In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propag
ating in free space. In the presence of any Hermitian potential, a waves constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole new class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study, for the first time, the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.
A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the syst
ems boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.
When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called Exceptional Point occurs which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natura
l setting to study such non-Hermitian degeneracies, since they feature resonant modes and a gain material as their basic constituents. Here we show that Exceptional Points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled micro-disk quantum cascade lasers, we demonstrate that in the vicinity of these Exceptional Points the laser shows a characteristic reversal of its pump-dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power. This result establishes photonic molecule lasers as promising tools for exploring many further fascinating aspects of Exceptional Points, like a strong line-width enhancement and the coherent perfect absorption of light in their vicinity as well as non-trivial mode-switching and the accumulation of a geometric phase when encircling an Exceptional Point parametrically.
PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry brea
king points of such an unbounded scattering system to those of underlying bounded systems. In particular, we show how the PT-thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT-transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result that can be tested experimentally and visualized using the concept of Smith charts.
We perform classical three-dimensional Monte Carlo simulations of ultracold neutrons scattering through an absorbing-reflecting mirror system in the Earths gravitational field. We show that the underlying mixed phase space of regular skipping motion
and random motion due to disorder scattering can be exploited to realize a vectorial velocity filter for ultracold neutrons. The absorbing-reflecting mirror system proposed allows beams of ultracold neutrons with low angular divergence to be formed. The range of velocity components can be controlled by adjusting the geometric parameters of the system. First experimental tests of its performance are presented. One potential future application is the investigation of transport and scattering dynamics in confined systems downstream of the filter.
We introduce a procedure to generate scattering states which display trajectory-like wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates to the Wign
er-Smith time-delay matrix and to the transmission matrix with classical (noiseless) transmission eigenvalues close to 0 or 1. Our procedure to create such beam-like states is based solely on the scattering matrix and successfully tested numerically for regular, chaotic and disordered cavities. These results pave the way for the experimental realization of highly collimated wave fronts in transport through complex media with possible applications like secure and low-power communication.
We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex pl
ane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through quantum dots. These results open up new possibilities for studying the effect of decoherence in a wide array of physical systems where Fano resonances are present.
We consider a Kondo spin that is coupled antiferromagnetically to a large chaotic quantum dot. Such a dot is described by the so-called universal Hamiltonian and its electrons are interacting via a ferromagnetic exchange interaction. We derive an eff
ective Hamiltonian in the limit of strong Kondo coupling, where the screened Kondo spin effectively removes one electron from the dot. We find that the exchange coupling constant in this reduced dot (with one less electron) is renormalized and that new interaction terms appear beyond the conventional terms of the strong-coupling limit. The eigenenergies of this effective Hamiltonian are found to be in excellent agreement with exact numerical results of the original model in the limit of strong Kondo coupling.
