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Bulletin of the American Physical Society

Classical magnetic impurity in ultracold fermi superfluids

Lei Jiang, Leslie O. Baksmaty, Han Pu, Hui Hu, Yan Chen

Published Jun 15, 2011• 0 citations
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Abstract

In cold atom experiments, we have tools to create spin dependent optical potential, which gives us the possibility to achieve classical magnetic impurity in cold atom systems. Here we study the physics of magnetic impurity. A localized magnetic impurity can induce a mid-gap bound state, the Yu-Shiba state, in superfluid Fermi gas. We propose a modified RF spectroscopy to measure the local density of states, as a cold-atom analog of STM, which may be used to detect Yu-Shiba state. In addition, magnetic impurity can locally induce population imbalance in the system, potentially providing a method to realize FFLO-like state in a controlled way. We demonstrate such a possibility by solving the self-consist Bogoliubov-de Gennes equations.

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In cold atom experiments, we have tools to create spin dependent optical potential, which gives us the possibility to achieve classical magnetic impurity in cold atom systems. Here we study the physics of magnetic impurity. A localized magnetic impurity can induce a mid-gap bound state, the Yu-Shiba state, in superfluid Fermi gas. We propose a modified RF spectroscopy to measure the local density of states, as a cold-atom analog of STM, which may be used to detect Yu-Shiba state. In addition, magnetic impurity can locally induce population imbalance in the system, potentially providing a method to realize FFLO-like state in a controlled way. We demonstrate such a possibility by solving the self-consist Bogoliubov-de Gennes equations.
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.
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.
Ultracold Fermi gas is an exciting field benefiting from atomic physics, optical physics and condensed matter physics. It covers many aspects of quantum mechanics. Here I introduce some of my work during my graduate study. We proposed an optical spectroscopic method based on electromagnetically-induced transparency (EIT) as a generic probing tool that provides valuable insights into the nature of Fermi paring in ultracold Fermi gases of two hyperfine states. This technique has the capability of allowing spectroscopic response to be determined in a nearly non-destructive manner and the whole spectrum may be obtained by scanning the probe laser frequency faster than the lifetime of the sample without re-preparing the atomic sample repeatedly. Both quasiparticle picture and pseudogap picture are constructed to facilitate the physical explanation of the pairing signature in the EIT spectra. Motivated by the prospect of realizing a Fermi gas of 40 K atoms with a synthetic non-Abelian gauge field, we investigated theoretically BEC-HCS crossover physics in the presence of a Rashba spin-orbit coupling in a system of two-component Fermi gas with and without a Zeeman field that breaks the population balance. A new bound state (Rashba pair) emerges because of the spin-orbit interaction. We studied the properties of Rashba pairs using a standard pair fluctuation theory. As the two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to an anisotropic superfluid. We discussed in detail the experimental signatures for observing the condensation of Rashba pairs by calculating various physical observables which characterize the properties of the system and can be measured in experiment. The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we studied the effect of a single classical impurity in trapped ultracold Fermi superfluids. Although a non-magnetic impurity does not change macroscopic properties of s-wave Fermi superfluids, depending on its shape and strength, a magnetic impurity can induce single or multiple mid-gap bound states. The multiple mid-gap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the Scanning Tunneling Microscope, we proposed a modified radio frequency spectroscopic method to measure the focal 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.
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.
We theoretically investigate the introduction of magnetic impurities into a superfluid Fermi gas. In the presence of a population imbalance (${N}_{\ensuremath{\uparrow}}>{N}_{\ensuremath{\downarrow}}$, where ${N}_{\ensuremath{\sigma}}$ is the number of Fermi atoms with pseudospin $\ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow}$), we show that nonmagnetic potential scatterers embedded in the system are magnetized in the sense that some of the excess spin-$\ensuremath{\uparrow}$ atoms are localized around them. They destroy the superfluid order parameter around them, as in the case of the magnetic impurity effect discussed in the superconductivity literature. This pair-breaking effect naturally leads to localized excited states below the superfluid excitation gap. To confirm our idea in a simple manner, we consider an attractive Fermi-Hubbard model within the mean-field theory at T=0T=0T=0. We determine consistent superfluid properties around a nonmagnetic impurity, such as the superfluid order parameter, local population imbalance, as well as the single-particle density of states, in the presence of a population imbalance. Since competition between superconductivity and magnetism is one of the most fundamental problems in condensed-matter physics, our results would be useful for the study of this important issue in cold Fermi gases.
For a two-dimensional ultra-cold Fermi superfluid with an effective static magnetic impurity, we theoretically investigated the variation of the Yu–Shiba–Rusinov (YSR) bound state in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover regime. Within the framework of mean-field theory, analytical results of the YSR bound state energy were obtained as a function of the interaction parameters. First, when the background Fermi superfluid system stays in the weakly interacting BCS regime, we found that the YSR bound state energy is linearly dependent on the gap parameter with its coefficient slightly different from previous results. Second, we discovered re-entrance phenomena for the YSR state and an upper bound of the strength of the interaction between the paired atoms. By carefully analyzing the bound state energy as a function of the interaction parameters, we obtained a phase diagram showing the existence of the YSR state. Finally, we concluded that the re-entrance phenomena and the critical point can be easily experimentally detected through measurement of radio-frequency spectroscopy and density of states using current experimental techniques.