Resonance fluorescence spectrum of a $\mathrm{\Lambda }$-type quantum emitter close to a metallic nanoparticle

We theoretically study the resonance fluorescence spectrum of a three-level quantum emitter coupled to a spherical metallic nanoparticle. We consider the case in which the quantum emitter is driven by a single laser field along one of the optical transitions. We show that the development of the spectrum depends on the relative orientation of the dipole moments of the optical transitions in relation to the metal nanoparticle. In addition, we demonstrate that the location and width of the peaks in the spectrum are strongly modified by the exciton-plasmon coupling and the laser detuning, allowing one to achieve a controlled strongly subnatural spectral line. A strong antibunching of the fluorescent photons along the undriven transition is also obtained. Our results may be used for creating a tunable source of photons which could be used for a probabilistic entanglement scheme in the field of quantum information processing.

Figure 1

Three-level scheme illustrating the ground and excited states. Transition $|2\rangle \leftrightarrow |3\rangle$ is driven by a laser field polarized along the $X$ axis with angular frequency ${\omega }_L$ and Rabi frequency ${\mathrm{\Omega }}_3$. (b) The quantum system is located at a distance $D$ from the boundary of a nanosphere whose radius is $a$. The dipole moments ${\vec{\mu }}_{23}$ and ${\vec{\mu }}_{13}$ are oriented along the $X$ and $Y$ axis, respectively. $\theta$ is the angle with the $X$ axis of the line joining the MNP's center and the QD's center.

Figure 2

(a) Plasmon modified radiative decay rates of the quantum emitter ${\mathrm{\Gamma }}_x^p$ (dash-dotted curve) and ${\mathrm{\Gamma }}_y^p$ (solid curve) in units of ${\mathrm{\Gamma }}_0$ vs the distance $D$ in nm. (b) Field enhancement factor ($|F_{e,x}|$) vs distance $D$ when the angle is $\theta =0^{\circ }$ (dash-dotted curve), and $\theta ={90}^{\circ }$ (solid curve).

Figure 3

(a) Steady-state RFS $\left[S\right(\omega \left)\right]$ of the system driven on resonance $\delta =0$ when ${\mathrm{\Omega }}_3^0=2.5{\mathrm{\Gamma }}_0$, in the absence of MNP (solid curve) and with a distance $D=20$ nm: dashed curve when $\theta =0$, and dash-dotted curve for the case with $\theta ={90}^{\circ }$. (b) Contributions to RFS of correlations $U_{13}\left(\tau \right)$ (solid curve) and $U_{24}\left(\tau \right)$ (dashed curve) for the isolated quantum emitter. (c) Full RFS $\left[S\right(\omega )$, thin dashed curve] and RFS computed in the DSP $[S_{\mathrm{DSP}}\left(\omega \right)$, thick dashed curve] for ${\mathrm{\Omega }}_3^0=2.5{\mathrm{\Gamma }}_0, D=20$ nm, and $\theta ={90}^{\circ }$. (d) Time evolution of intensity-intensity correlation $\left[g^{\left(2\right)}\left(\tau \right)\right]$ for the fluorescent photons produced along transition $|1\rangle \leftrightarrow |3\rangle$ in the cases considered in (a). Thin solid curves are the corresponding normalized second-order correlations computed in the DSP. $\tau =t{\mathrm{\Gamma }}_0$ stands for normalized time. Other numerical values used are ${\omega }_{21}=30{\mathrm{\Gamma }}_0, {\mathrm{\Gamma }}_{12}={\mathrm{\Gamma }}_{21}=0.008{\mathrm{\Gamma }}_0$, and ${\gamma }_{22}=0.0014{\mathrm{\Gamma }}_0$.

Figure 4

Steady-state RFS $\left[S_{13}\left(\omega \right)\right]$ of the singly driven quantum emitter for different Rabi frequencies: (a) ${\mathrm{\Omega }}_3^0=0.1{\mathrm{\Gamma }}_0$ and (b) ${\mathrm{\Omega }}_3^0=0.2{\mathrm{\Gamma }}_0$. (c) Time evolution of normalized second-order correlation function when ${\mathrm{\Omega }}_3^0=0.2{\mathrm{\Gamma }}_0$. Isolated emitter (solid curve), $\theta =0$ (dashed curve), and $\theta ={90}^{\circ }$ (dash-dotted curve). The rest of the parameters are as in Fig. 3.

Figure 5

(a) Steady-state RFS $\left[S_{13}\left(\omega \right)\right]$ of the singly driven hybrid system with $\theta ={90}^{\circ }$ for several interparticle distances: $D=20$ nm (dashed curve), $D=40$ nm (dotted curve), and $D=\infty$ (isolated quantum emitter, solid curve). (a) $\delta =-30{\mathrm{\Gamma }}_0$ and ${\mathrm{\Omega }}_3^0=2{\mathrm{\Gamma }}_0$; (b) $\delta =+10{\mathrm{\Gamma }}_0$ and ${\mathrm{\Omega }}_3^0={\mathrm{\Gamma }}_0$. The thin solid curves are the spectral feature associated to the Raman photons determined in the DSP. (c), (d) Transitions between dressed states accounting for $S_{13}\left(\omega \right)$ in the case considered in (a), (b): the solid vertical arrow indicates the transition responsible for the Raman photons, whereas the dashed vertical arrow stands for the other sideband.

Figure 6

(a) Linewidth of the Raman photons (${\mathrm{\Gamma }}_{+1}$) vs distance $D$ for different values of the optical detuning $\delta$. (b) Spectral location of the Raman photons (${\lambda }_{+}$) vs distance for different values of the optical detuning $\delta$. $\delta =-30{\mathrm{\Gamma }}_0$ (solid curve), $\delta =-20{\mathrm{\Gamma }}_0$ (dashed curve), and $\delta =-10{\mathrm{\Gamma }}_0$ (dash-dotted curve). (c) Time evolution of intensity-intensity correlation for the Raman spectral line: isolated emitter (solid curve), and $D=20$ nm (dash-dotted curve) with $\theta ={90}^{\circ }$.