Loop parametric scattering of cavity polaritons

Within the framework of the mean-field approximation, a coherently excited two-dimensional system of weakly repulsive bosons is predicted to show a giant loop scattering when the rotational symmetry is reduced. The considered process combines (i) the parametric decay of the driven condensate into different $k$ states and (ii) their massive backscattering owing to spontaneous synchronization of several four-wave mixing channels. The hybridization of the direct and inverse scattering processes, which are different and thus do not balance each other, makes the condensate oscillate under constant one-mode excitation. In particular, the amplitude of a polariton condensate excited by a resonant electromagnetic wave in a uniform polygonal GaAs-based microcavity is expected to oscillate in the subterahertz frequency domain.

Figure 1

(a) One-mode response of a driven condensate; the dashed line indicates unstable solutions; $D=E_p-E_g=40\gamma$ is the pump detuning from the resonance at ${\mathbf{k}}_p=0$; $f_{★}=\sqrt{(\gamma /V)\left[{(D-\gamma )}^2+{\gamma }^2\right]}$ [22]. (b) Dispersion law, position of the pumped mode, and scheme of the parametric scattering. The scattering wave number $k_{★}\approx 0.9\mu {\mathrm{m}}^{-1}$.

Figure 2

(a) Steady-state response to excitation in a square microcavity mesa. Parameters are indicated in the main text. Circles represent independent solutions. Intensities ${\left|\psi (\mathbf{r},t)\right|}^2$ are averaged in space (over the mesa) and time (over 0.1 ns) after a 1-ns-long period of increasing $\left|f\right|$ from zero to a given amplitude and an extra 2-ns-long period allotted for the establishment of a particular solution at a fixed $\left|f\right|$. (b) and (c) Explicit spatial dependences for two solutions.

Figure 3

Dynamics of the intensities of the pumped [(a) and (b)] and scattered [(c) and (d)] modes. The pump power ${\left|f\right|}^2$ is linearly increased in 1 ns from 0 to $\sim 0.22f_{★}^2$. (b) and (d) represent an established solution on a more detailed time scale.

Figure 4

(a) Scheme of the loop parametric scattering. (b)–(d) The spectra of the main $k$ states at the stage of regular oscillations.

Figure 5

Typical real-space [(a) and (b)] and momentum-space [(c) and (d)] field patterns at the stage of regular oscillations for two time instants separated by 7 ps (approximately half of a period). The full evolution can be seen in the Supplemental Material [34].