Rayleigh scattering in an emitter-nanofiber-coupling system

Scattering is a general process in both fundamental and applied physics. In this paper, we investigate Rayleigh scattering of a solid-state-emitter coupled to a nanofiber, by $S$-matrix-like theory in $k$-space description. Under this model, both Rayleigh scattering and dipole interaction are studied between a two-level artificial atom embedded in a nanocrystal and fiber modes (guided and radiation modes). It is found that Rayleigh scattering plays a critical role in the transport properties and quantum statistics of photons. On the one hand, Rayleigh scattering produces the transparency in the optical transmitted field of the nanofiber, accompanied by the change of atomic phase, population, and frequency shift. On the other hand, the interference between two kinds of scattering fields by Rayleigh scattering and dipole transition modifies the photon statistics (second-order autocorrelation function) of output fields, showing a strong wavelength dependence. This study provides guidance for the solid-state emitter acting as a single-photon source and can be extended to explore the scattering effect in many-body physics.

Figure 1

(a) Schematic illustration of the system composed of a nanofiber and a solid-state emitter (a two-level artificial atom embedded in a nanocrystal). (b) The $n$-times scattering process diagram. The excited input mode $E_{\mathit{k}{}^{\prime }}$ is scattered into other guided or radiation modes $E_{{\mathit{k}}_j}$ ($j=1,2,...,n$) by the emitter, through Rayleigh scattering and atomic dipole transition with strength $p_s+p_d$. Subsequently, each mode propagates described by transmission matrix $N$. The two procedures take place repeatedly $n$ times.

Figure 2

Transmission $\mathcal{T}$ (a), reflection $\mathcal{R}$ (b), energy loss $\mathcal{L}$ (c), and phase shift $\delta \psi$ (d) of the corresponding transmitted field as a function of the detuning of incident light from the atomic resonance. The following three different cases are plotted: (i) in the absence of the artificial atom ($a=80\mathrm{nm}$, $|{\mathit{P}}_{\mathrm{atom}}|=0$, black dashed curves); (ii) in the absence of the nanocrystal ($a=0$, $|{\mathit{P}}_{\mathrm{atom}}|=1.71\times {10}^{-8}e\mathrm{cm}$, blue dotted curves); and (iii) in the presence of both the two-level atom and nanocrystal ($a=80\mathrm{nm}$, $|{\mathit{P}}_{\mathrm{atom}}|=1.71\times {10}^{-8}e\mathrm{cm}$, red solid curves). The red stars indicate the transparent point at $\mathrm{\Delta }\omega =1/\xi$. The fiber radius is $200\mathrm{nm}$ and the position of the nanocrystal is $({\rho }_0=280\mathrm{nm},\varphi =0,z=0)$.

Figure 3

(a) Rayleigh-scattering-induced resonant frequency shift ${\mathrm{\Delta }}_{\mathrm{RSFS}}$ of a two-level atom, as a function of the atomic dipole moment $|{\mathit{P}}_{\mathrm{atom}}|$. (b) The shift (black solid curve) and the ratio ${\mathrm{\Delta }}_{\mathrm{RSFS}}/({\gamma }_{d,1}+{\gamma }_{d,0})$ (red dotted curve) as a function of radium $a$ of nanocrystal.

Figure 4

Phase change of atom (a) and population of the atomic excited state (b) as a function of the detuning $\mathrm{\Delta }\omega$, in the absence (blue dotted curves) and presence (red solid curves) of Rayleigh scattering. The input power is 1.5 pW. The red star indicates transparent point $\mathrm{\Delta }\omega =1/\xi$.

Figure 5

Second-order autocorrelation function of the reflected field (a) and transmitted field (b). The following three different cases are plotted: (i) in the absence of the two-level artificial atom (black dashed curves); (ii) in the absence of the nanocrystal (blue dotted curves); and (iii) in the presence of both the two-level artificial atom and nanocrystal (red solid curves).

Figure 6

Second-order autocorrelation function of reflected field of the on-resonance incident optical field $\omega ={\omega }_0$ as a function of the radius $a$ (a) and refractive index (b) of a nanocrystal.