Turbulence in a Bose-Einstein condensate of dipolar excitons in coupled quantum wells

The nonlinear dynamics of a Bose-Einstein condensate (BEC) of dipolar excitons trapped in an external confining potential in coupled quantum wells is analyzed. It is demonstrated that under typical experimental conditions the dipolar exciton BEC can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, which depends on the exciton distribution function. It is shown that, if the system is pumped at sufficiently high frequencies, a steady turbulent state can be formed.

Figure 1

Steady-state spatial distribution for the dipolar exciton BEC density in a trap for low-frequency driving at $R_0=0.1$. (Inset) The evolution of the exciton density profile with rising the pumping rate $R_0$: 0.1 ($\blacksquare$), 0.3 ($•$), and 0.5 ($▴$). The curves represent the Thomas-Fermi distribution function. The coordinates $x$ and $y$ are expressed in units of ${\ell }_0$.

Figure 2

The exciton density profiles at $t=200t_0$ for (a) $R_0=0.1$ and (b) $R_0=0.3$ for high-frequency driving at $p_1=4$, $p_2=6$. (Inset) The exciton density plotted at $y=0$ and averaged over the time period $50t_0<t<200t_0$ and three independent runs (points). Curve shows the fitting by use of the Thomas-Fermi distribution. The coordinates $x$ and $y$ are expressed in units of ${\ell }_0$.

Figure 3

Dependence of the dipolar exciton interaction strength on time for high-frequency driving at $p_1=4$, $p_2=6$. (Inset) Time dependence of the spectral amplitudes $|A_{\mathit{n}}|$ at $\mathit{n}=(0,0)$ (the fundamental mode) and $(8,8)$.

Figure 4

Angle-averaged occupation number of the excitonic modes in the BEC, $N_{n_r}$, as a function of the radial number $n_r$, plotted in log-log scale. The data are averaged over three independent runs. The center of the pumping region is labeled by a vertical arrow, $\Delta n=3$. The lines show a powerlike distribution for $N_{n_r}=\mathrm{const}\times n_r^m$ at $m=0$ and $m=-2$. (Inset) The averaged spectral amplitude distribution $|A_{\mathit{n}}{|}^2$; the dashed curves show the boundaries of the pumping domain.