Single-Photon Nonlinear Optics with Graphene Plasmons

We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch.

Figure 1

(a) A doped graphene disk confines photons as plasmons to mode volumes millions of times smaller than free space. (b) This induces a large dispersive nonlinearity $\eta$ [defined in Eq. (5)] so that only a single photon can resonantly excite the cavity. (c) Integrated nonlinear optical circuit for using the graphene plasmon cavity to realize a single photon switch. First the photons are converted into planar plasmons of a graphene waveguide via a grating, then they couple to the plasmon cavity, after which they are converted back into waveguide photons. For the frequencies we consider the waveguide and grating could be fabricated from etched Si. (d) Top down view of the plasmon cavity from (c) showing the width $W$ of the plasmon cavity, the width $W^{\prime }$ of the graphene nanoribbon, and the spacing $d$ between the cavity and nanoribbon.

Figure 2

(a) Nonlinear shift [calculated from Eq. (5)] for the fundamental mode relative to the plasmon linewidth with decreasing mode volume $V_0=({\lambda }_{\mathrm{sp}}/{\lambda }_0{)}^3$. Here we take the linewidth as $\gamma =e{v}_F^2/\mu \hslash {\omega }_F$ with the Fermi energy $\hslash {\omega }_F=0.2$ eV and a mobility of $\mu ={10}^5({10}^4){\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ corresponding to a quality factor of roughly 600(60). (b) $g^{(2)}(t)$ for the graphene plasmon cavity driven by a weak coherent state for $\hslash {\omega }_{\mathrm{sp}}=0.2\mathrm{eV}$ and two different mobilities. $g^{(2)}(0)<1$ indicates a transition to an effective two-level system as illustrated schematically in Figs. 1a, 1b.

Figure 3

(a) Single photon transmission through the device depicted in Figs. 1c, 1d. We take $\xi =k_0/2$ and $P\gg 1$ so the only losses are in the nanoribbons. The plasmon frequency is 0.2 eV and we assume the decay rate $\gamma$ is dominated by impurity scattering. The three curves are for a fixed plasmon frequency with increasing Fermi energy, which increases the spatial propagation length of the plasmons. (b) Bunching in reflection for two incident photons from the left with $\hslash {\omega }_{\mathrm{sp}}=0.2\mathrm{eV}$, $E_F=0.23\mathrm{eV}$, $P=2$, and mobility $\mu ={10}^4({10}^5){\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ [dashed(solid)] corresponding to a lifetime of 0.2(2) ps and a cavity quality factor of 60(600). (c) Antibunching in transmission for $P=0.1$ with other parameters as in (a).