Entangled light from bimodal optical nanoantennas

We suggest a hybrid plasmonic device made of a bimodal metallic nanoantenna coupled to an incoherently pumped quantum emitter. This device emits light into the two modes entangled in the number of photons. The process is a prime example of losses changing from being a nuisance into something beneficial, since, although it is counterintuitive, the entanglement is enabled by strong incoherent processes, i.e., the dominant scattering and absorption rates of the nanoantenna. This renders the nanoantenna an active source of nonclassicality. Both the high emission rate and the degree of entanglement of the emitted light are insensitive with respect to imperfections in the nanoantenna length, rendering the scheme feasible for an implementation.

Figure 1

Illustration of the generation of entangled light based on the bimodal properties of a nanoantenna.

Figure 2

(a) Generic spectrum of a considered doubly resonant nanoantenna that features two modes at resonance frequency ${\omega }_{\alpha }$ and ${\omega }_{\beta }$. Their spectral overlap $\mathrm{\Delta }{\omega }_{\alpha \beta }$ contains a quantum emitter with a transition frequency of ${\omega }_{\mathrm{qe}}$. (b) Schematic depicting the two-step operation principle of the hybrid system consisting of a nanoantenna (NA) and a quantum emitter (QE). Included are pump $P$, bimodal coupling with coupling constants ${\kappa }_{\alpha }$ and ${\kappa }_{\beta }$, and entangled emission of $|{\psi }_{\varphi }\rangle$ in modes $\alpha$ and $\beta$. To keep the emission channel well separated from the pump beam, a third auxiliary level of the quantum emitter may be used to realize the pumping step.

Figure 3

(a) Schematic of the nanoantenna. The blue dot corresponds to the position of the quantum emitter. (b) Scattering spectra $P^{\mathrm{scat}}\left(\omega \right)$ for quantum emitter orientations $\vartheta$ in $\left[0^{\circ },{180}^{\circ }\right]$ for $\mathrm{\Delta }L=90$ nm. The two orientations corresponding to single-mode excitations are marked in white.

Figure 4

Depiction of the normalized field distributions of the real part of the out-of-plane component of the electric field of both modes for individual excitation via specific dipole orientation. The field distributions are visualized 5 nm above the top faces of the nanorods, and the dipole orientations are indicated by the orientation of the small green arrow positioned in the vertex of the L-shaped nanoantenna.

Figure 5

(a) Scattering spectra $P^{\mathrm{scat}}\left(\omega \right)$ for quantum emitters with $\vartheta ={45}^{\circ }$ and varying $\mathrm{\Delta }L$. (b) As in (a), but with $\vartheta ={135}^{\circ }$. White dashed lines in (a) and (b) mark the length differences selected for further analysis.

Figure 6

(a) Total photon emission rate $r$ and (b) logarithmic negativity $E_{\mathcal{N}}\left({\rho }_{\mathrm{ff}}\right)$, depending on ${\omega }_{\mathrm{qe}}$ and pump $P$. Results in (a) and (b) correspond to nanoantennas with $\mathrm{\Delta }L=0$.

Figure 7

(a) Total photon emission rate $r$ and (b) logarithmic negativity $E_{\mathcal{N}}\left({\rho }_{\mathrm{ff}}\right)$ as functions of the dipole moment magnitude $d$ and orientation $\vartheta$ for $P=1$ GHz and ${\omega }_{\mathrm{qe}}^{\mathrm{opt}}$. Results in (a) and (b) correspond to nanoantennas with $\mathrm{\Delta }L=0$.

Figure 8

(a) $E_{\mathcal{N}}\left({\rho }_{\mathrm{ff}}\right)$ (red solid line) and probabilities of the Bell-like entangled state $|{\mathrm{\Psi }}_{\varphi }\rangle$ (blue dot-dashed line) and the separable state $|10\rangle$ (green dashed line) as a function of $\vartheta$ for nanoantennas with $\mathrm{\Delta }L=0$. (b) Emission rate for the representative nanoantennas, depending on $P$ and for ${\omega }_{\mathrm{qe}}^{\mathrm{opt}}$.

Figure 9

(a) Absorption spectra $P^{\mathrm{abs}}\left(\omega \right)$ for electric dipolar sources oriented at $\vartheta ={45}^{\circ }$ and varying $\mathrm{\Delta }L$. (b) As in (a), but with $\vartheta ={135}^{\circ }$.

Figure 10

Spectra of scattered and absorbed electromagnetic power for individual mode resonance due to dipole excitation according to (a) $\vartheta ={45}^{\circ }$ and (b) $\vartheta ={135}^{\circ }$ for a nanoantenna of $\mathrm{\Delta }L=93$ nm. Additionally shown are Lorentzian fits of the line shapes and the characteristic parameters derived from these fits. Please note that the amplitudes have been scaled to 1 for convenience, since thereby neither the linewidth nor the central frequency is affected.

Figure 11

(a) Stationary expectation values of the number of photons in modes 1 (blue solid line) and 2 (red dashed line) as functions of the pump rate $P$. (b) Photon number ratios ${log}_{10}\left[\frac{p\left(1\right)}{p\left(0\right)}\right]$ (purple solid line) and ${log}_{10}\left[\frac{p\left(2\right)}{p\left(1\right)}\right]$ (green dashed line), where $p\left(n\right)$ denotes that exactly $n$ photons in total are present in the system. The plots correspond to the equal-arms nanoantenna $\left(\mathrm{\Delta }L=0\right)$ for ${\omega }_{\mathrm{qe}}=({\omega }_1+{\omega }_2)/2$, and the dipole moment oriented along one of the nanorods.

Figure 12

(a) Schematic illustration of investigated misplacement. (b) Scattered power as a function of dipole emitter frequency and orientation for a shift of 2 nm. The white dashed lines mark the original central frequencies. The areas with green frames show different behavior: I, approximative individual excitation of mode 1 at about ${\omega }_1$; II, approximative individual excitation of mode 2 at about ${\omega }_2$.