Chiral topological states in Bose-Fermi mixtures

Topological states were initially discovered in solid state systems and have generated widespread interest in many areas of physics. The advances in cold atoms create novel settings for studying topological states that would be quite unrealistic in solid state systems. One example is that the constituents of quantum gases can be various types of bosons, fermions, and their mixtures. This paper explores interaction-induced topological states in two-dimensional Bose-Fermi mixture. We propose a class of topological states which have no fractionalized excitations but possess maximally chiral edge states. For previously known topological states, these two features can only be found simultaneously in the integer quantum Hall states of fermions and the $E_{8}$ state of bosons. The existences of some proposed states in certain continuum and lattice models are corroborated by exact diagonalization and density matrix renormalization group calculations. This paper suggests that Bose-Fermi mixture is a very appealing platform for studying topological states.Comment: 10 pages, 8 figure

Dynamic gesture recognition using PCA with multi-scale theory and HMM

In this paper, a dynamic gesture recognition system is presented which requires no special hardware other than a Webcam. The system is based on a novel method combining Principal Component Analysis (PCA) with hierarchical multi-scale theory and Discrete Hidden Markov Models (DHMM). We use a hierarchical decision tree based on multiscale theory. Firstly we convolve all members of the training data with a Gaussian kernel, which blurs differences between images and reduces their separation in feature space. This reduces the number of eigenvectors needed to describe the data. A principal component space is computed from the convolved data. We divide the data in this space into two clusters using the k-means algorithm. Then the level of blurring is reduced and PCA is applied to each of the clusters separately. A new principal component space is formed from each cluster. Each of these spaces is then divided into two and the process is repeated. We thus produce a binary tree of principal component spaces where each level of the tree represents a different degree of blurring. The search time is then proportional to the depth of the tree, which makes it possible to search hundreds of gestures in real time. The output of the decision tree is then input into DHMM to recognize temporal information

Emergent Fermi sea in a system of interacting bosons

An understanding of the possible ways in which interactions can produce fundamentally new emergent many-body states is a central problem of condensed matter physics. We ask if a Fermi sea can arise in a system of bosons subject to contact interaction. Based on exact diagonalization studies and variational wave functions, we predict that such a state is likely to occur when a system of two-component bosons in two dimensions, interacting via a species independent contact interaction, is exposed to a synthetic magnetic field of strength that corresponds to a filling factor of unity. The fermions forming the SU(2) singlet Fermi sea are bound states of bosons and quantized vortices, formed as a result of the repulsive interaction between bosons in the lowest Landau level