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arXiv:1801.09016 · Physical Review A

Polaron in a non-Abelian Aubry-André-Harper model with p -wave superfluidity

Xiaodong Bai, Jia Wang, Xia-Ji Liu, Jun Xiong, Fu‐Guo Deng, Hui Hu

Published Aug 24, 2018• 6 citations
arXivHTMLPDF

Abstract

We theoretically investigate the behavior of a mobile impurity immersed in a one-dimensional quasiperiodic Fermi system with topological $p$-wave superfluidity. This polaron problem is solved by using a standard variational approach, the so-called Chevy ansatz. The polaron states are found to be strongly affected by the strength of the quasidisorder and the amplitude of the $p$-wave pairing. We analyze the phase diagram of the polaron ground state and find four phases: two extended phases, a weakly localized phase, and a strongly localized phase. It is remarkable that these polaron phases are directly corresponding to the four distinct phases experienced by the underlying background Fermi system. In particular, the weakly localized polaron phase corresponds to an intriguing critical phase of the Fermi system. Therefore, the different phases of the background system can be unambiguously probed by measuring the polaron properties via radio-frequency spectroscopy. We also investigate the high-lying polaron excited states at an infinite temperature and address the possibility of studying many-body localization of these states. We find that the introduction of $p$-wave pairing may delocalize the many-body localized states and make the system easier to thermalize. Our results could be observed in current state-of-the-art cold-atom experiments.

DOI
10.1103/physreva.98.023627

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We theoretically investigate the behavior of a mobile impurity immersed in a one-dimensional quasiperiodic Fermi system with topological ppp-wave superfluidity. This polaron problem is solved by using a standard variational approach, the so-called Chevy ansatz. The polaron states are found to be strongly affected by the strength of the quasidisorder and the amplitude of the ppp-wave pairing. We analyze the phase diagram of the polaron ground state and find four phases: two extended phases, a weakly localized phase, and a strongly localized phase. It is remarkable that these polaron phases are directly corresponding to the four distinct phases experienced by the underlying background Fermi system. In particular, the weakly localized polaron phase corresponds to an intriguing critical phase of the Fermi system. Therefore, the different phases of the background system can be unambiguously probed by measuring the polaron properties via radio-frequency spectroscopy. We also investigate the high-lying polaron excited states at an infinite temperature and address the possibility of studying many-body localization of these states. We find that the introduction of ppp-wave pairing may delocalize the many-body localized states and make the system easier to thermalize. Our results could be observed in current state-of-the-art cold-atom experiments.
We theoretically investigate the behavior of a moving impurity immersed in a sea of fermionic atoms that are confined in a quasiperiodic (bichromatic) optical lattice within a standard variational approach. We consider both repulsive and attractive contact interactions for such a simple many-body localization problem of Fermi polarons. The variational approach enables us to access relatively large systems and therefore may be used to understand many-body localization in the thermodynamic limit. The energy and wave function of the polaron states are found to be strongly affected by the quasirandom lattice potential and their experimental measurements (i.e., via radio-frequency spectroscopy or quantum gas microscope) therefore provide a sensitive way to underpin the localization transition. We determine a phase diagram by calculating two critical quasirandom disorder strengths, which correspond to the onset of the localization of the ground-state polaron state and the many-body localization of all polaron states, respectively. Our predicted phase diagram could be straightforwardly examined in current cold-atom experiments.
Immersing a mobile impurity into a many-body quantum system represents a theoretically intriguing and experimentally effective way of probing its properties. In this work, we study the polaron spectral function in various environments, within the framework of Fermi-Hubbard models. Inspired by possible realizations in cold atoms and semiconductor heterostructures, we consider different configurations for the background Fermi gas, including charge density waves, multiple Fermi seas and pair superfluids. While our calculations are performed using an exact-diagonalization approach, hence limiting our analysis to systems of few interacting Fermi particles, we identify robust spectral features supported by theoretical results. Our work provides a benchmark for computations based on mean-field approaches and reveal surprising features of polaron spectra, inspiring new theoretical investigations.
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We study polaron excitations induced by an impurity interacting with a two-dimensional p+ipp+ipp+ip Fermi superfluid. As the Fermi-Fermi pairing interaction is tuned, the background Fermi superfluid undergoes a topological phase transition. We show that such a transition is accompanied by a discontinuity in the second derivative of the polaron energy, regardless of the impurity-fermion interaction. We also identify a polaron to trimer crossover when the Fermi superfluid is in the strongly interacting, thus topologically trivial, regime. However, the trimer state is metastable against the molecular state where the impurity binds a Bogoliubov quasiparticle from the Fermi superfluid. By comparing the polaron to molecule transition in our system with that of an impurity in a noninteracting Fermi sea, we find that pairing interactions in the background Fermi superfluid effectively facilitate the impurity-fermion binding. Our results suggest the possibility of using the impurity as a probe for detecting topological phase transitions in the background; they also reveal interesting competitions between various many-body states in the system.
An impurity atom immersed in an ultracold atomic Fermi gas can form a quasiparticle, so-called Fermi polaron, due to impurity-fermion interaction. We consider a three-dimensional homogeneous dipolar Fermi gas as a medium, where the interatomic dipole-dipole interaction (DDI) makes the Fermi surface deformed into a spheroidal shape, and, using a Chevy-type variational method, investigate the ground-state properties of the Fermi polaron: the effective mass, the momentum distribution of a particle-hole excitation, the drag parameter, and the medium-density modification around the impurity. These quantities are shown to exhibit spatial anisotropies in such a way as to reflect the momentum anisotropy of the background dipolar Fermi gas. We also give numerical results for the polaron properties at the unitarity limit of the impurity-fermion interaction in the case in which the impurity and fermion masses are equal. It has been found that the transverse effective mass and the transverse momentum drag parameter of the polaron both tend to decrease by $\ensuremath{\sim}10%$ when the DDI strength is raised from 0 up to around its critical value, while the longitudinal ones exhibit a very weak dependence on the DDI.
Immersing a mobile impurity in a quantum many-body environment can reveal fundamental properties of the background medium, hence providing a powerful probe of quantum matter. This approach is particularly intriguing when considering media with exotic properties, such as strongly-correlated phases and topological states of matter. In this work, we study the dressing of a mobile impurity interacting with a chiral mode, at the edge of topological quantum matter. The resulting “chiral polaron” is characterized by an asymmetric spectral function, which reflects the chirality and group velocity of the topological edge mode. We first build our theoretical understanding from an effective one-dimensional chiral model, which captures the hallmark signatures of chiral polaron. We then demonstrate how this simple picture extends to realistic models of integer and fractional Chern insulator states, by adapting tensor-network methods to polaron spectroscopy. Injecting mobile impurities on the edge of topological quantum matter is shown to be a powerful tool to probe exotic edge properties, particularly suitable for cold-atom experiments. Mobile impurities can be useful probes of quantum states. Here, the authors theoretically identify polarons formed on the edge of topological insulating states, termed chiral polarons, that can be used to probe topological matter.