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Journal of Physics B Atomic Molecular and Optical Physics

The effect of speckle disorder on a spin-polarized Fermi gas under harmonic confinement in one dimension

Jingjing Wang, Gao Xianlong

Published Oct 19, 2011• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/44/21/215302

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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.
A numerical study was conducted on a one-dimensional attractive Gaudin model of confined two-component polarized Fermi gas in the presence of the speckle disorder by making use of the local-density approximation based on the exact Bethe-ansatz solution.For a clean system without trapping,the ground state was a partially polarized Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) state,a fully paired Bardeen-Cooper-Schrieffer(BCS) state,or a fully polarized normal state.For a clean system in the presence of a harmonic trap,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 existed a critical polarization where a pure FFLO state would happen.In the presence of speckle disorder with fixed polarization,the system could be changed from FFLO-BCS to FFLO-N phase upon increasing the disorder amplitude.
We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one-dimensional configurations. The ground state properties are determined with the local density approximation, starting from the exact Bethe-ansatz equations for the homogeneous case. We predict that the atoms are distributed according to a two-shell structure: a partially polarized phase in the center of the trap and either a fully paired or a fully polarized phase in the wings. The partially polarized core is expected to be a superfluid of the Fulde-Ferrell-Larkin-Ovchinnikov type. The size of the cloud as well as the critical spin polarization needed to suppress the fully paired shell are calculated as a function of the coupling strength.
Based on the integrable Gaudin model and local density approximation, we discuss the ground state of a one-dimensional trapped Fermi gas with imbalanced spin population, for an arbitrary attractive interaction. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density compressional mode. We identify the polarized superfluid as having an Fulde-Ferrell-Larkin-Ovchinnikov structure, and predict the resulting mode frequency as a function of the spin polarization.
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 present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov--de Gennes equations, as well as the exact Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired Bardeen-Cooper-Schrieffer (BCS) state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimensions. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure appears, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.
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)(P<{P}_{c})(P<Pc​) or a fully polarized normal gas (P>Pc)(P>{P}_{c})(P>Pc​), depending on the smallness of the spin polarization PPP, relative to a critical value Pc{P}_{c}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.