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Chinese Physics B

Landau-like quantized levels of neutral atom induced by a dark-soliton shaped electric field*

Yueming Wang, Zhen Jin

Published Nov 20, 2019• 0 citations
Publisher

Abstract

Motivated by the fascinating progresses in the cold atom experiments and theories, especially the artificial gauge field induced spin–orbit coupling of neutral atoms, we present a novel dispersion of neutral atoms carrying a non-vanishing magnetic moment in a special gauge field, an external electric field of dark-soliton shaped profile. By means of WKB approximation, we obtain discrete quantized landau-like energy levels, which is instructive for the quantum Hall effect of neutral particles. The observability of the results is also discussed.

DOI
10.1088/1674-1056/ab5938

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Motivated by the fascinating progresses in the cold atom experiments and theories, especially the artificial gauge field induced spin–orbit coupling of neutral atoms, we present a novel dispersion of neutral atoms carrying a non-vanishing magnetic moment in a special gauge field, an external electric field of dark-soliton shaped profile. By means of WKB approximation, we obtain discrete quantized landau-like energy levels, which is instructive for the quantum Hall effect of neutral particles. The observability of the results is also discussed.
We show the emergence of a new type of dispersion relation for neutral atoms with an interesting similarity to the spectrum of two-dimensional electrons in an applied perpendicular constant magnetic field. These neutral atoms can be confined in toroidal optical traps and give quasi-Landau spectra. In strong contrast to the equidistant infinitely degenerate Landau levels for charged particles, the spectral gap for such two-dimensional neutral particles increases in particular electric-field configurations. The idea in the paper is motivated by the development in cold atom experiments and builds on the seminal paper of Aharonov and Casher [Phys. Rev. Lett. 53, 319 (1984)].
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
The quest of utilizing neutral particles to simulate the behaviour of charged particles in a magnetic field makes the generation of artificial magnetic field of great interest. The previous and the only proposal for the production of synthetic magnetic field for the dark state polaritons in electromagnetically induced transparency invokes the mechanical rotation of a sample. Here, we put forward an optical scheme to generate effective gauge potentials for stationary-light polaritons. 5To demonstrate the capabilities of our approach, we present recipes for having dark state polaritons in degenerate Landau levels and in driven quantum harmonic oscillator. Our scheme paves a novel way towards the investigation of the bosonic analogue of the fractional quantum Hall effect by electromagnetically induced transparency.
We investigate the properties of the Lieb lattice, that is, a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term---a non-Abelian gauge field---and demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold atoms.
The Higgs-like excitations, which distinguish from the Higgs amplitude mode in many-body system, are single-particle excitations in system with non-Abelian gauge potential. We investigate the Higgs-like excitations of cold atom system in artificial non-Abelian gauge potential. We demonstrate that when a non-Abelian gauge potential is reduced to Abelian potential, its Abelian part constructs spin-orbit coupling, and its non-Abelian part emerges Higgs-like excitations. The Higgs-like excitations induce a mass of the non-Abelian gauge field, which offsets the defect of massless of the gauge theories. We show that the mass of gauge field can affect the spin Hall currents which are produced by the spin-orbit coupling. We also discuss the observation of these phenomena in real experiment.