A microscopic study of spin-polarized 40K atoms in one dimension using the static fluctuation approximation (SFA)

Abstract

The thermodynamic and magnetic properties of a spin-mixture of 40K atoms in a 1D harmonic trap, in the presence of an external magnetic field H, are studied using the static fluctuation approximation (SFA). The two-body interaction used is the contact potential. The thermodynamic properties include the chemical potential, energy per particle, specific heat capacity, and entropy per particle. The magnetic properties comprise the magnetization per particle and susceptibility per particle. A phase transition is observed for the repulsive interactions around 0.35TF and 0.5TF in the channels {–9/2, –7/2} and {–9/2, –5/2}, respectively. A peak appears in the entropy and susceptibility at effective scattering length |a1d| ≈ 0.16 μm. For the attractive interactions, three different behaviors depending on H are found in the low-temperature limit. The first behavior is when H < Hc, where Hc is the critical magnetic field, and typical peaks emerge. The second behavior is at H = Hc, and a magnetic phase transition occurs. The third behavior is when H > Hc and the system becomes a partially polarized phase. Our results are consistent with the reported results obtained by the local density approximation, thermal Bethe ansatz method, mean-field approximation, and quantum transfer matrix method.