Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes

Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially deformed $su(2)$ algebra. In the mean-field limit of large particle numbers, these systems become classical and their Hamiltonian dynamics can again be described by polynomial deformations of a Lie algebra, where quantum commutators are replaced by Poisson brackets. The Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres with cusp singularities depending on $m$ and $n$. It is demonstrated that the many-particle eigenvalues can be recovered from the mean-field dynamics using a WKB type quantization condition. The many-particle state densities can be semiclassically approximated by the time-periods of periodic orbits, which show characteristic steps and singularities related to the fixed points, whose bifurcation properties are analyzed.Comment: 13 pages, 13 figure

Tooth shell technique: A proof of concept with the use of autogenous dentin block grafts

Background Autogenous bone block graft is considered the gold standard for lateral bony defects. Dentin has been identified to be a suitable autogenous bone graft material due to its structural and chemical similarities to the alveolar bone. Methods This proof of concept study describes the clinical application of the tooth shell technique in 24 sites with 27 implants of 22 patients. A tooth shell was fixed laterally to the defect with microscrews. Distance between the shell and the residual bone was filled with particulate remnants of the tooth root. Implant was inserted simultaneously. Cone beam computed tomography was done after implant insertion (T1) and 3 months later at time of implant exposure (T2). Target parameters were biological complications and the resorption of hard tissue graft. Results Even though a graft exposure occurred in one case (4.5% on patient-level), all implants showed enough implant stability and were able to be loaded. At T2, the evaluation of the X-rays showed no case with hard tissue loss at the mesial or distal implant shoulder. All implants were completely osseointegrated. Conclusions The tooth shell technique showed promising results for the reconstruction of lateral alveolar crest defects. It may be considered to serve as an alternative material to avoid bone harvesting procedures

Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and $PT$-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.Comment: 20 pages, 8 figures, typos corrected, slightly extended, accepted for publication in New Journal of Physics in Focus Issue on Parity-Time Symmetry in Optics and Photonic

Wannier-Stark resonances in optical and semiconductor superlattices

In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.Comment: 94 pages, 41 figures, typos corrected, references adde

Resonance solutions of the nonlinear Schr\"odinger equation in an open double-well potential

The resonance states and the decay dynamics of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed, as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two basis states in terms of a nonlinear, nonhermitian matrix problem.Comment: 21 pages, 14 figure

Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances

We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schroedinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.Comment: 12 pages, 17 figure

A Sensitive Faraday Rotation Setup Using Triple Modulation

The utilization of polarized targets in scattering experiments has become a common practice in many major accelerator laboratories. Noble gases are especially suitable for such applications, since they can be easily hyper-polarized using spin exchange or metastable pumping techniques. Polarized helium-3 is a very popular target because it often serves as an effective polarized neutron due to its simple nuclear structure. A favorite cell material to generate and store polarized helium-3 is GE-180, a relatively dense aluminosilicate glass. In this paper, we present a Faraday rotation method, using a new triple modulation technique, where the measurement of the Verdet constants of SF57 flint glass, pyrex glass, and air were tested. The sensitivity obtained shows that this technique may be implemented in future cell wall characterization and thickness measurements. We also discuss the first ever extraction of the Verdet constant of GE-180 glass for four wavelength values of 632 nm, 773 nm, 1500 nm, and 1547 nm, whereupon the expected 1/{\lambda}^{2} dependence was observed.Comment: 4 pages, 2 figures Updated version for RSI submissio

Barrier transmission for the Nonlinear Schr\"odinger Equation: Surprises of nonlinear transport

In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case of an exact property of a nonlinear wave function which will be of interest, e.g., for studies of coherent transport of Bose-Einstein condensates through mesoscopic waveguideComment: 7 pages, 2 figure

Computing quantum eigenvalues made easy

An extremely simple and convenient method is presented for computing eigenvalues in quantum mechanics by representing position and momentum operators in a simple matrix form. The simplicity and success of the method is illustrated by numerical results concerning eigenvalues of bound systems and resonances for hermitian and non-hermitian Hamiltonians as well as driven quantum systems