零仍然存在的质量比为15。对于p波的贡献，我们的研究低于8.17的质量比，那里出现了费米子二聚体束缚态。我们发现，一个强大的p波共振是目前在低能量，由于一个虚拟的束缚态，在费米子二聚体系统，这是一个先驱的真实的束缚态。这种共振在对应于$^{40}$ K - $^6$ Li混合物的质量比范围附近变得突出，实验研究得很多。这种共振会影响许多物理性质。这些方程包括非平衡混合物在极低温度下的状态方程，也包括平衡混合物在中温或高温下的状态方程。集体模式的频率和阻尼也应该提供一种方便的方式来证明这种共振。最后，利用光晶格来改变一种费米子物质的有效质量应该是可能的。这将允许研究作为两个费米子元素的质量比的函数的共振的强依赖性。特别是，可以检查虚拟的束缚态是否与这些混合物的不稳定性有关。
Collective oscillations of superfluid mixtures of ultra cold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation (PDE) models and ordinary differential equation (ODE) models for the dynamics. An application to the recent experiment with fermionic $^{6}$Li and bosonic $^{7}$Li atoms, which approximately have the s…
Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of new non-trivial insulator phases that depend on the sign of the boson-fermion interaction. These non-trivial insulator phases satisfy the conditions $ρ_B\pmρ_F=n$ and $ρ_B\pm \tfrac{1}{2}ρ_F=n$, with the plus (minus…
