Two-Photon Rabi Splitting in a Coupled System of a Nanocavity and Exciton Complexes

Two-photon Rabi splitting in a cavity-dot system provides a basis for multiqubit coherent control in a quantum photonic network. Here we report on two-photon Rabi splitting in a strongly coupled cavity-dot system. The quantum dot was grown intentionally large in size for a large oscillation strength and small biexciton binding energy. Both exciton and biexciton transitions couple to a high-quality-factor photonic crystal cavity with large coupling strengths over $130\mu \mathrm{eV}$. Furthermore, the small binding energy enables the cavity to simultaneously couple with two exciton states. Thereby, two-photon Rabi splitting between the biexciton and cavity is achieved, which can be well reproduced by theoretical calculations with quantum master equations.

Figure 1

(a) Atomic force microscope image of QDs in $1\mu {\mathrm{m}}^2$. The diameter of the biggest QD is around 50 nm. (b) Scanning electron microscope image of $L3$ PC cavity. Two red circles schematize the positions of two edge holes in an unmodified $L3$ cavity. The two edge holes were optimized by a shift of $0.15a$ and a shrink of $0.13a$. (c) One-cavity mode measured at room temperature with $Q=12000$. (d) Energy-level structure of the cavity-dot system with large coupling strength. (e) Upper panel: Calculated eigenenergies of three polaritons from coupling between $|XX,0⟩$, $|X,1⟩$, and $|G,2⟩$, at $g=70\mu \mathrm{eV}$ (red dashed line) and at $g=120\mu \mathrm{eV}$ (blue solid line). Inset: Two-photon Rabi splitting occurs when $g=120\mu \mathrm{eV}$. Bottom panel: Two-photon Rabi splitting energy as a function of $g$.

Figure 2

(a) PL spectra of X and XX transitions and a cavity mode collected from 6 to 20 K with the excitation power of 500 nW. Peak1, peak2 and peak3 are color-coded in black, red, and blue, respectively. (b) Detuning between three peaks and bare cavity mode as a function of temperature. The detunings between uncoupled QDs and the cavity are indicated by brown dashed lines.

Figure 3

(a) Peak intensity as a function of excitation power. Peak2 is weaker than peak3 at low excitation power but grows faster with increasing pumping power. (b) Four-level energy structure of QD. The X state consists of $X_H$ and $X_V$ with a fine-structure splitting energy $\delta$. (c) Energy difference at different linear polarization angles. The solid red line shows a sinusoidal fitting with a $\pi$ period, and the fitted fine-structure splitting energy is around $37\mu \mathrm{eV}$.

Figure 4

(a) Contour plot of PL spectra with two suppression regions, as shown in the insets. (b) Simulated PL map with $g=130\mu \mathrm{eV}$. The green dashed line represents the XX-C polariton, the purple dashed line shows the X-C polariton, and the orange dashed line is the bare cavity. The red dashed line is a polariton-polariton transition containing two-photon Rabi splitting. Inset: Linewidth variation during two-photon Rabi splitting. (c) Linewidth variation of peak2 at different temperatures in experiment (solid line) and calculation (dashed lines). The difference of $\sim 0.1\mathrm{nm}$ between experimental data and calculation with $g=130\mu \mathrm{eV}$ results from the broadening of the spectrometer. (d) Intensity variation of experimental data at different temperatures. The large suppression region results from two-photon Rabi splitting.