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.
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.
By introducing spatially varying profiles of pairing interaction or spin polarization to quasi one-dimensional two-component atomic Fermi gases confined in box potentials, we analyze the ground state structures and properties when multiple phases coexist in real space by implementing the Bogoliubov--de~Gennes equation suitable for describing inhomogeneous fermion systems. While the BCS, Fulde--Ferrell--Larkin--Ovchinnikov (FFLO), and normal phases occupy different regions on the phase diagram when the parameters are uniform, a spatial change of pairing strength or spin polarization can drive the system from the FFLO phase to a normal gas or from a BCS superfluid to the FFLO phase in real space. The FFLO phase exhibits its signature modulating order parameter at the FFLO momentum due to population imbalance, and the pair correlation penetrates the polarized normal phase and exhibits proximity effects. Meanwhile, the BCS phase tends to repel population imbalance and maintain a plateau of pairing. Interestingly, a buffer FFLO phase emerges when the spatial change attempts to join the BCS and normal phase in the presence of spin polarization. By analyzing the pairing correlations, interfacial properties, and momentum-space spectra of the inhomogeneous structures, relevant length- and momentum- scales and their interplay are characterized. We also briefly discuss implications of inhomogeneous multi-phase atomic Fermi gases with population imbalance.
We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (NPP). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.
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.
We investigate the finite-temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a nonpolarized Bardeen-Cooper-Schrieffer superfluid (P<Pc) or a fully polarized normal gas (P>Pc), depending on the smallness of the spin polarization P, relative to a critical value Pc. In this work, we show how these two phase-separation phases evolve with increasing temperature, and thereby construct a finite-temperature phase diagram. For typical interactions, we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy temperature, which seems to be accessible in the current experiment. The density profile, equation of state, and specific heat of the polarized system have been calculated and discussed in detail. Our results are useful for the ongoing experiment at Rice University on the search for FFLO states in quasi-one-dimensional polarized Fermi gases.
We present a numerical study on one-dimensional attractive Fermi gases with spin polarization in the presence of the harmonic confinement and the speckle disorder by making use of the local-density approximation based on the exact Bethe-ansatz solution. The effects of the disorder are investigated on the ground-state properties. For a clean system without trapping, the ground state is a partially polarized Fulde?Ferrell?Larkin?Ovchinnikov (FFLO) state, a full paired Bardeen?Cooper?Schrieffer (BCS) state or a fully polarized normal state. For a clean system in the presence of trapping, a two-shell structure exists with a polarized superfluid core surrounded by wings composed of either an unpolarized superfluid (FFLO-BCS) or a fully polarized normal (FFLO-N) gas. Between these two different phases, there exists a critical polarization where a pure FFLO state happens. In the presence of speckle disorder with fixed polarization, the system can be changed from FFLO-BCS to FFLO-N upon increasing the disorder amplitude, irrelevant to the attractive or repulsive nature of the speckle disorder. Given the dimensionless interaction strength ?0 and the disorder amplitude A, there is a critical polarization Pc below which the system is in a FFLO-BCS phase and above which it is in a FFLO-N phase.