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We consider different properties of small open quantum systems coupled to an environment and described by a non-Hermitian Hamilton operator. Of special interest is the non-analytical behavior of the eigenvalues in the vicinity of singular…
We propose that the finite-frequency susceptibility of matter near a class of zero-temperature phase transition exhibits distinctive excitonic structure similar to meson resonances. The specific case of a Landau level undergoing a…
We clarify how intense laser irradiation leads to an enhancement of rare processes that may occur within atoms. Non-perturbative calculation using a coherent laser beam gives an exact, time dependent formula of the enhancement factor in the…
The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the energies but also the lifetimes of the states of the system. They show a non-analytical behavior at singular (exceptional) points (EPs). The…
One of the key features of non-Hermitian systems is the occurrence of exceptional points (EPs), spectral degeneracies where the eigenvalues and eigenvectors merge. In this work, we propose applying neural networks to characterize EPs by…
Exceptional points, resulting from non-Hermitian degeneracies, have the potential to enhance the capabilities of quantum sensing. Thus, finding exceptional points in different quantum systems is vital for developing such future sensing…
Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for…
While adaptive optical systems are able to remove moderate wavefront distortions in scintillated optical beams, phase singularities that appear in strongly scintillated beams can severely degrade the performance of such an adaptive optical…
We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of…
Exceptional points (EPs) are singularities that arise in non-Hermitian physics. Current research efforts focus only on systems supporting isolated EPs characterized by increased sensitivity to external perturbations, which makes them…
The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here…
Exceptional points (EPs), singularities in non-Hermitian systems where eigenvalues and eigenstates coalesce, exhibit a dramatically enhanced response to perturbations compared to Hermitian degeneracies. This makes them exceptional…
We review some recent work on the occurrence of coalescing eigenstates at exceptional points in non-Hermitian systems and their influence on physical quantities. We particularly focus on quantum dynamics near exceptional points in open…
We examine the physical manifestations of exceptional points and passage times in a two-level system which is subjected to quantum measurements and which admits a non-Hermitian description. Using an effective Hamiltonian acting in the…
We investigate the rich physics of photonic molecule lasers using a non-Hermitian dimer model. We show that several interesting features, predicted recently using a rigorous steady state ab-initio laser theory (SALT), can be captured by…
Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms and condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states…
Rydberg atoms, with their large transition dipole moments and extreme sensitivity to electric fields, have attracted widespread attention as promising candidates for next-generation quantum precision electrometry. Meanwhile, exceptional…
Theories in physics can provide a kind of map of the physical system under investigation, showing all of the possible types of behavior which may occur. Certain points on the map are of greater significance than others, because they…
The past few years have witnessed growing interests in exceptional points (EPs) in various domains, including photonics, acoustics and electronics. However, EPs have mainly been realized based on the degeneracy of resonances of physical…
We theoretically explore the role of mesoscopic fluctuations and noise on the spectral and temporal properties of systems of $\mathcal{PT}$-symmetric coupled gain-loss resonators operating near the exceptional point, where eigenvalues and…