Polarization degenerate solid-state cavity quantum electrodynamics

A polarization degenerate microcavity containing charge-controlled quantum dots (QDs) enables equal coupling of all polarization degrees of freedom of light to the cavity QED system, which we explore through resonant laser spectroscopy. We first measure interference of the two fine-split neutral QD transitions and find very good agreement of this V-type three-level system with a coherent polarization-dependent cavity QED model. We also study a charged QD that suffers from decoherence and find also in this case that availability of the full-polarization degrees of freedom is crucial to reveal the dynamics of the QD transitions. Our results pave the way for postselection-free quantum devices based on electron-spin–photon polarization entanglement.

Figure 1

(a) Schematic of the setup. Light is coupled into a microcavity mode, and the reflection and transmission spectra are recorded using single-photon avalanche photodiodes. The elements with names between brackets can be introduced for polarization analysis with either linear or circularly polarized light. $\lambda /2 \left(\lambda /4\right)$: half-wave (quarter-wave) plate. (b) Optical microscope image of a sample. (c) Electron micrograph of the cavity region.

Figure 2

(a) Reflectivity measurement of two neutral QDs as a function of the scanning laser frequency and applied voltage. The incoming polarization ${\theta }_{\mathrm{in}}=0^{\circ },P_{\mathrm{laser}}=1$ pW, and $\lambda \approx 940$ nm. (b) Reflectivity and (c) transmittivity spectra of QD1 recorded at $V=0.725$ V for various incoming linear polarizations. Blue points: experimental data. Red line: fitted curve using Eqs. (1) and (2). Gray curve: empty cavity, calculated from the fits. Vertical dashed lines: frequencies corresponding to the two fine-split transitions. (d) Transmittivity spectra when a crossed polarizer is used with respect to the incoming polarization, relative to the maximum transmittivity of an uncoupled cavity. The red line is calculated using Eqs. (1) and (2) and the parameters obtained from the fits in (b) and (c). (e) Energy-level diagram of the ground-state and lowest-energy excited states of a neutral QD.

Figure 3

Resonant (a) reflection and (b) transmission spectroscopy with a neutral QD (QD1 in Fig. 2) for ${\theta }_{\mathrm{in}}={45}^{\circ }$ and for various ${\theta }_{\mathrm{out}}={\theta }_{\mathrm{in}}+{90}^{\circ }+\Delta {\theta }_{\mathrm{out}}$. Blue dots: experimental data. Red lines: predicted curves using Eqs. (1) and (2) and the parameters obtained from the fits in Figs. 2 and 2. Gray lines: predicted curves corresponding to an empty cavity. Vertical dashed lines mark the two transitions split by the fine-structure interaction.

Figure 4

(a) Energy-level diagram of a singly charged QD. Transmission spectra for $P_{\mathrm{laser}}=10$ pW are shown for circular and linear polarization, analyzed with a (b) and (c) parallel or (d) and (e) crossed polarizer. The red-black dashed line in (b) is a fit of Eq. (4) (coherent model, M1) to the data, which yields the same result as Eq. (5) (decoherent model, M2). The red (black) solid lines in (c) and (e) predict the experimental data using Eq. (4) [Eq. (5)]. Black (red) dashed curves: empty (coupled) cavity calculations.

Figure 5

Spatial PL scans of the Hermite-Gaussian modes, where (a) is the fundamental mode ${\Psi }_{00}$ and (b) and (c) are the first-order ${\Psi }_{10}/{\Psi }_{01}$ modes. Light: more PL counts. The labels denote the wavelength ${\lambda }_{00}$ of the fundamental mode or the wavelength splitting $\Delta {\lambda }_{10/01}={\lambda }_{00}-{\lambda }_{10/01}$.