THE QUANTUM INTELLIGENCER

Exceptional Points and Majorana Modes in Dissipative p-Wave Josephson Junctions In Plain English: This research looks at how electric current flows in a special kind of superconducting wire joint where energy is lost (like heat or radiation). The scientists studied a setup where two exotic superconductors are connected, and they found that certain special quantum states—like 'Majorana particles'—can still exist even when energy is leaking out. These states turn into unique kinds of quantum points that are surprisingly stable. This matters because such stable states could be used to build more robust quantum computers that are less affected by outside disturbances. Summary: This theoretical study investigates the Andreev bound state spectrum and supercurrent in a one-dimensional p-wave non-Hermitian Josephson junction (NHJJ), composed of two topological p-wave superconductors coupled via a dissipative, non-Hermitian interface. Using an effective non-Hermitian Bogoliubov-de Gennes Hamiltonian, the authors discover that the introduction of non-Hermiticity leads to the formation of a pair of exceptional points in the complex energy spectrum of Andreev quasi-bound states. These zero-energy exceptional points are symmetrically located around the Josephson phase difference ϕ = π, where a Majorana zero mode remains stable. The exceptional points are shown to originate from a pair of Majorana zero modes in the Hermitian limit and are topologically protected. Through non-Hermitian scattering analysis, the decay of scattering amplitudes confirms quasiparticle loss at the junction. The supercurrent is derived directly from inelastic Andreev reflection amplitudes, offering a physically intuitive picture of transport. The supercurrent varies continuously across the exceptional points, with no observed enhancement in critical current. The analysis is extended to a mixed s-p wave NHJJ, broadening the applicability of the findings. This work provides new insights into the transport properties of Josephson junctions in the presence of Majorana modes, exceptional points, and dissipation (citation: arXiv paper on 'Exceptional Andreev spectrum and supercurrent in p-wave non-Hermitian Josephson junctions'). Key Points: - A pair of zero-energy exceptional points emerges in the complex Andreev bound state spectrum of a p-wave non-Hermitian Josephson junction. These exceptional points are symmetrically located around the Josephson phase ϕ = π, where a Majorana zero mode persists. The exceptional points evolve from a pair of Majorana zero modes upon introducing non-Hermiticity and are topologically protected. Non-Hermitian scattering analysis demonstrates quasiparticle loss through decay of scattering amplitudes. The supercurrent is calculated from inelastic Andreev reflection amplitudes and varies continuously across the exceptional points. No enhancement in critical supercurrent is observed. The model is generalized to mixed s-p wave non-Hermitian junctions. Notable Quotes: - "a pair of exceptional points emerge in the complex spectrum of Andreev quasi-bound states." - "The two exceptional points with zero energy locate symmetrically with respect to Josephson phase difference ϕ=π, at which a Majorana zero mode persists." - "the exceptional points descend from a pair of Majorana zero modes after turning on the non-Hermiticity and are topologically protected." - "we explicitly demonstrate the loss of quasiparticles through the decay of scattering amplitude probabilities." - "The supercurrent varies continuously as a function of ϕ across the exceptional points. No enhancement of critical current is observed." Data Points: - The exceptional points are located symmetrically around ϕ = π. The energy of the exceptional points is zero. The system is one-dimensional. The junction connects two topological p-wave superconductors. The analysis includes a generalization to mixed s-p wave non-Hermitian Josephson junctions. Controversial Claims: - The claim that exceptional points descending from Majorana zero modes are topologically protected in a non-Hermitian setting may be subject to debate, as the definition and robustness of topological protection in open quantum systems are still active areas of research. Additionally, the absence of critical current enhancement—despite the presence of exceptional points and Majorana modes—contradicts some expectations in non-Hermitian transport, where such features are sometimes predicted to amplify responses, potentially sparking discussion on the conditions under which non-Hermiticity enhances or suppresses supercurrent. Technical Terms: - Andreev bound states, non-Hermitian Josephson junction (NHJJ), p-wave superconductivity, Bogoliubov-de Gennes Hamiltonian, exceptional points, Majorana zero modes, topological protection, non-Hermitian scattering, inelastic Andreev reflection, supercurrent, quasiparticle loss, Josephson phase difference (ϕ), complex energy spectrum, dissipative junction, topological superconductors —Ada H. Pemberley Dispatch from The Prepared E0