Quantum interference near graphene layers: Observing the surface plasmons with transverse electric polarization

The spontaneous emission of a V-type three-level quantum emitter near graphene layers is investigated. With appropriate doping densities, graphene layers support transverse electric- (TE-) polarized surface plasmons. This kind of plasmon can enhance the decay rates of dipoles parallel to the layers, and subsequently, strong quantum interference presents between the two orthogonal transition dipoles of the emitter. As a result, the emission field polarization and the spectrum can be radically changed. This can be evidence of the TE-polarized surface plasmons in the graphene layers.

Figure 1

$N$-separated located graphene layers are parallel to the $x\text{−}y$ plane. The direction normal to the layers is the $z$ axis. The distance from the atom to the graphene layers is $z_0$. The inset circle is the atomic energy configuration.

Figure 2

The plasmonc wave number as a function of $\hslash \omega /E_F$ [36]. Here, ${\varepsilon }_1=1,\hslash \omega =1.99\mathrm{eV}$, and $\mu ={10}^4{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$.

Figure 3

The plasmonic wave number versus the layer number with different layer distances. The black line is the single-layer approximation result. Here, $E_F=0.1\mathrm{eV},\hslash \omega =1.99E_F$, and $\mu ={10}^5{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$.

Figure 4

The dispersion relations of the TE-polarized GPs with different layer numbers. Here, $E_F=0.1\mathrm{eV}$ and $d=5\mathrm{nm}$.

Figure 5

The decay rates ${\mathrm{\Gamma }}_p$ and ${\mathrm{\Gamma }}_n$ resulting from different modes. Here, $d=5\mathrm{nm}$ and the other parameters are the same as Fig. 3.

Figure 6

The decay rates ${\mathrm{\Gamma }}_p$. The red dashed line denotes the difference value between the total decay rate and the decay rate resulting from the propagation modes.

Figure 7

The plasmonic wave number versus the layer number when ${\varepsilon }_1=2.25$ and ${\varepsilon }_2=1$. Here, $\hslash \omega =1.99E_F,z_R=300$, and $d=3\mathrm{nm}$.

Figure 8

The decay rates ${\mathrm{\Gamma }}_p$ and ${\mathrm{\Gamma }}_n$. Here, $N=60$, and the other parameters are the same as in Fig. 7.

Figure 9

The quantum interference varying with the $z_0$. The solid black, red dashed, blue dotted lines refer to the cases that the layer number $N=50,N=60$, and $N=80$, respectively.

Figure 10

(a) The decay rates and (b) the quantum interference for the case that $\hslash {\omega }_a=1.95E_F$. Here, $\hslash {\omega }_a=1.99\mathrm{eV},N=120$, and the other parameters are the same as in Fig. 8.

Figure 11

The dynamic evolutions of the atomic population with different upper level detunings. Here, $z_0$ is set to be at the position of the intersection in Fig. 8.

Figure 12

The spontaneous emission spectrum of a quantum emitter initially prepared on level $|a\rangle$. The spectrum contains two parts, i.e., $S_x$ and $S_z$. To show the contributions of the two parts clearly, $S_z$ has been added by the maximum value of $S_x$. The parameters are the same as in Fig. 8.