Fig. 2: The time-varying evolutionary state \(| \psi (t)\left.\right\rangle\) starting from either the \({{{\mathcal{PTS}}}}\) or \({{{\mathcal{PTB}}}}\) regime with the \({{{\mathcal{PT}}}}\) Hamiltonian.
From: Dynamical topology of chiral and nonreciprocal state transfers in a non-Hermitian quantum system
a, c, e, g Clockwise and counterclockwise encircling the EP starting from \(| {\alpha }_{A}(0)\left.\right\rangle\) and \(| {\beta }_{A}(0)\left.\right\rangle\) are shown as trajectories 1 to 4. i, k, m, o Similar encircling starting from \(| {\alpha }_{B}(0)\left.\right\rangle\) and \(| {\beta }_{B}(0)\left.\right\rangle\) are depicted as trajectories 5 to 8. b, d, f, h Overlaps 〈αA(t)∣ψ(t)〉 and 〈βA(t)∣ψ(t)〉 between the instantaneous eigenstates and the evolutionary state from the \({{{\mathcal{PT}}}}\)-symmetric (\({{{\mathcal{PTS}}}}\)) regime. j, l, n, p Overlaps 〈αB(t)∣ψ(t)〉 and 〈βB(t)∣ψ(t)〉 from the \({{{\mathcal{PT}}}}\)-broken (\({{{\mathcal{PTB}}}}\)) regime. Nonadiabatic dynamics are shown in the cyan shaded regions. The solid (dashed) box depicts the state evolution trajectories in the visual four-dimensional picture of the eigenspectrum as a function of the detuning Δ and the coupling rate J, with colors on the Riemann sheet representing imaginary (real) values. Circles with error bars represent experimental results obtained from the raw measured data, while lines correspond to numerical simulation results.The error bars are estimated as the standard deviation (1σ) from 5 rounds of quantum state tomography experiments.
