Fig. 4: Spectral line and winding topology.
From: Quantum tomography of a third-order exceptional point in a dissipative trapped ion
a The spectral line (the remaining population in \(\left\vert a\right\rangle\) at the end of the dynamics at ta = 200 μs with respect to the detuning δa) for Ω/γ = 0.8. Here, the half-width of the outer dips is mainly determined by \({{{\rm{Im}}}}({E}_{0}-{{{\rm{i}}}}\gamma )\), while the half-width of the inner peak is mainly determined by \({{{\rm{Im}}}}({E}_{+}-{{{\rm{i}}}}\gamma )\). Both the theoretical results (red line) and fitted ones (black line) are calculated according to Eq. (21). The former ones are computed using the parameter Ω/γ = 0.8, while the fitted results employ parameters obtained from a fitting procedure based on the experimental data (circles). b Argument of En(θ) − EB as a function of θ with EB = − 0.016 − 0.032i plotted using the data in Fig. 1f. The y-axis is shifted so that \({{\arg }}({E}_{0}(0)-{E}_{B})=0\), and the n-th band is shifted along the x-axis by 2πn to show the spectral winding around EB. The units of energy is 2π × 1 MHz. Here, γ = 2π × 0.040 MHz and Ωa = 2π × 0.004 MHz. The experimental results are averaged over 5 rounds of experiments (each contains 200 shots) with error bars being the standard deviation of the 5 experimental repetitions.
