Non-Hermitian physics has emerged as a unifying framework for understanding open systems where energy, probability, or coherence is not conserved. Such systems are prevalent across many domains of physics, from quantum tunneling and scattering to photonic and condensed matter systems. To systematically describe open quantum dynamics, the Lindblad master equation was introduced, incorporating quantum jumps and noise while preserving fundamental commutation relations. While crucial for microscopic systems, many macroscopic systems can still be effectively described using non-Hermitian mean-field Hamiltonians, allowing tractable modeling of dissipative processes. A significant theoretical breakthrough came with Bender and Boettcher’s discovery that non-Hermitian Hamiltonians can exhibit entirely real spectra if they possess parity-time (PT) symmetry. In quantum systems, this corresponds to a complex potential, implying balanced gain and loss. These systems exhibit non-orthogonal eigenstates, resulting in a biorthogonal structure. At critical gain/loss thresholds, the system reaches exceptional points (EPs), degeneracies where both eigenvalues and eigenvectors coalesce, leading to spontaneous PT-symmetry breaking and dramatic changes in system dynamics.
In strongly correlated materials like high-temperature superconductors and Mott insulators, quasiparticles acquire finite lifetimes from interactions, yielding complex energy spectra even in equilibrium. In mesoscopic systems, the transport properties, such as resonant tunneling, Fano resonances, and current noise, are effectively modeled using non-Hermitian Hamiltonians. Semiconductor microcavities supporting exciton-polaritons offer examples of driven-dissipative quantum systems. These hybrid quasiparticles exhibit gain and loss via photon pumping and leakage, and their condensation, lasing, and switching behavior are governed by non-Hermitian coupled-mode theory. The practical realization of PT symmetry in optical and solid-state systems has been made possible through advances in metamaterials, artificially structured media with tailored electromagnetic responses. Metamaterials offer control over permittivity, permeability, and refractive index across positive, negative, and near-zero regimes, enabling precise tuning of both electric and magnetic field interactions. In PT-symmetric metamaterials, the spontaneous symmetry breaking causes unique phenomena such as bright and dark meta-atom formation, coherent perfect absorption (anti-lasing), and unidirectional invisibility. The associated scattering matrices can evolve from unimodular to superunitary or subunitary, and the system’s non-orthogonal eigenmodes contribute to exceptional sensitivity and mode selectivity. This makes them compelling candidates for exploring next-generation photonic and quantum systems, especially in structured light–matter interactions and topological device applications.
Motivated by these theoretical and experimental advances, we now focus on a specific class of non-Hermitian solid-state systems: GaAs-based nanostructures embedded in FIR photon cavities and subjected to external magnetic fields. Experiments show that a two-dimensional electron gas (2DEG) in an AlGaAs-GaAs heterostructure with extraordinary purity and mobility can be placed in a high-quality-factor terahertz cavity in an external magnetic field, and the high polarizability of the 2DEG makes it possible to attain a nonperturbative coupling of electrons with the cavity photons. These systems, which lie at the intersection of quantum optics, transport theory, and cavity QED, offer a highly controllable platform for investigating light–matter interactions, non-Hermitian dynamics, and collective quantum phenomena in open, multiscale settings.