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.
We study the classical dynamics of a membrane inside a cavity in the situation where this optomechanical system possesses a reflection symmetry. Symmetry breaking occurs through supercritical and subcritical pitchfork bifurcations of the static fixed point solutions. Both bifurcations can be observed through variation of the laser-cavity detuning, which gives rise to a boomerang-like fixed point pattern with hysteresis. The symmetry-breaking fixed points evolve into self-sustained oscillations when the laser intensity is increased. In addition to the analysis of the accompanying Hopf bifurcations we describe these oscillations at finite amplitudes with an ansatz that fully accounts for the frequency shift relative to the natural membrane frequency. We complete our study by following the route to chaos for the membrane dynamics.
The inelastic scattering and conversion process between photons and phonons by laser-driven quantum dots is analyzed for a honeycomb array of optomechanical cells. Using Floquet theory for an effective two-level system, we solve the related time-dependent scattering problem, beyond the standard rotating-wave approximation approach, for a plane Dirac-photon wave hitting a cylindrical oscillating barrier that couples the radiation field to the vibrational degrees of freedom. We demonstrate different scattering regimes and discuss the formation of polaritonic quasiparticles. We show that sideband-scattering becomes important when the energies of the sidebands are located in the vicinity of avoided crossings of the quasienergy bands. The interference of Floquet states belonging to different sidebands causes a mixing of long-wavelength (quantum) and short-wavelength (quasiclassical) behavior, making it possible to use the oscillating quantum dot as a kind of transistor for light and sound. We comment under which conditions the setup can be utilized to observe zitterbewegung. arXiv:1809.10043v3 [cond-mat.mes-hall]
Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address various quantum coherence and interference phenomena. First, a perpendicular magnetic field, penetrating the graphene ring, gives rise to Aharonov-Bohm oscillations in the conductance as a function of the magnetic flux, on top of the universal conductance fluctuations. At very high fluxes the interference gets suppressed and quantum Hall edge channels develop. Second, applying an electrostatic potential to one of the ring arms, nn n-or npn-junctions can be realized with particle transmission due to normal tunneling or Klein tunneling. In the latter case the Aharonov-Bohm oscillations weaken for smooth barriers. Third, if potential disorder comes in to play, both Aharonov-Bohm and Klein tunneling effects rate down, up to the point where particle localization sets in.Keywords mesocopic transport · quantum interferece · graphene-based nanostructures · Aharonov-Bohm effect · disorder effects PACS 73.23.-b · 72.80.Vp · 73.43.Jn · 73.20.Fz
We consider a Dice model with Dirac cones intersected by a topologically flat band at the charge neutrality point and analyze the inelastic scattering of massless pseudospin-1 particles on a circular, gate-defined, oscillating barrier. Focusing on the resonant scattering regime at small energy of the incident wave, we calculate the reflection and transmission coefficients and derive explicit expressions for the time-dependent particle probability, current density and scattering efficiency within (Floquet) Dirac-Weyl theory, both in the near-field and the far-field. We discuss the importance of sideband scattering and Fano resonances in the quantum limit. When resonance conditions are fulfilled, the particle is temporarily trapped in vortices located close to edge of the quantum dot before it gets resubmitted with strong angular dependence. Interestingly even periodically alternating forward and backward radiation may occur. We also demonstrate the revival of resonant scattering related to specific fusiform boundary trapping profiles.
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