Chiral near-field control of quantum light generation using magneto-optical graphene

TL;DR

This work addresses active, nanoscale control of quantum light emission near graphene under a perpendicular magnetic field. It develops a macroscopic quantum electrodynamics framework and semianalytical models for extended graphene, graphene nanoribbons, and graphene nanodisks, incorporating Landau-level transitions and SdH oscillations to compute the Green's tensor–based local photonic density of states. The results show that while extended graphene yields infrared magnetoplasmon-enhanced emission with limited intrinsic chirality, patterned geometries—particularly nanoribbons and nanodisks—produce large chiral dissymmetry between left- and right-circularly polarized emission, tunable via carrier density and field. Overall, magneto-optical graphene emerges as a versatile, tunable platform for nanoscale quantum light generation and chiral quantum optics, with a general framework applicable to other gyrotropic 2D materials.

Abstract

We theoretically explore strategies to actively control photon emission from quantum light sources by leveraging the large magneto-optical response of graphene. The quantum electrodynamic response of graphene -- characterized by the Purcell factor and the Lamb shift of a proximal emitter -- is analyzed for extended two-dimensional sheets, one-dimensional nanoribbons, and zero-dimensional nanodisks, all of which are endowed with an intrinsic chiral near-field response under a static perpendicular magnetic field. Using rigorous semianalytical models of these systems, we reveal that the emission properties can be readily tuned by variations in doping charge carrier density and applied magnetic field strength, both with respect to magnetoplasmon resonances (at infrared frequencies) and Shubnikov-de-Haas oscillations (entering telecommunication bands) associated with optical transitions between discrete Landau levels. Localized magnetoplasmons in graphene nanoribbons are predicted to induce large dissymmetry in the spontaneous emission from left-hand and right-hand circularly polarized transitions in a proximal quantum emitter, presenting applications for chiral quantum optical waveguiding. This chiral dissymmetry is further enhanced in gyrotropic graphene nanodisks, signaling that the spatial shaping of near-fields in nanostructured graphene can significantly boost the intrinsic chiral response induced by the magnetic field. These results indicate that magneto-optical graphene constitutes a versatile and highly tunable platform for quantum light generation and manipulation at the nanoscale.

Figures (4)

• Figure 1: Electrical manipulation of a quantum light emitter near an extended magneto-optical graphene sheet. (a) Illustration of a quantum emitter (QE) located a distance $z$ above a graphene sheet on a dielectric substrate that is subjected to an external magnetic field of amplitude $B$ oriented normally to the graphene plane. (b) Energy level diagram of a two-level atom with bare transition frequency $\varepsilon$, exhibiting a Lamb shift $\delta\varepsilon$ and enhanced spontaneous emission at the rate $\Gamma$ in the presence of graphene. (c) Schematic of the conical graphene electron dispersion relation (dashed lines), populated up to Fermi energy ${E_{\rm F}}$ for $B=0$, that is fragmented in discrete Landau levels (horizontal solid lines), populated up to level $N_{\rm F}$ with energy $E_{N_{\rm F}}$, in the presence of a static magnetic field. The Purcell factor (d) and Lamb shift (e) corresponding to a dipole with transition dipole moment $p=1\,e\cdot$nm at $z=25$ nm above and oriented parallel to a graphene sheet with fixed carrier density $n\approx 4.6 \times 10^{12}$ cm$^{-2}$ (Fermi energy ${E_{\rm F}}=0.25$ eV for $B=0$) are plotted for $B=0$ (black curves), $B=2.5$ T (blue curves), and $B=5$ T (red curves) as a function of the dipole transition energy $\hbar\varepsilon$. The inset shows the Purcell factors around the graphene interband transition threshold $\hbar\varepsilon\sim 2{E_{\rm F}}$. Under the same conditions, spectra of the Purcell factor (f) and Lamb shift (g) at $B=5$ T are shown as functions of the $B=0$ Fermi energy, i.e., by fixing the carrier density, with the vertical dashed lines indicating the corresponding results shown in (d) and (e). The results in panels (h) and (i) are obtained by repeating the calculations in (f) and (g) by specifying the Fermi energy in the magneto-optical graphene sheet. All results are obtained by setting the phenomenological inelastic scattering rate in graphene to $\tau^{-1}=e v_{\rm F}^2/\mu_{\rm DC}{E_{\rm F}}$ with DC mobility $\mu_{\rm DC}=10^4$ cm$^2/$Vs, choosing the substrate permittivity $\epsilon_2=2\epsilon_0$, and assuming zero temperature.
• Figure 2: Far field response of localized magnetoplasmons in graphene ribbons. (a) Illustration of magnetoplasmons in a graphene nanoribbon excited by a plane wave impinging normally to the graphene plane with electric field linearly polarized along $\hat{{\bf x}}$. Extinction cross sections of a $W=1$$\mu$m graphene ribbon are shown for the magnetic field strengths indicated in each panel as a function of (b) charge carrier density specified by the graphene Fermi energy for $B=0$ and (c) fixing the Fermi energy when $B\neq0$. Here the phenomenological damping rate $\tau^{-1}=e v_{\rm F}^2/\mu_{\rm DC} {E_{\rm F}}$ is specified for a DC mobility of $\mu_{\rm DC}=5000$ cm$^2/$Vs, the substrate permittivity is $\epsilon_2=\epsilon_0$, and temperature effects are neglected.
• Figure 3: Dipolar excitation and chiral near-field response of magneto-optical graphene ribbons. (a) Illustration of a graphene ribbon in the $z=0$ plane subjected to a perpendicular static magnetic field of magnitude $B$ and interacting with a nearby point dipole emitter. The wave-vector-resolved Green's tensor, $\mathcal{G}_{q,xx}$, is plotted for (b) $B=0$ and (c) $B=5$ T as a function of the wave vector $q$ along the direction of translational invariance and emitter transition energy, while the corresponding Purcell factors (obtained after integrating $(2\pi)^{-1}\int{\rm d q}\mathcal{G}_{q,xx}$) are presented in panel (d). Note that the contour plots in panels (b) and (c) are saturated to highlight the plasmon dispersion, and in all cases the dipole is oriented along $\hat{\bf x}$ and located 25 nm directly above the ribbon edge. The spectral dependence of (e) the Purcell factor $\Gamma_x/\Gamma_0$ for a dipole polarized in $\hat{\bf x}$ and (f) the chiral dissymmetry factor $g$ given by Eq. \ref{['eq:dissymmetryfactor_g_definition']} for circularly polarized dipoles are shown as a function of the dipole position along $x$ while maintaining a height $z=25$ nm above the ribbon when it is subjected to a magnetic field of $B=5$ T. All results here are obtained for a ribbon of width $W=200$ nm doped with a charge carrier density corresponding to ${E_{\rm F}}=0.2$ eV for $B=0$ and mobility $5000$ cm$^2/$Vs.
• Figure 4: Active tuning of linearly and circularly polarized quantum light emitters mediated by a magneto-optical graphene disk. (a) Illustration of a quantum emitter of left-circularly (LCP) and right-circularly (RCP) polarized photons located directly above a magnetooptical graphene disk. (b) Purcell factor and (c) Lamb shift corresponding to a dipole directly above and oriented parallel to a graphene disk at $B=0$ (black curve), $B=2.5$ T (purple curve) and $B=5$ T (blue curve). (d) The dissymmetry factor of Eq. \ref{['eq:dissymmetryfactor_g_definition']} quantifying chiral photon generation is plotted for the same parameters as in panels (b) and (c). (e) Lamb shift for a RCP (dashed curves) and a LCP (solid curves) dipole emitter with transitions frequencies near the dipolar plasmonic resonance. In all cases the dipole emitters are located a distance $z=30$ nm directly above the center of a disk with diameter $D=200$ nm, charge carrier doping density corresponding to ${E_{\rm F}}=0.4$ eV for $B=0$, mobility $\mu_{\rm DC}=5000$ cm$^2/$Vs, and at zero temperature.