Ensemble-Induced Strong Light-Matter Coupling of a Single Quantum Emitter

We discuss a technique to strongly couple a single target quantum emitter to a cavity mode, which is enabled by virtual excitations of a nearby mesoscopic ensemble of emitters. A collective coupling of the latter to both the cavity and the target emitter induces strong photon nonlinearities in addition to polariton formation, in contrast to common schemes for ensemble strong coupling. We demonstrate that strong coupling at the level of a single emitter can be engineered via coherent and dissipative dipolar interactions with the ensemble, and provide realistic parameters for a possible implementation with ${\mathrm{SiV}}^{-}$ defects in diamond. Our scheme can find applications, amongst others, in quantum information processing or in the field of cavity-assisted quantum chemistry.

Figure 1

(a) A single target emitter $A$ is weakly coupled to a resonant (${\omega }_A={\omega }_c$) cavity with strength $g_A^{(0)}$, and close to a small ensemble $B$. As $B$ we consider a cube of $N$ emitters identical to $A$ but with different transition frequencies ${\omega }_B>{\omega }_A$. When $l_B\ll r$, $B$ can be approximated by a single point-dipole at distance $|\overrightarrow{r}|\equiv r$. (b) The normalized cavity transmission spectrum ${\mathcal{T}}_c$ probed by a weak laser field with frequency ${\omega }_L$ [70] shows a splitting increasing with $N$, which results from an enhanced effective cavity-coupling strength $g_A^{\mathrm{eff}}>g_A^{(0)}$ of the single target emitter $A$. We find $g_A^{\mathrm{eff}}-g_A^{(0)}\propto N$ (see inset and text). (c) Equal-time cavity photon-photon correlation function $g^{(2)}(0)$. The induced cavity-coupling strength occurs on a single emitter level, giving rise to photon blockade effects, $g^{(2)}(0)\ll 1$ and $\min [g^{(2)}(0)]$ decreasing with $N$ (inset). [Parameters for (b) and (c): $g_A^{(0)}\equiv 1$, ${\gamma }_A=0.01$, $\kappa =2$, ${\omega }_B-{\omega }_A=1000$, cavity-wavelength $\lambda$, ${\overrightarrow{r}}_A=(0,0,0)$, $\overrightarrow{r}=(0,0,\lambda /20)$, $d={10}^{-3}\lambda$ (lattice spacing)].

Figure 2

(a),(c) Contour plots of $|g_A^{\mathrm{eff}}/{\gamma }_{+}|$ vs separation $\overrightarrow{r}(r,\theta )$ between $A$ and $B$ (point dipole, see Fig. 1). $|g_A^{\mathrm{eff}}/{\gamma }_{+}|>1$ (inside the green contour line) indicates strong coupling. The parameters are chosen to illustrate either coherent coupling inheritance (a) or dissipative linewidth narrowing (c) for reaching strong coupling of $A$ (see text). (b),(d) Time evolution of population in $A$, cavity (initial state with one photon) and $B$ (barely visible). Oscillations exemplify strong coupling [parameters for green dots in (a) and (c), we adapt ${\omega }_c$ such that ${\mathrm{\Delta }}_A^{\mathrm{eff}}\simeq {\mathrm{\Delta }}_c^{\mathrm{eff}}$]. Lines: Full master equation simulation [Eq. (1) with two emitters], points: effective model [Eq. (2)], dashed line: cavity decay without $B$. [Parameters (a),(b): As in Fig. 1, but choosing $g_B^{(0)}=100$ and thus ${\gamma }_B={\gamma }_A(g_B^{(0)}/g_A^{(0)}{)}^2=100$, $A$ and $B$ in the $x-z$ plane, $\overrightarrow{r}=r(\sin (\theta ),0,\cos (\theta ))$. (c),(d): ${\gamma }_A=2.5$, $\kappa =0.1$, ${\omega }_B={\omega }_A$, $g_B^{(0)}=20$ and thus ${\gamma }_B=1000$, ${\overrightarrow{r}}_A=(0,-1/4,0)\lambda$, $A$ and $B$ in the $y-z$ plane, $\overrightarrow{r}=r(0,\sin (\theta ),\cos (\theta ))$].

Figure 3

Implementation with ${\mathrm{SiV}}^{-}$ centers coupled to a microcavity mode (red). (a) A single ${\mathrm{SiV}}^{-}$ center ($A$) is deposited above the bottom distributed Bragg reflector (DBR). A nanodiamond of size $l_B$ (modeled as a cube with lattice spacing $d=8\mathrm{nm}\simeq 0.01\lambda$) separated from $A$ by a distance $\overrightarrow{r}=(0,0,60)\mathrm{nm}$ contains an ensemble of $N$ ${\mathrm{SiV}}^{-}$ centers ($B$). (b) Energy levels of a ${\mathrm{SiV}}^{-}$ center under a magnetic field $H$ along $z$. The optical transitions $|2⟩\to |3⟩$ and $|1⟩\to |4⟩$ with frequencies ${\omega }_A$ (wavelength $\lambda =737\mathrm{nm}$) and ${\omega }_B$ correspond to $A$ and $B$, respectively. (c) Scaling of $g_A^{\mathrm{eff}}$ (black) showing that the system can be brought into strong coupling ($g_A^{\mathrm{eff}}>{\gamma }_{+}$) by increasing $N$. The $g^{(2)}(0)$ for $N=1000$ is shown in the inset as a function of the detuning ${\omega }_L-{\omega }_c$. Other parameters are $g_A^{(0)}\equiv 1$, ${\omega }_A={\omega }_c$, ${\gamma }_A={\gamma }_B=0.044$, $\kappa =2$, and ${\mathrm{\Delta }}_B=265$, ${\overrightarrow{r}}_A=(0,0,0)$.