Exciting Polaritons with Quantum Light

We discuss the excitation of polaritons—strongly coupled states of light and matter—by quantum light, instead of the usual laser or thermal excitation. As one illustration of the new horizons thus opened, we introduce “Mollow spectroscopy”—a theoretical concept for a spectroscopic technique that consists of scanning the output of resonance fluorescence onto an optical target—from which weak nonlinearities can be read with high precision even in strongly dissipative environments.

Figure 1

Scheme of our proposal. (a) A typical optical excitation scenario of quantum optics, a laser excites a quantum system, e.g., a quantum dot. (b) Instead of the conventional scenario of also exciting polaritons with a laser, we excite polaritons with quantum light: specifically, from the output of the quantum system excited by the laser. (c) Mollow spectroscopy: the photoluminescence of a strongly driven two-level system provides the Mollow triplet, shown on the left with energy on the vertical axis. Various spectral windows provide different types of photon correlations, sketched here as photon balls with different temporal spacing. Exciting the lower polariton (LP) with leapfrog photon pairs allows us to measure accurately very small values of the interaction.

Figure 2

Pure quantum states in the steady state. The red area of (b) shows where the system is in a pure state. The density plot of $g^{(2)}(0)$ in (a) shows that this corresponds to states with $g^{(2)}\le 1$. Four isolines of constant populations are shown on both panels. (c) Antibunching and ratio of the effective linewidths of the target and source along the line I-II, showing a transfer of properties from the source to its target. (d) Antibunching, purity and diagonal elements ${\rho }_{n,n}=⟨n|\rho |n⟩$ of the density matrix along the line III-IV. (e) Density matrices for three pumping powers. At ${\mathrm{\Omega }}_3$, the system is in state $|1⟩$, with over 60% probability, although not in a pure state anymore.

Figure 3

Mollow spectroscopy of weakly interacting polaritons. (a) Population (dot-dashed yellow line) and photon-statistics (solid blue line) when scanning the Mollow triplet onto the lower polariton branch. (b) Magnitude of the deviation from the noninteracting polariton statistics as a function of $U/{\gamma }_a$. (c) Hopfield coefficients ${\chi }_{nm}$ of relative light ($n$)-matter ($m$) content, as a function of detuning. (d) Mollow splitting required for the measurement of ${\omega }_0$ to be $\mathrm{\Omega }$ independent, allowing an absolute measurement of $U$.