Fourth-order non-Hermitian topological loops with multi-jump in rare-earth-ion-doped microcrystals

Abstract

We investigate fourth-order non-Hermitian dynamics in rare-earth-ion-doped microcrystals using phase-controlled loops and four-wave mixing. We demonstrate that the complex eigenvalue space enables transitions in nontrivial topological loops. First, single-, double-, and triple-dressing configurations form a perfect nontrivial topological loop at the exceptional point (EP) with less quantum jumps due to weak dressing phase interactions. Still, the loop breaks down far from the EP. Such a topological loop is protected by PT–APT symmetry, which can be broken down by sequence quantization. Moreover, nested and cascade triple dressing form a quasi-topological nontrivial loop due to sequential interactions resulting multi-jump. Here, nested displays more jumps (above 100) due to strong three-dressing interaction, while cascade, nested–cascade, and cascade–nested triple dressing show above 50 jumps due to relatively weaker three-dressing interaction. However, at critical points in the phase-controlled topological loop, the system merged from four to two eigenvalues, creating stable degeneracies and enabling fourth-order non-Hermitian switching between multi-quantum states. Thus, multi-jump dynamics result from high-order dressing phase interaction and internal–external dressing interaction. We propose a quantum random number generator device that generates multi-jumps with 96% efficiency. Non-Hermitian topology enables controlled fourth-order quantum-state switching via quantum jump statistics, applicable to quantum random number generation and information processing.