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arXiv:1806.01582 · Physical Review A

Fulde-Ferrell-Larkin-Ovchinnikov pairing states of a polarized dipolar Fermi gas trapped in a one-dimensional optical lattice

Xingbo Wei, Chao Gao, Reza Asgari, Pei Wang, Gao Xianlong

Published Aug 27, 2018• 8 citations
arXivHTMLPDF

Abstract

We study the interplay between the long- and short-range interaction of a one-dimensional optical lattice system of two-component dipolar fermions by using the density matrix renormalization group method. The atomic density profile, pairing-pairing correlation function, and compressibility are calculated in the ground state, from which we identify the parameter region of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state, half-metal (HM) state, FFLO-HM state, and the normal polarized state, and thus the phase diagram in the coordinates of the long- and short-range interaction strength. The effect of the long-range dipolar interaction on the FFLO state is discussed in detail. We find that the long-range part of the dipole-dipole interaction does not sweep away the FFLO superconducting region that is driven by the short-range interaction in the Hubbard model, and thus the FFLO state survives in the wide parameter space of the long-range interaction, polarization, and filling.

DOI
10.1103/physreva.98.023631

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We study the interplay between the long- and short-range interaction of a one-dimensional optical lattice system of two-component dipolar fermions by using the density matrix renormalization group method. The atomic density profile, pairing-pairing correlation function, and compressibility are calculated in the ground state, from which we identify the parameter region of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state, half-metal (HM) state, FFLO-HM state, and the normal polarized state, and thus the phase diagram in the coordinates of the long- and short-range interaction strength. The effect of the long-range dipolar interaction on the FFLO state is discussed in detail. We find that the long-range part of the dipole-dipole interaction does not sweep away the FFLO superconducting region that is driven by the short-range interaction in the Hubbard model, and thus the FFLO state survives in the wide parameter space of the long-range interaction, polarization, and filling.
We study the phase diagram of one-dimensional two-component attractive fermions on optical lattices with an off-diagonal confinement. We identify in this system a pure Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with spatially modulated superfluidity and polarization in a large parameter window, which provides an easier playground in which to detect the FFLO state experimentally. The clear signature of the FFLO state is analyzed in the ground-state properties, the pair correlation function, and the magnetic structure factor, using the density-matrix renormalization-group method.
Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for a small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long-range order into long-range order by coupling many identical 1D systems, such as in quasi-1D optical lattices.
We study the properties of a one-dimensional (1D) gas of fermions trapped in a lattice by means of the density matrix renormalization group method, focusing on the case of unequal spin populations, and strong attractive interaction. In the low-density regime, the system phase separates into a well-defined superconducting core and a fully polarized metallic cloud surrounding it. We argue that the superconducting phase corresponds to a 1D analog of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasicondensate of tightly bound bosonic pairs with a finite center-of-mass momentum that scales linearly with the magnetization. In the large density limit, the system allows for four phases: in the core, we either find a Fock state of localized pairs or a metallic shell with free spin-down fermions moving in a fully filled background of spin-up fermions. As the magnetization increases, the Fock state disappears to give room for a metallic phase, with a partially polarized superconducting FFLO shell and a fully polarized metallic cloud surrounding the core.
We calculate the zero-temperature (T=0) phase diagram of a polarized two-component Fermi gas in an array of weakly coupled parallel one-dimensional (1D) "tubes" produced by a two-dimensional optical lattice. Increasing the lattice strength drives a crossover from three-dimensional (3D) to 1D behavior, stabilizing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superfluid phase. We argue that the most promising regime for observing the FFLO phase is in the quasi-1D regime, where the atomic motion is largely 1D but there is weak tunneling in the other directions that stabilizes long-range order. In the FFLO phase, we describe a phase transition where the quasiparticle spectrum changes from gapless near the 3D regime to gapped in quasi-1D.
We investigate a one-dimensional two-component system in an optical lattice of attractive interactions under a spin-dependent external potential. Based on the density-matrix renormalization group methods, we obtain its phase diagram as a function of the external potential imbalance and the strength of the attractive interaction through the analysis on the density profiles and the momentum pair correlation functions. We find that there are three different phases in the system, a coexisted fully polarized and Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase, a normal polarized phase, and a Bardeen–Cooper–Schrieffer (BCS) phase. Different from the systems of spin-independent external potential, where the FFLO phase is normally favored by the attractive interactions, in the present situation, the FFLO phases are easily destroyed by the attractive interactions, leading to the normal polarized or the BCS phase.
We explore the pairing properties of the one-dimensional attractive Hubbard model in the presence of finite spin polarization. The correlation exponents for the most important fluctuations are determined as a function of the density and the polarization. We find that in a system with spin population imbalance, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type pairing at wave vector $Q=\ensuremath{\mid}{k}_{F,\ensuremath{\uparrow}}\ensuremath{-}{k}_{F,\ensuremath{\downarrow}}\ensuremath{\mid}$ is always dominant and there is no Chandrasekhar-Clogston limit. We then investigate the case of weakly coupled one-dimensional (1D) systems and determine the region of stability of the 1D FFLO phase. This picture is corroborated by density-matrix-renormalization-group simulations of the spatial noise correlations in uniform and trapped systems, unambiguously revealing the presence of fermion pairs with nonzero momentum QQQ. This opens up an interesting possibility for experimental studies of FFLO states.