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Modern Physics Letters B

TOPOLOGICAL FERMI LIQUID EMERGING FROM A BOSONIC MODEL IN OPTICAL SUPERLATTICES

Bo-Lun Chen, Su-Peng Kou

Published Apr 20, 2011• 3 citations
Publisher

Abstract

In this paper, we systematically analyze the properties of the bosonic t–J model simulated in optical superlattices. In particular, by using a slave-particle approach, we show the emergence of a strange topological Fermi liquid with Fermi surfaces from a purely bosonic system. We also discuss the possibility of observing these phenomena in ultracold atom experiments. The result may provide some crucial insights into the origin of high-Tc superconductivity.

DOI
10.1142/s0217984911026498

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In this paper, we systematically analyze the properties of the bosonic t–J model simulated in optical superlattices. In particular, by using a slave-particle approach, we show the emergence of a strange topological Fermi liquid with Fermi surfaces from a purely bosonic system. We also discuss the possibility of observing these phenomena in ultracold atom experiments. The result may provide some crucial insights into the origin of high-Tc superconductivity.
Recent experiments on quantum degenerate gases give an opportunity for simulating strongly-correlated electronic systems in optical lattices. It may shed light on some long-standing puzzles in condensed-matter physics, like the nature of high-temperature superconductivity in cuprates that had baffled people over two decades. It is believed that the two-dimensional fermionic Hubbard model, or t-J model, contains the key to this problem; but the difficulty of unveiling the mystery of a strongly-interacting fermionic system is also generally acknowledged. Here, as a substitute, we systematically analyze the property of bosonic t-J model simulated in optical superlattices near unit-filling. In particular, we show the emergence of a strange topological Fermi liquid with Fermi surfaces from a purely bosonic system. We also discuss the possibility of observing these phenomena in ultracold atom experiments. The result may provide some crucial insights into the origin of high-T_{c} superconductivity.
Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high- T c superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.
The Fermi-Hubbard model is a key concept in condensed matter physics and provides crucial insights into electronic and magnetic properties of materials. Yet, the intricate nature of Fermi systems poses a barrier to answering important questions concerning d-wave superconductivity and quantum magnetism. Recently, it has become possible to experimentally realize the Fermi-Hubbard model using a fermionic quantum gas loaded into an optical lattice. In this atomic approach to the Fermi-Hubbard model, the Hamiltonian is a direct result of the optical lattice potential created by interfering laser fields and short-ranged ultracold collisions. It provides a route to simulate the physics of the Hamiltonian and to address open questions and novel challenges of the underlying many-body system. This review gives an overview of the current efforts in understanding and realizing experiments with fermionic atoms in optical lattices and discusses key experiments in the metallic, band-insulating, superfluid, and Mott-insulating regimes.
A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far has been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.
We study quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice. The extended Bose–Hubbard model derived from the system of ultracold bosonic atoms in an optical superlattice is solved numerically with the Gutzwiller approach. We find that the modulated superfluid (MS), Mott-insulator (MI) and density-wave (DW) phases appear in some regimes of parameters. The experimental detection of the first-order correlations and the second-order correlations of different quantum phases with time-of-flight and noise-correlation techniques is proposed.
We analyze topological properties of the one-dimensional Bose-Hubbard model with a quasiperiodic superlattice potential. This system can be realized in interacting ultracold bosons in optical lattice in the presence of an incommensurate superlattice potential. We first analyze the quasiperiodic superlattice made by the cosine function, which we call Harper-like Bose-Hubbard model. We compute the Chern number and observe a gap-closing behavior as the interaction strength UUU is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of UUU and a continuous deformation parameter βββ between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.