Formation of an Exciton Polariton Condensate: Thermodynamic versus Kinetic Regimes

We measure the polariton distribution function and the condensation threshold versus the photon-exciton detuning and the lattice temperature in a CdTe microcavity under nonresonant pumping. The results are reproduced by simulations using semiclassical Boltzmann equations. At negative detuning we find a kinetic condensation regime: the distribution is not thermal and the threshold is governed by the relaxation kinetics. At positive detuning, the distribution becomes thermal and the threshold is governed by the thermodynamic parameters of the system. Both regimes are a manifestation of polariton lasing, whereas only the latter is related to Bose-Einstein condensation defined as an equilibrium phase transition.

Figure 1

(a) Experimental distributions of polaritons at different $T_{\mathrm{lat}}$ and at a constant pumping power close to threshold, $\delta =+6.8\mathrm{meV}=+0.26\Omega$. Inset: measured polariton dispersion $E(k_{\parallel })$ in PL, logarithmic color scale. (b) Calculated distributions of polaritons under the same conditions, (c) relative difference between effective and lattice temperatures, (d) the calculated distribution function at $T_{\mathrm{lat}}=20\mathrm{K}$ and $T_{\mathrm{lat}}=40\mathrm{K}$ in a wider energy window. Dashed lines: distributions for $T_{\mathrm{eff}}=21\mathrm{K}$ (blue) and $T_{\mathrm{eff}}=42\mathrm{K}$ (black).

Figure 2

Experimental (black circles) and calculated (black line) pumping threshold versus the lattice temperature at $\delta =+6\mathrm{meV}$. The red line shows the critical density for the polariton BEC, calculated in the thermodynamic limit (infinite particle lifetime). The red dashed line shows the thermodynamic density calculated using $T_{\mathrm{eff}}$ instead of $T_{\mathrm{lat}}$.

Figure 3

(a) Spectrally resolved far-field polariton emission as a function of $P_{\mathrm{ext}}$ at $T_{\mathrm{lat}}=5.2\mathrm{K}$ and for detuning $\delta =-1\mathrm{meV}=-0.038\Omega$, logarithmic color scale; (b) experimental and (c) calculated distribution functions for different $P_{\mathrm{ext}}$.

Figure 4

(a) Measured $P_{\mathrm{th}}$ as a function of $\delta$ at $T_{\mathrm{lat}}=5\mathrm{K}$ (solid blue circles) and $T_{\mathrm{lat}}=25\mathrm{K}$ (open brown squares), (b) corresponding simulation.

Figure 5

Sketch of the polariton phase diagram ($\delta$, $T_{\mathrm{lat}}$, $P_{\mathrm{th}}$) in the microcavity investigated. The surfaces symbolize the limits between the four possible phases. The arrows show the three possible types of condensation that can occur with increasing the pumping and keeping $\delta$ and $T_{\mathrm{lat}}$ constant.