Figure 1

Sketch of the experimental setup: In the microwave billiard (right part) the parameter $s$ refers to the length of the slit and $\delta$ to the position of the semicircular Teflon® disc, measured from the billiard center $c$. The antenna positions are shown as crosses. The vectorial network analyzer (left part) measures the ratio of the power of the signals received at the left antenna 1 and emitted at the right antenna 2, ${\mid S_{12}\mid }^2$, and their relative phase. Shown is a part of a typical transmission spectrum measured in dB. The arrow points at two nearly degenerate resonances which for a certain choice of the parameters $s$ and $\delta$ coalesce at the exceptional point at $2.757\pm 0.001\mathrm{GHz}$.Reuse & Permissions

Figure 2

The model [Eq. (3b)] describes the time spectrum very well. This is shown here for the exceptional point at $2.757\pm 0.001\mathrm{GHz}$ for the parameter setting $s=s^{\mathrm{EP}}\approx 48\mathrm{mm}$, $\delta ={\delta }^{\mathrm{EP}}-2\mathrm{mm}\approx 21.5\mathrm{mm}$. The echo frequency is $\Omega ∕2\pi \approx 1.1\pm 0.2\mathrm{MHz}$.Reuse & Permissions

Figure 3

At the EP the quantum echoes disappear and the predicted quadratic time decay of the echo amplitude could be verified. Shown is the result for the EP at $2.757\pm 0.001\mathrm{GHz}$ together with the theoretical prediction [Eq. (4)].Reuse & Permissions