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arXiv:1003.0532 · Physical Review A

Phase separation in optical lattices in a spin-dependent external potential

Ahai Chen, Gao Xianlong

Published Jan 28, 2010• 10 citations
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Abstract

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.

DOI
10.1103/physreva.81.013628

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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.
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 consider repulsively interacting, cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values of interaction UUU and spin imbalance ppp in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin-polarized phase, spatially separated from other domains in the trapping potential, appears for large enough UUU and ppp. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from the combined effect of the Nagaoka ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.
We study a multi-orbital Fermi gas loaded on a one-dimensional optical lattice with harmonic trap potential. We show that this multi-orbital gas contains various quantum phases, i.e., (i) the ferromagnetic phase in large on–site interaction and (ii) the Haldane phase at half filling. Furthermore, our density-matrix renormalization-group simulations lead to systematic studies about the ground state, varying on–site interaction, spin imbalance, and total particle number, under spatial inhomogeneity originating from the trap potential. This trap potential produces a rich phase structure. In a metallic region, the phase-separated ferromagnetism appears, whereas in a central Mott core the Haldane phase is found. One of the remarkable features is that the ferromagnetic metal phase behaves as the edge state of the Haldane phase when these two phases coexist.
We investigate effects of pseudospin population imbalance on Mott phases in one-dimensional trapped two-component atomic Fermi gases loaded on optical lattices based on the repulsive Hubbard model in harmonic traps. By using the density-matrix renormalization-group method, we numerically calculate density profiles of each component and clarify the pseudospin magnetism. Consequently, we find that all the features from weakly imbalance to fully polarized cases are well described by S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems.
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 calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local-density approximation (LDA) and density-matrix renormalization-group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, the LDA predicts that the gas phase separates into shells with a partially polarized core and fully paired wings, the latter occurring below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. We show that, unlike in the continuum case, the critical polarization is a nonmonotonic function of the interaction strength and vanishes in the limit of large interactions.