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Bulletin of the American Physical Society

Single magnetic impurity in a spin-imbalanced superfluid Fermi gas

Jian Li, C. S. Ting

Published Mar 1, 2012• 0 citations
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Abstract

A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.

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A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.
A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.
The imbalanced superfluid state of spin- 1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov-de Gennes equation at zero temperature in an annular disk geometry with narrow radial width. Two distinct types of systems are considered. The first case may be relevant to heavy fermion superconductors, where magnetic field causes spin imbalance via Zeeman interaction and the system is studied in a grand canonical ensemble. As the magnetic field increases, the system is transformed from the uniform superfluid state to the Fulde-Ferrell-Larkin-Ovchinnikov state, and finally to the spin polarized normal state. The second case may be relevant to cold fermionic systems, where the number of fermions of each species is fixed as in a canonical ensemble. In this case, the ground state depends on the pairing strength. For weak pairing, the order parameter exhibits a periodic domain wall lattice pattern with a localized spin distribution at low spin imbalance, and a sinusoidally modulated pattern with extended spin distribution at high spin imbalance. For strong pairing, the phase separation between the superfluid state and polarized normal state is found to be preferable, while the increase of spin imbalance simply changes the ratio between them.
The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we study the effect of a single classical magnetic impurity in trapped ultracold Fermi superfluids. Depending on its shape and strength, a magnetic impurity can induce single or multiple midgap bound states in a superfluid Fermi gas. The multiple midgap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the scanning tunneling microsope, we propose a modified rf spectroscopic method to measure the local density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self-consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.
We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (NPP{N}_{\text{PP}}NPP​). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.
The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced two-component fermion mixtures in harmonically trapped optical lattices. In the low density limit, the superfluid order parameter has Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type oscillations in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However, in the high density limit, while the order parameter has oscillations in the radial direction towards the trap center for low imbalances, it also has oscillations towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalances, but leads to double peaks for intermediate imbalances.
Superfluidity with imbalanced populations of harmonically trapped ultracold fermions in a two-dimensional optical lattice is investigated by solving the Bogoliubov-de Gennes equations. The intriguing richness of patterns between competing ferromagnetic and superfluid phases for different filling densities has been revealed. At low density, the main experimental features could be reproduced, especially the bimodal distribution of ferromagnetism. The superfluid-pairing gap oscillates radially, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the high-density regime, another type of FFLO state with gap oscillation along the angular direction shows up and the accompanying ferromagnetic order modulates accordingly. The square lattice like FFLO state may appear at the intermediate densities. Moreover, we suggest other experimental proposals of observing the unique FFLO features straightforwardly.