Polariton-polariton interaction constants in microcavities

Resonant transmission of light through a microcavity in the strong coupling regime is used to estimate the strength of the interaction between polaritons with parallel $\left({\alpha }_1\right)$ or antiparallel $\left({\alpha }_2\right)$ spins. The ratio ${\alpha }_2/{\alpha }_1$ is found to be strongly dependent on the detuning between exciton and photon modes. From negative to zero detuning it changes from about 0 to less than $-1$. Our observations indicate that at certain conditions the polaritons might rather condense in the real space than form a Bose-Einstein condensate. We analyze theoretically different mechanisms of polariton-polariton interaction including the mean-field electrostatic interaction, the direct exchange interaction, the Van-der-Waals interaction and the indirect exchange interaction via dark exciton and biexciton states.

Figure 1

(Color online) Phase diagram of a gas of interacting exciton-polaritons. Regions of the parameter space corresponding to the real (reciprocal) space condensation are shown by black (red) color. The polarization of the polariton gas is shown by hatching. Dense hatch stands for linearly and rare hatch for circularly polarized state. The values of interaction constants measured at $400\mu \text{W}$ excitation intensity for different values of the exciton-photon detuning are shown by circles. Calculated values of the interaction constants are shown by line. The arrow points the direction, where the detuning changes from negative to positive.

Figure 2

(Color online) (a) Color map of the low power transmission through the microcavity as a function of detuning between photon and exciton modes; normalized differential transmission spectra in linear (red dashed line) and circular (black solid line) polarizations. (b) The normalization is done independently for lower and upper polaritons (below and above dashed line); color map of the normalized differential transmission $T_{high}-T_{low}$ in (c) circular and (d) linear polarization; color map of the high power transmission at 1.5 mW in (e) circular and (f) linear polarization.

Figure 3

(Color online) Normalized differential transmission spectra $T_{high}-T_{low}$ of the lower polariton branch at two different photon-exciton detunings: [(a)–(c)] $\delta =-1.9\text{meV}$, [(d)–(f)] $\delta =-0.25\text{meV}$, and at three different pumping power values. Open symbols stand for linear polarization, solid symbols stand for circular polarization. Solid lines are fits with two fitting parameters, namely, the shift and the broadening (narrowing) of the transmission line at high power.

Figure 4

(Color online) (a) The lower polariton line shift per unit power obtained from the transmission spectra in circular (black squares) and linear (red circles) polarizations. The error bars are given by the averaging over three different excitation powers: $300\mu \text{W}$, $400\mu \text{W}$, and $550\mu \text{W}$. Solid and dashed lines are the values of ${\alpha }_1$ and ${\alpha }_2$, respectively, calculated as described in the Sec. 4. (b) Ratio between polariton interaction constants averaged over three different powers. (c) The same ratio as in (b) but without averaging. Solid lines show the theoretical results.

Figure 5

(Color online) An example of power dependence of the of the lower polariton line shift measured in linear (circles) and circular (squares) polarizations. Solid lines are linear fits of the data.

Figure 6

(Color online) Energies of the lower polariton state (black solid line), bright (red dashed line), and dark (green dotted line) exciton states, excited exciton state (blue dashed-dotted line) as a function of detuning. One can see that both ${\Delta }_{oe}$ and ${\Delta }_{bd}$ splittings decrease when the detuning changes from negative to positive values.

Figure 7

(Color online) Different contributions to the polariton energy shift due to polariton-polariton interaction.