Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group

The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on density-matrix renormalization group calculation, we provide a complete characterization of the universal properties of bosonic Moore-Read state on Haldane honeycomb lattice model at filling number $\nu=1$ for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states, for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through inserting the $U(1)$ charge flux, it is found that two of the ground states can be adiabatically connected through a fermionic charge-$\textit{e}$ QP being pumped from one edge to the other, while the ground state in Ising anyon sector evolves back to itself. Furthermore, we calculate the modular matrices $\mathcal{S}$ and $\mathcal{U}$, which contain all the information for the anyonic QPs. In particular, the extracted quantum dimensions, fusion rule and topological spins from modular matrices positively identify the emergence of non-Abelian statistics following the $SU(2)_2$ Chern-Simons theory.Comment: 5 pages; 3 figure

Laser Mode Bifurcations Induced by PT\mathcal{PT}-Breaking Exceptional Points

A laser consisting of two independently-pumped resonators can exhibit mode bifurcations that evolve out of the exceptional points (EPs) of the linear system at threshold. The EPs are non-Hermitian degeneracies occurring at the parity/time-reversal ($\mathcal{PT}$) symmetry breaking points of the threshold system. Above threshold, the EPs become bifurcations of the nonlinear zero-detuned laser modes, which can be most easily observed by making the gain saturation intensities in the two resonators substantially different. Small pump variations can then switch abruptly between different laser behaviors, e.g. between below-threshold and $\mathcal{PT}$-broken single-mode operation.Comment: 4 pages, 3 figure

Understanding the nucleation mechanisms of Carbon Nanotubes in catalytic Chemical Vapor Deposition

The nucleation of carbon caps on small nickel clusters is studied using a tight binding model coupled to grand canonical Monte Carlo simulations. It takes place in a well defined carbon chemical potential range, when a critical concentration of surface carbon atoms is reached. The solubility of carbon in the outermost Ni layers, that depends on the initial, crystalline or disordered, state of the catalyst and on the thermodynamic conditions, is therefore a key quantity to control the nucleation

Spin entanglement induced by spin-orbit interactions in coupled quantum dots

We theoretically explore the possibility of creating spin quantum entanglement in a system of two electrons confined respectively in two vertically coupled quantum dots in the presence of Rashba type spin-orbit coupling. We find that the system can be described by a generalized Jaynes - Cummings model of two modes bosons interacting with two spins. The lower excitation states of this model are calculated to reveal the underlying physics of the far infrared absorption spectra. The analytic perturbation approach shows that an effective transverse coupling of spins can be obtained by eliminating the orbital degrees of freedom in the large detuning limit. Here, the orbital degrees of freedom of the two electrons, which are described by two modes of bosons, serve as a quantized data bus to exchange the quantum information between two electrons. Then a nontrivial two-qubit logic gate is realized and spin entanglement between the two electrons is created by virtue of spin-orbit coupling.Comment: 7 pages, 5 figure

Controlling the topological sector of magnetic solitons in exfoliated Cr1/3_{1/3}NbS2_2 crystals

We investigate manifestations of topological order in monoaxial helimagnet Cr$_{1/3}$NbS$_2$ by performing transport measurements on ultra-thin crystals. Upon sweeping the magnetic field perpendicularly to the helical axis, crystals thicker than one helix pitch (48 nm) but much thinner than the magnetic domain size ($\sim$1 $\mu$m) are found to exhibit sharp and hysteretic resistance jumps. We show that these phenomena originate from transitions between topological sectors with different number of magnetic solitons. This is confirmed by measurements on crystals thinner than 48 nm --in which the topological sector cannot change-- that do not exhibit any jump or hysteresis. Our results show the ability to deterministically control the topological sector of finite-size Cr$_{1/3}$NbS$_2$ and to detect inter-sector transitions by transport measurements.Comment: 7 pages, 8 figure

Observation of dressed intra-cavity dark states

Cavity electromagnetically induced transparency in a coherently prepared cavity-atom system is manifested as a narrow transmission peak of a weak probe laser coupled into the cavity mode. We show that with a resonant pump laser coupling the cavity-confined four-level atoms from free space, the narrow transmission peak of the cavity EIT is split into two peaks. The two peaks represent the dressed intra-cavity dark states and have a frequency separation approximately equal to the Rabi frequency of the free-space pump laser. We observed experimentally the dressed intra-cavity dark states in cold Rb atoms confined in a cavity and the experimental results agree with theoretical calculations based on a semiclassical analysis.Comment: 10 pages, 6 figure