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Bound state formation is a classic feature of quantum mechanics, where a particle localizes in the vicinity of an attractive potential. This is typically understood as the particle lowering its potential energy. In this article, we discuss…
Previous work on imaging wave packet dynamics with x-ray scattering revealed that the scattering patterns deviate substantially from the notion of instantaneous momentum density of the wave packet. Here we show that scattering patterns can…
We theoretically study two atoms with $p$-wave interaction in a one-dimensional waveguide, and investigate how the transverse anisotropy of the confinement affects the two-body state, especially, the properties of the resonance. For…
We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even…
Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…
We investigate the effect of potential barriers in the form of step edges on the scattering properties of Bi$_2$Se$_3$(111) topological surface states by means of large-scale ab-initio transport simulations. Our results demonstrate the…
The advances in cold atom experiments have allowed construction of confining traps in the form of curved surfaces. This opens up the possibility of studying quantum gases in curved manifolds. On closed surfaces, many fundamental processes…
The interplay among interaction, non-Hermiticity, and disorder opens a new avenue for engineering novel phase transitions. We here study the spectral and localization features of two interacting bosons in one-dimensional nonreciprocal…
Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our…
We theoretically investigate the quantum scattering of a single-photon pulse interacting with an ensemble of $\Lambda$-type three-level atoms coupled to a one-dimensional waveguide. With an effective non-Hermitian Hamiltonian, we study the…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
The static and dynamic properties of many-body quantum systems are often well described by collective excitations, known as quasiparticles. Engineered quantum systems offer the opportunity to study such emergent phenomena in a precisely…
The static and dynamical properties of a one-dimensional quantum system described by a non-Hermitian Hamiltonian of the so-called Hatano-Nelson type; a tight-binding model with asymmetric (or non-reciprocal) hopping, are studied. The static…
Solitons are non-dispersive wave solutions that arise in a diverse range of nonlinear systems, stablised by a focussing or defocussing nonlinearity. First observed in shallow water, solitons have subsequently been studied in many other…
We analytically model a one-dimensional lattice with periodic impurities representing a photonic crystal from first principles. We then investigate bound states in the continuum by computing the transmission and reflection coefficients. It…
We propose a framework for calculating scattering and bound state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the…
We study the localization phenomena in a one-dimensional lattice system with a uniformly moving disordered potential. At a low moving velocity, we find a sliding localized phase in which the initially localized matter wave adiabatically…
Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy…
We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has…
Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a…