Experimental evidence for nonequilibrium Bose condensation of exciton polaritons

We observe dramatic changes in the near-field and far-field emission from a semiconductor microcavity excited by a pulsed and nonresonant optical pump with varying power. Above a threshold pumping power, light is emitted by a single quantum state lying at the bottom of the lower exciton-polariton band. Its intensity increases exponentially with the pump power and its linewidth becomes narrower than the cavity mode width. Near-field spectroscopy shows that the stimulated emission comes from several bright spots in the cavity plane, but no diffraction-induced angular broadening of the emission is observed. This is direct evidence for spontaneous formation of a nonequilibrium Bose condensate of coherent exciton polaritons with their wave function sharply peaked at structural imperfections.

Figure 1

(a) to (c): Gray-scale two-dimensional images of the far-field polariton PL intensity. Vertical and horizontal axes correspond to the emission energy and emission angle, respectively. PL intensity increases from white to black (see horizontal scale bars). Each map is obtained from direct observation of the Fourier plane. The excitation pumping was (a) $P_0=500\mathrm{W}∕{\mathrm{cm}}^2$, (b) $8.6P_0$, just below threshold, and (c) $10P_0$, just above threshold. (d) Spectrally integrated intensity of the emission from the polariton ground state ${\mathrm{k}}_{\Vert }=0$ $(\theta =0)$ normalized to the pumping power, as a function of pumping power. (e) PL spectra of the ground state, corresponding to these three pumping powers $P_0$, $8.6P_0$, and $10P_0$, normalized to the pumping power. (f) Angular profile of the emission at 1624.9 meV for the highest pumping power $10P_0$.

Figure 2

Gray-scale two-dimensional images of the near-field polariton PL for different pumping powers. Vertical and horizontal axes are in-plane coordinates on the sample surface. PL intensity increases from black to white. The pumping power used was $P_0=500\mathrm{W}∕{\mathrm{cm}}^2$, below threshold, in (a), and $10P_0$, above threshold, in (b) and (c). Images (b) and (c) were taken from two different areas on the sample. FWHM stands for full width at half maximum of the PL intensity profile.

Figure 3

(a) to (d) Gray-scale two-dimensional plots of the condensate density ${\mid ⟨\psi (\vec{r},t)⟩\mid }^2$ at (a) $t=0$, (b) $t=6\mathrm{ps}$, (c) $t=30\mathrm{ps}$, and (d) the time average over 100 ps. The density increases from black to white. (e) The PL spectrum of the condensate calculated from ${\int }_r{\mid ⟨\psi (\vec{r},\omega )⟩\mid }^{2}d\vec{r}$, where $⟨\psi (\vec{r},\omega )⟩$ is the time-Fourier transform of $⟨\psi (\vec{r},t)⟩$. (f) Angular profile of the condensate emission as deduced from ${\int }_r{\mid ⟨\psi (\vec{k},t)⟩\mid }^{2}d\vec{r}$, where $⟨\psi (\vec{k},t)⟩$ is the space-Fourier transform of $⟨\psi (\vec{r},t)⟩$.