Abstract
Analyzing the scattering and conversion process between photons and phonons coupled via radiation pressure in a circular quantum dot on a honeycomb array of optomechanical cells, we demonstrate the emergence of optomechanical Dirac physics. Specifically we prove the formation of polaritonic quasi-bound states inside the dot, and angle-dependent Klein tunneling of light and emission of sound, depending on the energy of the incident photon, the photon-phonon interaction strength, and the radius of the dot. We furthermore demonstrate that forward scattering of light or sound can almost switched off by an optically tuned Fano resonance; thereby the system may act as an optomechanical translator in a future photon-phonon based circuitry.
Highlights
Going beyond the prototyp cavity-optomechanical system consisting of a Fabry-Perot cavity with a movable end mirror, the currently most promising platforms are optomechanical crystals or arrays[17,18,19,20,21,22]
The logical step would be the creation of ‘optomechanical metamaterials’ with an in situ tunable band structure, which–if adequately designed–should allow to mimic classical dynamical gauge fields[23], Dirac physics[24], optomechanical magnetic fields[25], or topological phases of light and sound[26], just as optical lattices filled with ultracold quantum gases[27] and topological photonic crystals[28]
Solving the scattering problem for a plane photon wave injected by a probe laser, we discuss Dirac polariton formation, possible Klein tunneling and photon-phonon conversion triggered by the tunable interaction between the co-localized optical and mechanical modes in the quantum dot region
Summary
Without photon-phonon coupling the photon (orange) and phonon (black) Dirac cones (obtained in low-energy approximation) intersect. In the quantum dot region with g > 0, weakly nonlinear (photon-phonon) polariton bands (green) emerge. V = modes, τ and σ are vectors of Pauli m21 a(vtori+cesv,mk)(,rδ)vg =iv veos −th vemw, wavitehvevco/tmoras(pthoesivtieoloncviteicetsoorf) the optical/mechanical of the Dirac wave, R is the quantum-dot radius, and g parametrizes the photon-phonon coupling strength, cf Fig. 1. For g = 0, the bandstructure simplifies to two independent photonic and phononic Dirac cones, and the scattering problem can be solved as for a graphene quantum dot[29,30,31]. We expand the incident photonic wave (in x direction), the transmitted wave inside the dot (ψt = ψ+t + ψ−t) and the reflected wave (ψref = ψoref + ψmref ) in polar coordinates (l–quantum number of angular momentum):.
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