Coherent Control of Polariton Parametric Scattering in Semiconductor Microcavities

In a pump-probe experiment, we have been able to control, with phase-locked probe pulses, the ultrafast nonlinear optical emission of a semiconductor microcavity, arising from polariton parametric amplification. This evidences the coherence of the polariton population near $k=0$, even for delays much longer than the pulse width. The control of a large population at $k=0$ is possible although the probe pulses are much weaker than the large polarization they control. With rising pump power the dynamics of the scattering get faster. Just above threshold the parametric scattering process shows unexpected long coherence times, whereas when pump power is risen the contrast decays due to a significant pump reservoir depletion. The weak pulses at normal incidence control the whole angular emission pattern of the microcavity.

Figure 1

Experimental setup: the pump (spectrally narrow and temporally long) hits the sample with a variable angle ($\simeq 10°$ in the experiments presented here), while the two probe pulses (spectrally broad and temporally short) are in the normal direction. The reflected or transmitted probe, which is greatly amplified by the parametric scattering, is spectrally dispersed and detected. The angular pattern of the emitted light is also detected. The parametric scattering process is sketched along the polariton dispersion curve. The sample structure is also represented, with the cavity $\lambda$ spacer delimited by the two Bragg mirrors and the quantum well at the cavity center.

Figure 2

(a) Probe-transmission spectra with (full line) and without (dashed line) pump excitation; one probe pulse only hits the sample. At the chosen position on the sample, the energy of the empty-cavity mode (1486.0 meV) is slightly lower than the bare exciton energy (1487.0 meV). (b) Evolution of the time integrated signal emission as the probe to pump delay is scanned. The intensity has been integrated over the whole peak width of the LP emission. (c),(d) Transmission spectra as a function of relative phase (control phase) between the two phase-controlled probe pulses. On the right the value of the intensity [integrated over the peak width as in (b)] is extracted. The signal is normalized with respect to the intensity of a single probe pulse and the pump luminescence has been subtracted. The second probe pulse is delayed with respect to the first one by $\Delta t=0$ (c), 8 ps (d). (e) Contrast of coherent control oscillations versus the delay between the two probe pulses; the first probe pulse is synchronous with the pump. If $I_{\max }$ and $I_{\min }$ are the maximum and minimum values observed in the coherent-control oscillations, the contrast $C$ is defined as $C=(I_{\max }-I_{\min })/(I_{\max }+I_{\min })$. The incident pump polariton densities are normalized to $I_0=9\times {10}^9\mathrm{\text{polaritons}}/({\mathrm{c}\mathrm{m}}^2\mathrm{\text{pulse}})$ which is the density at which the stimulation threshold is reached, whereas the density of a single probe is ${10}^6\mathrm{\text{polaritons}}/({\mathrm{c}\mathrm{m}}^2\mathrm{\text{pulse}})$. Each curve is measured for a different pump density, as indicated in the legend. The calculated contrast has been obtained from the experimental data shown in panel (b) as explained in the text.

Figure 3

Angular pattern of the emission in transmission geometry as a function of the control phase. The delay between the two phase-locked probe pulses is 2 ps. The lower panel shows two sections of the surface plot corresponding to a constructive and a destructive control phase. The signal and pump emissions were attenuated (up to $14°$) by 4 orders of magnitude with a neutral density filter in order to show the whole angular pattern in the same picture. To evidence the effects of the coherent control on the pump beam, the probe density employed here was higher [$2.5\times {10}^8\mathrm{\text{polaritons}}/({\mathrm{c}\mathrm{m}}^2\mathrm{\text{pulse}})$] than that in the measurements in Fig. 2, while the pump density was lower [$\simeq {10}^{11}\mathrm{\text{polaritons}}/({\mathrm{c}\mathrm{m}}^2\mathrm{\text{pulse}})$].