Long-distance radiative coupling between quantum dots in photonic crystal dimers

We study the mutual interaction between two identical quantum dots coupled to the normal modes of two-site photonic crystal molecules in a planar waveguide geometry, i.e., photonic crystal dimers. We find that the radiative coupling between the two quantum emitters is maximized when they are in resonance with either the bonding or the antibonding modes of the coupled-cavity system. Moreover, we find that such effective interdot coupling is sizable, in the range of $\sim 1$ meV, and almost independent from the cavities' distance, as long as a normal-mode splitting exceeding the radiative linewidth can be established (strong cavity-cavity coupling condition). In realistic and high-quality-factor photonic crystal cavity devices, such distance can largely exceed the emission wavelength, which is promising for long-distance entanglement generation between two qubits in an integrated nanophotonic platform. We show that these results are robust against position disorder of the two quantum emitters within their respective cavities.

Figure 1

Schematic representation of the system investigated in this work: two strongly coupled nanocavities, each containing a single QD. The distance between the nanocavities, $d_c$, can be larger than the characteristic QD emission wavelength in vacuum, ${\lambda }_0$.

Figure 2

Photonic dispersion of the bonding (solid lines) and antibonding (dashed lines) modes for the (a) $0^{\circ }$, (b) ${30}^{\circ }$, (c) ${60}^{\circ }$, and (d) ${90}^{\circ }$ cases, respectively. Electric field components $E_y$ associated with the (e) bonding and (f) antibonding states for the ${30}^{\circ }$ PC dimer at $d_c=5\sqrt{3}a$.

Figure 3

Quality factors, $Q$ (left axis), and loss rates, ${\gamma }_m$ (right axis), for the (a) ${30}^{\circ }$ and (b) ${60}^{\circ }$ cases as a function of the intercavity distance, $d_c$.

Figure 4

(a) Real part of the eigenfrequencies of the PC-QD system for the ${30}^{\circ }$ PC dimer at $d_c=5\sqrt{3}a$, for zero dot-dot detuning. (b) The square modulus of the Hopfield coefficients associated with (a). (c) and (d) correspond to the same case as in (a) and (b), respectively, but with a finite dot-dot detuning of $\Delta =300 \mu \mathrm{eV}$. In panels (b) and (d), ${\lambda }_y^1$ and ${\lambda }_y^2$ are associated with the QDs 1 and 2, respectively, and ${\lambda }_1$ and ${\lambda }_2$ are associated with the PC modes with frequencies ${\omega }_1$ and ${\omega }_2$, respectively.

Figure 5

(a) Absolute value of the Green's tensor component $G_{yy}^{12}\left(\omega \right)$ for the ${30}^{\circ }$ dimer as a function of the exciton transition frequency as a function of interdot distance. Each curve is displaced vertically by 1.7 meV from the previous curve; the vertical scale is valid for the smallest interdot distance. (b) Absolute value of the component $G_{yy}^{12}\left(\omega \right)$ evaluated at $\omega ={\omega }_1,\omega ={\omega }_2$, and $\omega ={\omega }_{\mathrm{av}}=({\omega }_1+{\omega }_2)/2$ as a function of the interdot distance. (c) and (d), same as (a) and (b), respectively, but for the ${60}^{\circ }$ dimer. The insets of panels (a) and (c) evidence the two split peaks in $|G_{yy}^{12}\left(\omega \right)|$.

Figure 6

(a) Absolute value of the effective interdot coupling strength at $\omega ={\omega }_1$, in the ${30}^{\circ }$ dimer, as a function of the cavity-cavity distance, for QD positions generated randomly with a Gaussian probability distribution of variance $\sigma$. (b) The same as (a) with $\omega ={\omega }_2$. The standard error is shown with vertical error bars.