Non-Hermitian Control of Multimode Duan-PPT Criteria and Steering in Energy-Level Cascaded Four-Wave Mixing Processes

The non-Hermitian singularity control of multimode entanglement in the energy-level cascaded four-wave mixing system within a single atomic vapor is of great significance and importance. In this study, a non-Hermiticity system by means of quasi-quantization of energy-band based on non-Hermiticity systems is constructed. By employing atomic coherence in the non-Hermiticity system, high-dimensional quantized photon correlations underdressed field-induced parity-time (PT) symmetry and symmetry breaking through the quantization of energy levels are studied. Such a phenomenon happens at microscopic (nanoscale) when the eigenvalues of dressed energy-level and multimode entanglement are considered for both real and imaginary parts symmetry breaking. Double dressing effect is observed with more coherent channels and larger information capacity than single dressing in the energy-level cascaded four-wave mixing system. The study found that the splitting of the real part is larger than an imaginary part in a second-order system, and the imaginary part splitting is also greater than the real part splitting in a third-order system. The real part (in phase) is constructive dressing quantization, and the imaginary (out of phase) is destructive dressing quantization. Exceptional points (EP points) can be used to enhance sensitivity detection of entanglement quantum state.