We describe a novel phenomenon occurring when a polarized Gaussian beam of light is observed in a Cartesian reference frame whose axes are not parallel to the direction of propagation of the beam. Such phenomenon amounts to an intriguing spin-dependent shift of the position of the center of the beam, with manners akin to the spin Hall effect of light. We demonstrate that this effect is unavoidable when the light beam possesses a nonzero transverse angular momentum.
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 introduce a quench of the geometry of Landau level orbitals as a probe of nonequilibrium dynamics of fractional quantum Hall (FQH) states. We show that such geometric quenches induce coherent many-body dynamics of neutral degrees of freedom of FQH fluids. The simplest case of mass anisotropy quench can be experimentally implemented as a sudden tilt of the magnetic field, and the resulting dynamics reduces to the harmonic motion of the spin-$2$ "graviton" mode, i.e., the long wavelength limit of the Girvin-MacDonald-Platzman magnetoroton. We derive an analytical description of the graviton d…
We present a new approach to obtaining the scaling behavior of the entanglement entropy in fractional quantum Hall states from finite-size wavefunctions. By employing the torus geometry and the fact that the torus aspect ratio can be readily varied, we can extract the entanglement entropy of a spatial block as a continuous function of the block boundary. This approach allows us to extract the topological entanglement entropy with an accuracy superior to what is possible on the spherical or disc geometry, where no natural continuously variable parameter is available. Other than the topological …
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.
Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall (FQH) phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the non-perturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that…
We study the effects of the quantum geometric tensor, i.e., the Berry curvature and the Fubini-Study metric, on the steady state of driven-dissipative bosonic lattices. We show that the quantum-Hall-type response of the steady-state wave function in the presence of an external potential gradient depends on all the components of the quantum geometric tensor. Looking at this steady-state Hall response, one can map out the full quantum geometric tensor of a sufficiently flat band in momentum space using a driving field localized in momentum space. We use the two-dimensional Lieb lattice as an exa…
The geometric effects of two-dimensional curved systems have been an interesting topic for a long time. A Möbius surface is specifically considered. For a relativistic particle confined to the nontrivial surface, we give the effective Dirac equation in the thin-layer quantization formalism, and we find a geometric gauge potential that results from the rotation transformation of the local frame moving on Möbius strip, and an effective mass that is from the rescaling transformation. Intriguingly, the geometric gauge potential can play a role of monopole magnetic field for the particles with spin…
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.
We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for various ground and excited states, with or without mass anisotropy. We focus on an important class of regions that contain sharp corners or cusps, leading to a geometric angle-dependent contribution to the EE. We unravel surprising relations by comparing this corner term at different fillings. We further find that the corner term, when properly normalized, has …
Light-tunable quantum metric non-linear Hall response in Berry dipole semimetals
Centre for Nanotechnology, Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校纳米技术中心）；Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore（印度科学学院固态与结构化学单元）
Hall viscosity of the Laughlin state on noisy quantum computers
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；City College of the City University of New York（纽约市立学院）；Western Washington University（西华盛顿大学）；Graduate Center of City University of New York（纽约市立大学研究生中心）
Orbital Hall Effect in Weyl Semimetals from quantum geometric band interference
University of Bologna（博洛尼亚大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普结构动力学研究所）；Universität Würzburg（维尔茨堡大学）；Universidad del País Vasco（巴斯克大学）；The Flatiron Institute（平顿研究所）
Optics naturally provides us with some powerful mathematical operations. Here we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a s…
When nanometric, noncoplanar spin textures with scalar spin chirality (SSC) are coupled to itinerant electrons, they endow the quasiparticle wavefunctions with a gauge field, termed Berry curvature, in a way that bears analogy to relativistic spin-orbit coupling (SOC). The resulting deflection of moving charge carriers is termed geometrical (or topological) Hall effect. Previous experimental studies modeled this signal as a real-space motion of wavepackets under the influence of a quantum-mechanical phase. In contrast, we here compare the modification of Bloch waves themselves, and of their en…
We investigate the quantum dynamics of systems involving small numbers of strongly interacting photons. Specifically, we develop an efficient method to investigate such systems when they are externally driven with a coherent field. Furthermore, we show how to quantify the many-body quantum state of light via correlation functions. Finally, we apply this method to two strongly interacting cases: the Bose-Hubbard and fractional quantum Hall models, and discuss an implementation of these ideas in atom-photon system.
Topological insulators have attracted abundant attention for a variety of reasons -- notably, the possibility for lossless energy transport through edge states `protected' against disorder. Topological effects like the Quantum Hall state can be induced through a gauge field, which is however hard to create in practice, especially for charge-neutral particles. One way to induce an effective gauge potential is through a dynamic, time-periodic modulation of the lattice confining such particles. In this way, the Haldane Quantum Hall effect was recently observed in a cold atom system. Here, we show…
