Marie Ericsson, Erik Sjoqvist
An atomic analogue of Landau quantization based on the Aharonov-Casher (AC) interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate.
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In recent years, the spin Hall effect has received great attention because of its potential application in spintronics and quantum information processing and storage. However, this effect is usually studied under the external homogeneous electric field. Understanding how the inhomogeneous electric field affects the spin Hall effect is still lacking. Here, we investigate a two-dimensional two-band time-reversal symmetric system and give an expression for the intrinsic spin Hall conductivity in the presence of the inhomogeneous electric field, which is shown to be expressed through gauge-invaria…
We propose an experimental scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the characteristic geometry of electronic motion in the presence of magnetic and electric fields. The geometric picture we provide motivates the following conjecture: non-uniform electric fields mimic the presence of spatial curvature. Consequently, the gravitational coupling constant also appears in the charge response to non-uniform electric fields.
We propose an optical means to realize a spin hall effect (SHE) in neutral atomic system by coupling the internal spin states of atoms to radiation. The interaction between the external optical fields and the atoms creates effective magnetic fields that act in opposite directions on "electrically" neutral atoms with opposite spin polarizations. This effect leads to a Landau level structure for each spin orientation in direct analogy with the familiar SHE in semiconductors. The conservation and topological properties of the spin current, and the creation of a pure spin current are discussed.
The paper introduces a semi-analytical method for calculating the Hall conductivity in the single-band approximations. The method goes beyond the linear response theory and, thus, imposes no limitation on the electric fields magnitude. It is shown that the Hall current decreases with increase of the electric field, if the Bloch frequency (which is proportional to the electric field) exceeds the cyclotron frequency (which is proportional to the magnetic field). The obtained results can be directly applied to the system of cold Bose atoms in a 2D optical lattice, where the single-band approximat…
Nonlinear phonon Hall effects in ferroelectrics: its existence and non-volatile electrical control
本文提出并推导了铁电体中非线性声子霍尔效应的理论，揭示了其与电子非线性霍尔效应的本质差异，实现了对热霍尔电流的非易失性电场控制。
We propose fractional spin hall effect (FSHE) by coupling pseudospin states of cold bosonic atoms to optical fields. The present scheme is an extension to interacting bosonic system of the recent work \cite{liu,zhu} on optically induced spin hall effect in non-interacting atomic system. The system has two different types of ground states. The 1st type of ground state is a 1/3-factor Laughlin function, and has the property of chiral - anti-chiral interchange antisymmetry, while the 2nd type is shown to be a 1/4-factor wave function with chiral - anti-chiral symmetry. The fractional statistics c…
Topologically-ordered matter is a novel quantum state of matter observed only in a small number of physical systems, notably two-dimensional electron systems exhibiting fractional quantum Hall effects. It was recently proposed that a simple form of topological matter may be created in interacting systems of rotating ultra-cold atoms. We describe ensemble measurements on small, rotating clusters of interacting bosonic atoms, demonstrating that they can be induced into quantum ground states closely analogous to topological states of electronic systems. We report measurements of inter-particle co…
We examine off-resonant light scattering from ultracold atoms in the quantum Hall regime. When the light scattering is spin dependent, we show that images formed in the far field can be used to distinguish states of the system. The spatial dependence of the far-field images is determined by the two-particle spin-correlation functions, which the images are related to by a transformation. Quasiholes in the system appear in images of the density formed by collecting the scattered light with a microscope, where the quasihole statistics are revealed by the reduction in density at the quasihole posi…
We propose an experimental scheme to realize and detect the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental set-ups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detecti…
The quantum Hall effect in a 2D electron system expresses a topological invariant, leading to a quantized conductivity. The thermal Hall and thermoelectric Nernst conductances in two dimensions are also reported to be quantized in specific systems. However, a comprehensive study of these quantities within one formalism for quantum Hall systems is so far elusive. In this work, we investigate the Hall, thermal Hall, and Nernst effects analytically and numerically in 2D and 3D. In addition to the quantized values for the Hall and thermal Hall conductances in two dimensions, we also find quasi-qua…
We study the spin-orbital interaction and the spin Hall effect(SHE) of an electron moving on a noncommutative space under the influence of a vector potential A. On a noncommutative space we find that the commutator between the vector potential A and the electric potential V_1(r) of lattice induces a new term which can be treated as an effective electric field, and the spin-Hall conductivity obtains some correction. In addition, the spin current as well as spin-Hall conductivity have distinct values in different direction. On a noncommutative space we derive the spin-depended electric current w…
We consider a generalization of the 2-dimensional (2D) quantum-Hall insulator to a non-compact, non-Abelian gauge group, the Heisenberg-Weyl group. We show that this kind of insulator is actually a layered 3D insulator with nontrivial topology. We further show that nontrivial combinations of quantized transverse conductivities can be engineered with the help of a staggered potential. We investigate the robustness and topological nature of this conductivity and connect it to the surface modes of the system. We also propose a simple experimental realization with ultracold atoms in 3D confined to…
Measuring Hall voltage and Hall resistance in an atom-based quantum simulator
本研究在中性原子量子模拟器中首次直接测量霍尔电阻，揭示了强相互作用费米子系统中霍尔效应的特性。
The quantum Hall effect occuring in two-dimensional electron gases was first explained by Laughlin, who envisioned a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a quantum Hall cylinder periodically driven by an axial magnetic field, resulting in the quantized motion of electrons. We realize this milestone experiment with an ultracold gas of dysprosium atoms, the cyclic dimension being encoded in the electronic spin and the axial field controlled by the phases of laser-induced spin-orbit couplings. Our experiment prov…
We show that in the presence of a three-dimensional (Weyl) spin-orbit coupling, a transverse spin current is generated in response to either a constant spin-independent force or a time-dependent Zeeman field in an arbitrary direction. This effect is the non-Abelian counterpart of the universal intrinsic spin Hall effect characteristic to the two-dimensional Rashba spin-orbit coupling. We quantify the strength of such an omnidirectional spin Hall effect by calculating the corresponding conductivity for fermions and non-condensed bosons. The absence of any kind of disorder in ultracold-atom syst…
Electrically induced bulk and edge excitations in the fractional quantum Hall regime
本研究通过电压脉冲电致激发二维电子液体在 $ν=2/3$ 分数量子霍尔态的不可压缩区域，利用光致发光光谱研究边缘和体态集体激发，揭示体态激发动力学及其与磁等离激元模型的吻合，并突出了边缘与体态间的拓扑联系。
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects, indicate connections to topological matter, and discuss prospects for the realization of full-fledged gauge field theories where the synthetic magnetic field has its own dynamics. The advantages of these systems over traditional electronic systems are highlighted. Finally, interdisciplinary comparisons with other synthetic matter platforms based on photonic…
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