Suppressed antibunching via spectral filtering: An analytical study in the two-photon Mollow regime

Mollow physics in the two-photon regime shows interesting features such as versatile generation of highly correlated photon pairs, timely ordered and energy tunable. Here, we calculate analytically the power spectral density $S\left(\omega \right)$ and the two-photon correlations $g^{\left(2\right)}\left(\tau \right)$, which are essential to discuss and study such phenomena in the resonant-driven dressed-state regime. It is shown that there exist upper and lower bounds of the $g^{\left(2\right)}\left(\tau \right)$ function for certain spectrally selected photon pairs. Recently reported experiments agree with the presented theory and thereby it is shown that the resonant-driven four-level system is an interesting source for steerable quantum light in quantum cascade setups. We furthermore discuss the unlikeliness of observing antibunching for the delay time $\tau =0$ in the exciton-biexciton correlation functions in such experiments, since antibunching stems from a coherent and in-phase superposition of different photon-emission events. Due to the occurring laser photon scattering, this coherent superposition state is easily disturbed and leads to correlation functions of $g^{\left(2\right)}\left(0\right)=1$.

Figure 1

The energy schema of the setup. The biexciton state is driven via a continuous wave $H$-polarized excitation in two-photon resonance, while the exciton transitions are far detuned.

Figure 2

Power spectrum of $V$-polarized photons: When the driving is strong compared with the decay, $\mathrm{\Omega }=0.045\mathrm{\Delta },\mathrm{\Gamma }=0.002\mathrm{\Delta }$, Mollow splitting of the exciton and biexciton photon emission occurs due to the appearance of dressed states. The inset shows the spectrum for driving strength in the order of the radiative decay, $\mathrm{\Omega }=0.045\mathrm{\Delta },\mathrm{\Gamma }=0.040\mathrm{\Delta }$, where the radiative linewidth dominates the Mollow splitting. The numerical solution is derived from the full master equation. The analytical solution in the adiabatic limit is given in the text.

Figure 3

Photon-photon correlations between $+$ biexciton and $+$ exciton photon for different driving strengths ${\mathrm{\Omega }}_L\left[{\text{ps}}^{-1}\right]$ with $\mathrm{\Gamma }=0.002{\text{ps}}^{-1}$ and $\mathrm{\Delta }=3.0{\text{ps}}^{-1}$. The numerical solution is derived from the complete master equation. The analytical solutions are given in the text in the adiabatic limit.

Figure 4

Photon-photon correlations between $+$- and 0-state photons for different driving strengths ${\mathrm{\Omega }}_L\left[{\text{ps}}^{-1}\right]$ with $\mathrm{\Gamma }=0.002{\text{ps}}^{-1}$ and $\mathrm{\Delta }=3.0{\text{ps}}^{-1}$. The numerical solution is derived from the complete master equation. The analytical solutions are given in the text in the adiabatic limit.

Figure 5

Comparison between (a) experiment and (b) theory for two low $\left(30\mu \text{W}\right)$ and strong excitation $\left(100\mu \text{W}\right)$ power and the exciton-biexciton photon-photon correlations without $|-\rangle$-state contributions. The qualitative agreement is very good. Both plots show the symmetrization of detection events for stronger excitation (green) in comparison to lower excitation (orange). The experimental data are shown with a subtracted background, in particular for the lower excitation.

Figure 6

Photon-photon correlations between exciton and biexciton photons for different driving strengths ${\mathrm{\Omega }}_L\left[{\text{ps}}^{-1}\right]$ with $\mathrm{\Gamma }=0.002{\text{ps}}^{-1}$ and $\mathrm{\Delta }=3.0{\text{ps}}^{-1}$. The numerical solution is derived from the complete master equation. The analytical solutions are given in the text in the adiabatic limit. For moderate driving strength the agreement is very good.