Strong coupling of a quantum dot molecule to a photonic crystal cavity

Quantum dot molecules (QDMs) have widely tunable exciton transition energies and transition strengths that can be controlled with an applied electric field. We use these properties to demonstrate in situ tuning of the vacuum Rabi splitting for a quantum dot molecule embedded in a photonic crystal cavity. Both components of the anisotropic exchange doublet have a component parallel to the cavity and are strongly coupled. This produces two QDM-cavity polaritons with properties dominated by the cavity and a third mixed-spin hybrid state with little cavity component and unusual polarization.

Figure 1

(a) Calculated bias-dependent transition energies of an exciton in a QDM. The anticrossing curves are the eigenenergies, created by a tunneling-induced mixture of direct and indirect excitons (dotted gray lines). The magnitude of the anticrossing is twice the rate ($t$) of a single electron tunneling between the QDs. (b) Measured bias-dependent photoluminescence (PL) spectrum of the neutral exciton $X^0$. The yellow box indicates the lower branch of the $X^0$ anticrossing studied in this paper and corresponds to the same region shown in Fig. 2. Several other spectral lines correspond to charged excitons that are not studied in this paper. $X^{-},X^{+},X^{2+}$, and $X{X}^0$ are labeled here for clarity and further detail is given in Supplemental Material [19]. (c) Energy-level diagram of the neutral exciton $X^0$ (not to scale) showing the anisotropic exchange fine-structure splitting ${\delta }_1$ and dark-bright splitting ${\delta }_0$. (d) Polarization dependence of exciton PL intensity at 0.515 V. The fine-structure splitting ${\delta }_1$ is obtained from the extrema and the state orientation from the phase (24°).

Figure 2

PL spectrum of neutral exciton $X^0$ vs bias with the cavity resonance tuned to (a) 1294.27 and (b) 1294.77 meV. Measured spectra are in the left column and the results of modeling are on the right. Transition linewidths are phenomenologically accounted for by a complex term in the state energy [31]. In the region of the vacuum Rabi anticrossing, peaks $A$ and $C$ are cavity polaritons, while peak $B$ is a cavity-induced hybrid of $X_1$ and $X_2$. Integrated intensities of each component were normalized for visual clarity. Lines in the experimental data that do not appear in the simulations correspond to charged excitons and are not studied in this paper. (c) Coupling strength $2g$ as a function of direct exciton coefficient (and applied bias).

Figure 3

(a) PL spectra of the cavity-QDM system at different cavity-exciton detunings with the bias fixed at $\sim 0.460\mathrm{V}$. (b) PL spectra from the boxes i–iv in (a). The red lines are fits to the sum of four Lorentzian functions. Blue, red, and black fills denote fit components for polaritons $A$ and $C$, dark exciton $X_d$, and exciton hybrid state $B$. (c) Modeled spectrum in which peak intensities of each component are normalized for visual clarity. Fits do not include charged exciton peaks such as $X^{-}$ that are not relevant to the present paper.

Figure 4

(a) Polarization-dependent PL of the strongly coupled cavity-QDM system with the cavity tuned to resonance. Peaks $A$, $C$, and $X_d$ are copolarized with the cavity while $B$ has elliptical polarization. (b) Polar diagram of the normalized intensity of peaks $A$ and $C$ (blue circles) and $B$ (red squares) vs analyzer angle. The fits (black) are based on Eq. (1)), using the wave-function coefficients obtained by diagonalizing the model Hamiltonian (see Supplemental Material [19]). The orientations of the fine-structure states $X_1$ and $X_2$ with the cavity resonance detuned are shown by the purple arrows, while the cavity polarization is indicated by the black arrow at $0^{\circ }$.