Berry phases of quantum trajectories in semiconductors under strong terahertz fields

Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to understand extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz sideband generation (HSG). While HHG and ATI have been mostly studied in atoms and molecules, the HSG in semiconductors can have interesting effects due to possible nontrivial "vacuum" states of band materials. We find that in a semiconductor with non-vanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field can accumulate Berry phases. Taking monolayer MoS$_2$ as a model system, we show that the Berry phases appear as the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.Comment: 5 page

Quantum Hall Charge Kondo Criticality

The long-thought charge Kondo effects have recently been experimentally realized in the quantum Hall regime. This experiment, supported by numerics, exemplifies the realization of two-channel Kondo state, a non-Fermi Liquid, and its crossover to the one-channel counterpart, a Fermi liquid. Scaling up such a platform, we find a hierarchy of non-Fermi Liquids and their tunable crossovers based on a renormalization group analysis. Utilizing results from a conformal field theory, we further examine the universal conductances of this strongly correlated system and their finite temperature scaling, which elucidate the sharp distinctions between charge and spin Kondo physics.Comment: 5 pages, 2 figures, and 2 table

Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators

We propose a general framework of nonlinear optics induced by non-Abelian Berry curvature in time-reversal-invariant (TRI) insulators. We find that the third-order response of a TRI insulator under optical and terahertz light fields is directly related to the integration of the non-Abelian Berry curvature over the Brillouin zone. We apply the result to insulators with rotational symmetry near the band edge. Under resonant excitations, the optical susceptibility is proportional to the flux of the Berry curvature through the iso-energy surface, which is equal to the Chern number of the surface times $2\pi$. For the III-V compound semiconductors, microscopic calculations based on the six-band model give a third-order susceptibility with the Chern number of the iso-energy surface equal to three

Topological Majorana Two-Channel Kondo Effect

A one-dimensional time-reversal-invariant topological superconductor hosts a Majorana Kramers pair at each end, where time-reversal symmetry acts as a supersymmetry that flips local fermion parity. We examine the transport anomaly of such a superconductor, floating and tunnel-coupled to normal leads at its two ends. We demonstrate the realization of a topologically-protected, channel-symmetric, two-channel Kondo effect without fine-tuning. Whereas the nonlocal teleportation vanishes, a lead present at one end telecontrols the universal transport through the other end.Comment: 4 pages, 4 figure

Imaginary geometric phases of quantum trajectories

A quantum object can accumulate a geometric phase when it is driven along a trajectory in a parameterized state space with non-trivial gauge structures. Inherent to quantum evolutions, a system can not only accumulate a quantum phase but may also experience dephasing, or quantum diffusion. Here we show that the diffusion of quantum trajectories can also be of geometric nature as characterized by the imaginary part of the geometric phase. Such an imaginary geometric phase results from the interference of geometric phase dependent fluctuations around the quantum trajectory. As a specific example, we study the quantum trajectories of the optically excited electron-hole pairs, driven by an elliptically polarized terahertz field, in a material with non-zero Berry curvature near the energy band extremes. While the real part of the geometric phase leads to the Faraday rotation of the linearly polarized light that excites the electron-hole pair, the imaginary part manifests itself as the polarization ellipticity of the terahertz sidebands. This discovery of geometric quantum diffusion extends the concept of geometric phases.Comment: 5 pages with 3 figure

Boosting Generative Models by Leveraging Cascaded Meta-Models

Deep generative models are effective methods of modeling data. However, it is not easy for a single generative model to faithfully capture the distributions of complex data such as images. In this paper, we propose an approach for boosting generative models, which cascades meta-models together to produce a stronger model. Any hidden variable meta-model (e.g., RBM and VAE) which supports likelihood evaluation can be leveraged. We derive a decomposable variational lower bound of the boosted model, which allows each meta-model to be trained separately and greedily. Besides, our framework can be extended to semi-supervised boosting, where the boosted model learns a joint distribution of data and labels. Finally, we combine our boosting framework with the multiplicative boosting framework, which further improves the learning power of generative models

Flavor Quantum Dots and Artificial Quark Model in Transition Metal Dichalcogenides

We show that the triply degenerate Q valleys in few-layer transition metal dichalcogenides provide a unique platform for exploring the rare flavor SU(3) symmetry in quantum dot geometry. The single and double dots are reminiscent of the quark model and eightfold way, and their many-body triplets and octets may be regarded as artificial quarks and hadrons. For the artificial quark transistor, each level hosts one central and two side Coulomb peaks of irrational height ratios, and flavor Kondo effects occur at 1/3 and 2/3 fillings with fractional conductance quantization in the unitary limit.Comment: 5+ pages, 4 figure

Giant Faraday rotation induced by Berry phase in bilayer graphene under strong terahertz fields

High-order terahertz (THz) sideband generation (HSG) in semiconductors is a phenomenon with physics similar to high-order harmonic generation but in a much lower frequency regime. It was found that the electron-hole pairs excited by a weak optical laser can accumulate Berry phases along a cyclic path under the driving of a strong THz field. The Berry phases appear as the Faraday rotation angles of the emission signal under short-pulse excitation in monolayer MoS$_2$. In this paper, the theory of Berry phase in THz extreme nonlinear optics is applied to biased bilayer graphene with Bernal stacking, which has similar Bloch band features and optical properties to the monolayer MoS$_2$, such as time-reversal related valleys and valley contrasting optical selection rules. The bilayer graphene has much larger Berry curvature than monolayer MoS$_2$, which leads to a giant Faraday rotation of the optical emission ($\sim$ 1 rad for a THz field with frequency 1 THz and strength 8 kV/cm). This provides opportunities to use bilayer graphene and low-power THz lasers for ultrafast electro-optical devices.Comment: 6 pages, 3 figure

Towards Interpretable Deep Neural Networks by Leveraging Adversarial Examples

Deep neural networks (DNNs) have demonstrated impressive performance on a wide array of tasks, but they are usually considered opaque since internal structure and learned parameters are not interpretable. In this paper, we re-examine the internal representations of DNNs using adversarial images, which are generated by an ensemble-optimization algorithm. We find that: (1) the neurons in DNNs do not truly detect semantic objects/parts, but respond to objects/parts only as recurrent discriminative patches; (2) deep visual representations are not robust distributed codes of visual concepts because the representations of adversarial images are largely not consistent with those of real images, although they have similar visual appearance, both of which are different from previous findings. To further improve the interpretability of DNNs, we propose an adversarial training scheme with a consistent loss such that the neurons are endowed with human-interpretable concepts. The induced interpretable representations enable us to trace eventual outcomes back to influential neurons. Therefore, human users can know how the models make predictions, as well as when and why they make errors

Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphs

Unlike an irreducible $Z$-matrices, a weakly irreducible $Z$-tensor $\mathcal{A}$ can have more than one eigenvector associated with the least H-eigenvalue. We show that there are finitely many eigenvectors of $\mathcal{A}$ associated with the least H-eigenvalue. If $\mathcal{A}$ is further combinatorial symmetric, the number of such eigenvectors can be obtained explicitly by the Smith normal form of the incidence matrix of $\mathcal{A}$. When applying to a connected uniform hypergraph $G$, we prove that the number of Laplacian eigenvectors of $G$ associated with the zero eigenvalue is equal to the the number of adjacency eigenvectors of $G$ associated with the spectral radius, which is also equal to the number of signless Laplacian eigenvectors of $G$ associated with the zero eigenvalue if zero is an signless Laplacian eigenvalue