Fig. 1: Chiral dynamics for parametric loops in the vicinity of an LEP in the parameter space of a single trapped ion.

a The linear Paul trap. b Level scheme of the ion, where the solid arrows represent the transitions with Rabi frequencies \(\Omega\) and \(\widetilde{\Omega }\) driven by 729 and 854 nm lasers, respectively, and \(\Delta\) is the detuning between the energy level and 729 nm laser. The wavy arrow denotes the spontaneous emission with decay rate \(\Gamma\). This three-level model can be simplified to an effective two-level system with tunable drive and decay. c–f Trajectories without encircling the LEP on the Riemann sheets when completing a clockwise or counterclockwise encirclement in \(\triangle -{\gamma }_{{\rm{eff}}}\) parametric space starting from \(\left|{\psi }_{+}\right\rangle\) or \(\left|{\psi }_{-}\right\rangle\), where the parameters take the values \({\Delta }_{\min }/2\pi =\) 400 kHz, \({{\rm{\gamma }}}_{\min }\approx 100\) kHz, \({{\rm{\gamma }}}_{\min }\approx 1.45\) MHz. The empty circles represent the starting points. Five orange corner points A–E (A’–E’) are labeled for convenience of description in the text. The LEPs are labeled by stars