Strongly enhanced light-matter interaction in a hybrid photonic-plasmonic resonator

We propose a hybrid photonic-plasmonic resonant structure which consists of a metal nanoparticle (MNP) and a whispering-gallery-mode (WGM) microcavity. It is found that the hybrid mode enables a strong interaction between the light and matter, and the single-atom cooperativity is enhanced by more than two orders of magnitude compared to that in a bare WGM microcavity. This improvement originates from two aspects: the MNP offers a highly enhanced local field in the vicinity of an emitter, and, interestingly, the high-$Q$ property of WGMs can be maintained in the presence of the MNP. Thus the present system has advantages over a single microcavity or a single MNP, and holds potential in quantum optics, nonlinear optics, and highly sensitive biosensing.

Figure 1

(a) Sketch of the MNP-WGM composite system (not to scale). (b) Zoomed-in view of the MNP and the dipole emitter. The inset is the energy diagram of the dipole. (c)–(e) Three-dimensional finite-element simulations of the electric field distribution. Top view of the electric field profile (c) without and (d) with the MNP. (e) Zoomed-in view of the field distribution near the MNP (azimuthal cross section). The arrows show the electric field directions. The vertical line on the left of the MNP is the cavity boundary. The colors in (c)–(e) represent the norm of the electric field ($\left|E\right|$). (f) Comparison of the electric field with (blue/dark gray dot) and without (light gray dot) MNP for $\theta =0$ (left) and $\theta =\pi /2$ (right). The red solid curves are the theoretical result (see text). To save simulation resources, here we use a relatively small microcavity (major radius 0.8 $\mu$m) and a relatively large MNP ($r_m=30$ nm).

Figure 2

(a) Contour plot of the cooperativity enhancement ($C_{\mathrm{c},\mathrm{m}}/C_{\mathrm{c}}$) vs $r_{\mathrm{m}}$ and $d$. (b) Parameters $\{G_{\mathrm{c}},G_{\mathrm{c},\mathrm{m}},h,{\kappa }_0,{\kappa }_{\mathrm{R}},{\kappa }_{\mathrm{m}}\}/2\pi$ vs $r_{\mathrm{m}}$. (c) Cooperativity with the presence of the MNP ($C_{\mathrm{c},\mathrm{m}}$) and with its absence ($C_{\mathrm{c}}$). The horizontal line in (a) corresponds to $d=3$ nm. The vertical lines in (a)–(c) correspond to $r_{\mathrm{m}}=12$ nm. (d) Transmission spectra for $r_{\mathrm{m}}=12$ nm and $d=3$ nm in the presence of the dipole, with (solid line) and without the MNP (dashed line). $\{G_{\mathrm{c}},G_{\mathrm{c},\mathrm{m}},h,{\kappa }_0,{\kappa }_{\mathrm{R}},{\kappa }_{\mathrm{m}}\}/2\pi =\{760,9000,170,55,80,30\}$ MHz. The input-cavity detuning $\Delta =\omega -{\omega }_{\mathrm{c}}$. The inset is for no dipole case. For (b)–(d), $d=3$ nm; For (a)–(d), the cavity-MNP detuning ${\Delta }_{\mathrm{sp}}=0$.

Figure 3

(a) Cooperativity enhancement ($C_{\mathrm{c},\mathrm{m}}/C_{\mathrm{c}}$) vs cavity-MNP detuning ${\Delta }_{\mathrm{sp}}/{\gamma }_{\mathrm{m}}$ for several typical $r_{\mathrm{m}}$. (b) The cooperativity parameters $C_{\mathrm{c},\mathrm{m}}$, $C_{\mathrm{c},\mathrm{m}}^{\text{I}}$ (near resonance, $|{\Delta }_{\mathrm{sp}}|\ll {\gamma }_m$), and $C_{\mathrm{c},\mathrm{m}}^{\text{II}}$ (off resonance, $|{\Delta }_{\mathrm{sp}}|\gg {\gamma }_m$) for $r_{\mathrm{m}}=20$ nm.

Figure 4

Illustration of the fast quantum gate operation (a) and NOON state generation (b).