Quantum correlations and dissipative blockade of polaritons in a tunable fiber cavity

Abstract

Cavity exciton--polaritons are quasiparticles that form when quantum well excitons hybridize with a cavity mode. Here, we carry out photon correlation measurements under continuous wave resonant laser excitation to demonstrate quantum correlations between cavity--polaritons. Our experiments reveal an unexpectedly strong dependence of polariton interactions on cavity--exciton detuning. When the polaritons are predominantly exciton-like, we observe a transition from photon antibunching to bunching as the laser is tuned across the polariton resonance, in agreement with a simple Kerr-nonlinearity model. When the lower-branch polariton energy is tuned to induce a two-polariton Feshbach resonance with the biexciton mode, the degree of polariton antibunching becomes independent of the laser detuning: we explain our finding by invoking a dissipative blockade mechanism arising from large biexciton broadening. Our experiments demonstrate that the strong polariton blockade regime would be achieved by reducing the polariton decay rate by a factor of 10.

Figures (4)

• Figure 1: a Schematic of the hemispherical fiber cavity formed between a pair of DBR mirrors, enclosing the gate controlled InGaAs QW pair that hosts the direct excitons (dx). b Polariton transmission spectrum as function of the piezo voltage used to tune the cavity length. It shows the lower- and upper polariton separated by the normal mode splitting ($2\Omega=3.003\pm0.006meV$) and a smaller, additional anticrossing with a higher lying excitonic state. c Linewidth and d peak transmission of the lower polariton resonance as function of exciton content and energy. The fit of a model based on inhomogeneously broadened emitters coupled to a cavity Diniz2011 (orange line) to the measured linewidths allows to extract the exciton parameters $\gamma_\mathrm{inhom}=600\pm10µ eV$ and $\gamma_\mathrm{nonrad}=8.6\pm0.5µ eV$. Vertical dashed lines in c and d indicate the detuning of the correlation measurement shown in \ref{['fig:Fig2', 'fig:Fig3']}.
• Figure 2: a Polariton transmission spectrum at an exciton content of $|c_\mathrm{x}|^2=0.72$ with a polariton linewidth of 16.7µ eV extracted by a Lorentzian fit (gray line). b, c and d$g^\mathrm{(2)}(\tau)$ as function of the difference between photon arrival times ($\tau$) for the three detunings $\Delta=\qtylist{-0.3;0;0.3}{\Gamma_\mathrm{p}}$. The observation of non-classical correlations for negative detunings, coherent correlations on resonance and bunching for positive detunings is a clear signature of the polariton--polariton interactions. A heuristic fit of a Gaussian function to the data (orange lines), allows the extraction of $g^{(2)}(0)$ as function of the detuning, shown in e. The numerical solution (turquoise line) to \ref{['eq:hamiltonian']}+\ref{['eq:bxcoupling']} with the parameters presented in the main text shows good agreement with the extracted values.
• Figure 3: a Polariton transmission spectrum at an exciton content of $|c_\mathrm{x}|^2=0.54$ with a polariton linewidth of 16.8µ eV extracted by a Lorentzian fit (gray line). b, c and d$g^\mathrm{(2)}(\tau)$ as function of the difference between photon arrival times ($\tau$) for the three detunings $\Delta=\qtylist{-0.3;0;0.3}{\Gamma_\mathrm{p}}$. A heuristic fit to a Gaussian function allows to extract $g^{(2)}(0)$ shown in e. Contrary to the expected "S" shaped dependence found for exciton like polaritons (\ref{['fig:Fig2']}), we observe a weak, detuning independent antibunching over a wide range. This behavior is well described by including the coupling to the biexciton, as demonstrated by the good agreement of the data with the numerical solution (turquoise line) of the Hamiltonian (\ref{['eq:hamiltonian']}+\ref{['eq:bxcoupling']}) with the parameters listed in the main text.
• Figure 4: a Energy level scheme illustrating the dissipative blockade mechanism. Due to the broadening of the doubly excited polariton state $\ket{2p}$, caused by its weak coupling to the biexciton $\ket{bx}$, the excitation probability of $\ket{2p}$, and consequently the two-photon emission probability, is substantially reduced. This results in antibunching over a wide range of cavity--exciton detunings, largely independent of the detuning between the laser and the polariton resonance. b$g^\mathrm{(2)}(0)$ for three different laser detunings as a function of the exciton content compared to the estimated overlap of the biexciton (top panel). We distinguish different regimes depending on the detuning between the polariton and the biexciton. At high and low cavity contents the overlap with the biexciton is small and the correlations are determined by the polariton--polariton interactions or the coherence of the laser. Around the maximum of the distribution, the correlations are dominated by the dissipative coupling, followed by a hybrid regime at larger $|c_\mathrm{x}|^2$. c The calculated values of $g^\mathrm{(2)}(0)$ using the extracted parameters agrees well with the experimental data in $\textbf{b}$. d Polariton interaction strength ($g_\mathrm{pp}$) as a function of $|c_\mathrm{x}|^2$ estimated by matching the numerical solution of \ref{['eq:hamiltonian']}+\ref{['eq:bxcoupling']} to the correlation data. To highlight the deviation from the commonly used quadratic model, we also plot the interaction strength expected from the Born approximation Ciuti1998.