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arXiv:1309.5198 · Physical Review A

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory

Gao Xianlong

Published Feb 26, 2013• 7 citations
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Abstract

We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between the intercomponents. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.

DOI
10.1103/physreva.87.023628

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We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between the intercomponents. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.
We investigate the phase separation in one-dimensional Fermi gases on optical lattices. The density distributions and the magnetization are calculated by means of the density-matrix renormalization method. The phase separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between intercomponent fermions. We find the existence of a critical repulsive interaction strength above which the phase separation evolves. By increasing the trap imbalance, the composite phase of the Mott-insulating core is changed into one of the ferromagnetic insulating core, which is incompressible and originates from the Pauli exclusion principle.
The component separation of the trapped large-spin Fermi gas is studied within density functional theory. The ground state and ferromagnetic transition in the gas, with and without the spin mixing collision, are calculated. In the absence of spin mixing, two patterns of separation are observed as the interaction between atoms increases, whereas only one of them corresponds to a ferromagnetic transition. The phase diagram suggests that the pattern which the system chooses depends on the interaction strength in the collision channels. With the presence of spin mixing, the distribution of phase region changes because of the interplay between different collision channels. Specifically, the spin exchange benefits the FM transition, while it suppresses the component separation of CS-II pattern.
The demixing of two-component fermions in optical lattices under a spin-dependent external potential is investigated using the density-matrix renormalization group method. The influence of on-site interactions (uuu) and the ratio of the spin-dependent external potentials ($\ensuremath{\gamma}$) on the demixing is discussed. The $\ensuremath{\gamma}\ensuremath{-}u$ state diagram is numerically mapped out, from which we distinguish the phase-mixed region from the phase-separated one. A minimum point appears in the phase boundary. On the right part of the point an insulating core is formed in the spin-up densities during the demixing, while on the left one only metallic phase exists.
We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a linear external potential whose gradient is opposite for the two spin components, so that each spin species sees a potential minimum at a different end of the lattice. Using density-matrix renormalization group (DMRG) simulations, we map the ground-state density distributions and the number of doubly occupied sites as a function of the potential gradient βββ and interaction strength. We identify three distinct regimes separated by critical threshold gradients: (i) a small-βββ regime where fermion pairing remains robust against the external potential; (ii) an intermediate-βββ phase-separated regime characterized by a staircase-like decrease in the doublon number, corresponding to the successive, one-by-one breaking of bound pairs; and (iii) a large-βββ regime where the two spin components are completely spatially separated. We complement the numerical results with a phenomenological model and a local-density approximation analysis, from which we derive closed-form analytical estimates for these critical threshold values. We also verify that the staircase structure persists under additional harmonic confinement. Our results are directly testable in cold-atom experiments, and demonstrate that a spin-dependent linear potential enables precise, integer-level control of the number of bound fermion pairs.
We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [I. Brouzos and P. Schmelcher, Phys. Rev. Lett. 108, 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [G. Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012)].
We present a density-functional theory for the one-dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground-state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the local density approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for sufficiently strong interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in the Bose density curves, reflecting the strong correlation with fermions. For infinitely strong interaction, the ground-state energy of the mixture and the total density are consistent with the scenario that all atoms in the mixture are fully fermionized.