Observing movement of Dirac cones from single-photon dynamics

Graphene with honeycomb structure, critically important in understanding physics of matter, exhibits exceptionally unusual half-integer quantum Hall effect and unconventional electronic spectrum with quantum relativistic phenomena. Particularly, graphenelike structure can be used for realizing topological insulator which inspires an intrinsic topological protection mechanism with strong immunity for maintaining coherence of quantum information. These various peculiar physics arise from the unique properties of Dirac cones which show high hole degeneracy, massless charge carriers, and linear intersection of bands. Experimental observation of Dirac cones conventionally focuses on the energy-momentum space with bulk measurement. Here, we demonstrate a direct observation of the movement of Dirac cones from single-photon dynamics in photonic graphene under different biaxial strains. Sharing the same spirit of wave-particle nature in quantum mechanics, we identify the movement of Dirac cones by dynamically detecting the edge modes and extracting the diffusing distance of the packets with accumulation and statistics on individual single-particle registrations. Our results of observing movement of Dirac cones from single-photon dynamics, together with the method of direct observation in real space by mapping the band structure defined in momentum space, paves a novel way to understand and explore a variety of artificial structures.

Figure 1

Construction and modeling of photonic graphene with biaxial strains. (a) Schematic diagram of large-scale integrated photonic graphene on silica chip. Single photons are injected into the entry waveguide in the bottom boundary (bearded edge) and the top boundary (zigzag edge). (b) Anisotropic graphene model under the compressive strain in the horizontal direction and tensile strain in the vertical direction, resulting in $c_v<c_d$. (c) Isotropic graphene model with $c_v=c_d$. (d) Anisotropic graphene model under the tensile strain in the horizontal direction and compressive strain in the vertical direction, resulting in $c_v>c_d$.

Figure 2

Moving of Dirac cones via introducing of the anisotropy. (a) Microscopic image of cross section of three types of photonic graphene with the construction parameters. Parameters $r_d$ and $r_v$ are marked by the red dots in the relationship between the separation of adjacent waveguides and the nearest coupling coefficient. Panels (b)–(d) show the energy dispersion with Dirac cones or without Dirac cones in three cases. (e) Band structure of the three cases along the $k_x$ parametric plane. Red arrows indicate the movement of the Dirac cones when the anisotropy is introduced. (f) Edge band structure of three cases in limit. Bulk modes, bearded mode, and zigzag mode are denoted by wathet blue, dark blue, and red, respectively.

Figure 3

Experimental results for observing Dirac cones for $R<1$. (a), (b) Bearded edge band structure and zigzag edge band structure. The selected region of Bloch wave vectors is marked by the grey belt. The edge modes are marked by red lines. Ratio of the photons staying in the edge for $k_x=-\frac{\pi }{2}, k_x=\frac{\pi }{2}$ for exciting bearded edge (c), and $k_x=-\pi , k_x=\pi$ for exciting zigzag edge (d). (e) Dynamical distribution patterns of the output facet for exciting bearded edge at $k_x=\frac{\pi }{2}$. (f) Dynamical distribution patterns of the output facet for exciting zigzag edge at $k_x=\pi$. (g) Dynamical diffusing distance for $k_x=-\frac{\pi }{2}$(i) and $k_x=\frac{\pi }{2}$(ii). (h) Dynamical diffusing distance for $k_x=-\pi$(i) and $k_x=\pi$(ii).

Figure 4

Experimental results for observing Dirac cones for $R>1$. (a) Zigzag edge band structure. The selected region of the Bloch wave vectors is marked by the grey belt. The edge modes are marked by red lines. Ratio of the photons staying in the edge at $k_x=-\frac{\pi }{2}$ (b) and $k_x=0$ (c). Dynamical distribution patterns of the output facet for zigzag modes at $k_x=-\frac{\pi }{2}$ (d) and $k_x=0$ (e). (f) Dynamical diffusing distance for $k_x=-\frac{\pi }{2}$. (g) Dynamical diffusing distance for $k_x=0$.