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Canadian Journal of Physics

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

H.A. Al-Khzon, M.M. Al-Qahtani

Published Jan 17, 2022• 0 citations
Publisher

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.

DOI
10.1139/cjp-2021-0167

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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.
A system of a finite number of harmonically trapped fermions in one dimension, in the presence of a static magnetic field, is studied within the framework of the static fluctuation approximation, for different repulsive and attractive potential strengths. Specifically, the thermodynamic properties of the system (the chemical potential, total energy, heat capacity, and entropy), as well as its magnetic properties (the magnetization and susceptibility), are calculated. It is observed that the system remains in an ordered phase for a small number of particles N, even at high temperatures T. Disorder sets in for large N, even at low T. The effect of the potential strength on the heat capacity is particularly tangible in the region bordering the quantum and classical regimes. The effect of the temperature (representing disorder) is directly opposite to that of the magnetic field (representing order), as expected on basic physical grounds. These features are consistent with experimental results.
The thermodynamic properties of 6Li atomic gas system, with imbalanced spin populations trapped in one-dimension, were systematically investigated using the Static Fluctuation Approximation. The two-body interaction used is an attractive contact potential. The effects of gas parameter [Formula: see text] and spin polarization [Formula: see text], on the thermodynamic properties and effective magnetic field were investigated. We observed a decrease in [Formula: see text] and an enhancement in [Formula: see text] and [Formula: see text] with increasing [Formula: see text]. At strong interaction and at [Formula: see text], the behavior of entropy with [Formula: see text] indicated two different phases. At small spin polarization [Formula: see text], the system could be in Fulde–Ferrell–Larkin Ovchinnikov (FFLO) state, while above [Formula: see text], the system might be in normal state. In addition, we found a clear decrease in both [Formula: see text] and [Formula: see text] and an enhancement in [Formula: see text] with the increase of the interaction strength. Our results are consistent with the reported results obtained by the mean-field Bogoliubov–de Gennes method, the Bardeen–Cooper–Schrieffer (BCS) approximation and Nozieres–Schmitt–Rink (NSR) theory.
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In this paper we use the so-called static fluctuation approximation (SFA) to calculate the thermodynamic properties of spin-polarized atomic hydrogen. This approximation is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for neutral many-bosonic systems. This set is solved numerically by an iteration method for two triplet-state potentials: a Morse- and Silvera-type potentials. It is found that the mean internal energy per unit volume, the pressure, the entropy per unit volume, and the specific heat per unit volume increase with temperature and decrease with spin polarization in the low-temperature region (<8 mK ); whereas the condensate fraction increases with an applied magnetic field. It is also found that these quantities are nearly independent of spin polarization for high temperatures (>0.1 K ), and that they are independent of the number density up to 10-3Å-3 in the low-temperature region.
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