ℤ3 parafermionic chain emerging from Yang-Baxter equation.

We construct the 1D ℤ3 parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the ℤ3 parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the ℤ3 parafermionic model is a direct generalization of 1D ℤ2 Kitaev model. Both the ℤ2 and ℤ3 model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian H123 based on Yang-Baxter equation. Different from the Majorana doubling, the H123 holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P [formula in text] and emergent parafermionic operator Γ, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the ℤ3 parafermionic model and H123 can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.

Time Circular Birefringence in Time-Dependent Magnetoelectric Media.

Light traveling in time-dependent media has many extraordinary properties which can be utilized to convert frequency, achieve temporal cloaking, and simulate cosmological phenomena. In this paper, we focus on time-dependent axion-type magnetoelectric (ME) media, and prove that light in these media always has two degenerate modes with opposite circular polarizations corresponding to one wave vector , and name this effect "time circular birefringence" (TCB). By interchanging the status of space and time, the pair of TCB modes can appear simultaneously via "time refraction" and "time reflection" of a linear polarized incident wave at a time interface of ME media. The superposition of the two TCB modes causes the "time Faraday effect", namely the globally unified polarization axes rotate with time. A circularly polarized Gaussian pulse traversing a time interface is also studied. If the wave-vector spectrum of a pulse mainly concentrates in the non-traveling-wave band, the pulse will be trapped with nearly fixed center while its intensity will grow rapidly. In addition, we propose an experimental scheme of using molecular fluid with external time-varying electric and magnetic fields both parallel to the direction of light to realize these phenomena in practice.

More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation.

A new realization of doubling degeneracy based on emergent Majorana operator Γ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. -matrix. For 2-body interaction, R(θ) gives the "superconducting" chain that is the same as 1D Kitaev chain model. The 3-body Hamiltonian commuting with Γ is derived by 3-body R123-matrix, we thus show that the essence of the doubling degeneracy is due to [R(θ), Γ=0]. We also show that the extended Γ'-operator is an invariant of braid group BN for odd N. Moreover, with the extended Γ'-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing 2N-qubit Greenberger-Horne-Zeilinger state for odd N.

Dynamic ultraslow optical-matter wave analog of an event horizon.

We investigate theoretically the effects of a dynamically increasing medium index on optical-wave propagation in a rubidium condensate. A long pulsed pump laser coupling a D2 line transition produces a rapidly growing internally generated field. This results in a significant optical self-focusing effect and creates a dynamically growing medium index anomaly that propagates ultraslowly with the internally generated field. When a fast probe pulse injected after a delay catches up with the dynamically increasing index anomaly, it is forced to slow down and is prohibited from crossing the anomaly, thereby realizing an ultraslow optical-matter wave analog of a dynamic white-hole event horizon.

The geodesic form of light-ray trace in the inhomogeneous media.

The canonical equations of the optical cloaking proposed by Shurig, Pendry and Smith has been proved to be equivalent to the geodesic in a 3-dimensional curved space. Carrying out the argument we extend to the 4-dimensional Riemannian space where the extra time item appears as the potential term in the canonical equations. The physical meaning of the results is interpreted.