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Journal of Changchun University

The effects of disorder on one-dimensional fermi gas

Jingjing Wang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

This paper calculates the density of states and density distribution of one-dimensional fermi gas in homogeneous system or under harmonic confinement with open boundary condition,and compares the results of clean system,disorder system of on-site and hopping energy.The numerical calculation shows that disorder makes the system tend to localization.

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Journal of Zhejiang Normal University•Jan 1, 2011•0 citations
This paper calculates the density of states and density distribution of one-dimensional fermi gas in homogeneous system or under harmonic confinement with open boundary condition,and compares the results of clean system,disorder system of on-site and hopping energy.The numerical calculation shows that disorder makes the system tend to localization.
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.
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to an harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.
Abstract This study aims to investigate local density variations of Fermi gases confined in various geometries at the nano-scale, revealing irregularities even in thermodynamic equilibrium. Calculations show that density of the confined gas in a nano scale domain, decreases towards zero near domain boundaries due to a quantum boundary layer linked to the Planck constant. Additionally, Friedel-like density oscillations are observed in nano-confined Fermi gases. Analytical expressions for the local density distribution are derived for degenerate and one-dimensional scenarios, while numerical computations are conducted for complex geometries and weak degeneracy conditions. In line with existing literature, it is understood that the quantum-size effects observed in the global thermodynamic properties of confined gases are attributed to these local irregularities. It becomes evident that in areas smaller than the threshold determined by the quantum boundary layer, the gas empties the part of the domain or reaches lower densities in the considered part relative to other parts of the domain, despite being in thermodynamic equilibrium. The results indicate the potential for gases to benefit from these behaviors and suggest the possibility of designing and manufacturing new nano-scale machines that are not feasible on a macro-scale.
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.