Fig. 1: Noise-induced non-Hermitian dissipative quantum dynamics and experimental setup.
a Quantum quench process. Upper panel: The system is initialized to the fully polarized ground state \(\left|\downarrow \right\rangle\) of pre-quench Hamiltonian with ∣mz∣ ≫ ∣ξ0∣. Then mz is quenched to a nontrivial value, and the state evolves under the post-quench Hamiltonian. Middle panel: In the absence of noise, the spin polarization 〈σ(k, t)〉 (red arrows) precesses with respect to the Hamiltonian vector h (black arrow). The corresponding trajectory is shown as the blue line. On the BIS where hz = 0, the time-averaged spin texture \(\overline{\langle {{{\boldsymbol{\sigma }}}}({{{\bf{k}}}})\rangle }\) vanishes as the Hamiltonian vector h = (hx, hy) is orthogonal to the initial state. Across the BIS \(\overline{\langle {{{\boldsymbol{\sigma }}}}({{{\bf{k}}}})\rangle }\) shows nontrivial gradients, which encode the topological invariant. Lower panel: In the presence of noise, the precession axis is distorted, leading to the dissipative dynamics of stochastic averaged spin polarization s(k, t), as shown by the red arrows and distorted blue trajectories. b The non-Hermitian dissipative dynamics can be interpreted as the stochastic average over different noise configurations. Here the solid black arrows represent the Hamiltonian vector h without noise, and the dashed black arrows denote the Hamiltonian vector distorted by time-dependent noise. For each noise configuration (small spheres), the spin polarization is on the surface of Bloch sphere and obeys the unitary dynamics, in spite of the irregular blue trajectory caused by the noise-distorted Hamiltonian vector. However, the average over all noise configurations (big sphere) leads to a globally dissipative effect and a deformation of BISs. c Pulse sequence for simulating the 2D non-Hermitian QAH model. 1H is initially decoupled, and 13C is rapidly prepared to the \(\left|\downarrow \right\rangle\) state using the nuclear Overhauser effect. The control pulse is designed according to Eq. (12), where the green and blue circles represent rotations about the x-axis and y-axis with A and φ the amplitude and phase, respectively.
