Unidirectional flow of solitons with nonlinearity management.

Unidirectional flow of solitons is obtained with a localized modulation of the nonlinearity strength. The modulation takes the shape of an asymmetric double well with a slight difference between the potential depths. The results were established using numerical computations and then verified qualitatively using a variational approach. Our results suggest that the most important physics at the origin of the unidirectional flow is the excitation of the breathing modes in the scattering region. Simplified variational equations of motion suggested that the phenomenon can be observed if the soliton is scattered by a generic asymmetric effective double potential well.

Confined states in graphene quantum blisters.

Bilayer graphene samples may exhibit regions where the two layers are locally delaminated forming a so-called quantum blister in the graphene sheet. Electron and hole states can be confined in this graphene quantum blisters (GQB) by applying a global electrostatic bias. We scrutinize the electronic properties of these confined states under the variation of interlayer bias, coupling, and blister's size. The spectra display strong anti-crossings due to the coupling of the confined states on upper and lower layers inside the blister. These spectra are layer localized where the respective confined states reside on either layer or equally distributed. For finite angular momentum, this layer localization can be at the edge of the blister and corresponds to degenerate modes of opposite momenta. Furthermore, the energy levels in GQB exhibit electron-hole symmetry that is sensitive to the electrostatic bias. Finally, we demonstrate that confinement in GQB persists even in the presence of a variation in the inter-layer coupling.

Quantum transport across van der Waals domain walls in bilayer graphene.

Bilayer graphene can exhibit deformations such that the two graphene sheets are locally detached from each other resulting in a structure consisting of domains with different van der Waals inter-layer coupling. Here we investigate how the presence of these domains affects the transport properties of bilayer graphene. We derive analytical expressions for the transmission probability, and the corresponding conductance, across walls separating different inter-layer coupling domains. We find that the transmission can exhibit a valley-dependent layer asymmetry and that the domain walls have a considerable effect on the chiral tunnelling properties of the charge carriers. We show that transport measurements allow one to obtain the strength with which the two layers are coupled. We perform numerical calculations for systems with two domain walls and find that the availability of multiple transport channels in bilayer graphene significantly modifies the conductance dependence on inter-layer potential asymmetry.

Interaction potential between discrete solitons in waveguide arrays.

Using a variational approach, we obtained the interaction potential between two discrete solitons in optical waveguide arrays. The resulting potential bears the two features of soliton-soliton and soliton-waveguide interaction potentials where the former is similar to that of the continuum case and the latter is similar to the effective Pierls-Nabarro potential. The interplay between the two interaction potentials is investigated by studying its effect on the soliton molecule formation. It is found that the two solitons bind if their initial separation equals an odd number of waveguides, while they do not bind if their separation is an even number, which is a consequence of the two solitons being both either at the intersites (unstable) or being onsite (stable). We derived the equations of motion for the solitons' centre of mass and relative separation and provided analytic solutions for some specific cases. Favourable agreement between the analytical and numerical interaction potentials is obtained. Possible applications of our results to all-optical logic gates are pointed out.

All-optical switches, unidirectional flow, and logic gates with discrete solitons in waveguide arrays.

We propose a mechanism by which a number of useful all-optical operations, such as switches, diodes, and logic gates, can be performed with a single device. An effective potential well is obtained by modulating the coupling between the waveguides through their separations. Depending on the power of a control soliton injected through the potential well, an incoming soliton will either completely transmit or reflect forming a controllable switch. We show that two such switches can work as AND, OR, NAND, and NOR logic gates. Furthermore, the same device may also function as a perfect soliton diode with adjustable polarity. We discuss the feasibility of realising such devices with current experimental setups.

Scattering of a matter-wave single soliton and a two-soliton molecule by an attractive potential.

Scattering of a matter-wave single soliton and two-soliton molecule incident on the modified Pöschl-Teller potential well has been studied by means of a collective coordinate approach and numerical simulations of the Gross-Pitaevskii equation. Despite the attractive nature of the potential we observe total reflection of solitons in particular ranges of parameters, which is the signature of quantum behavior displayed by the matter-wave soliton. For other particular sets of parameters unscathed transmission of solitons and molecules through the potential well has been identified. A specific feature of this process is that the soliton passing through the potential well overtakes the freely propagating counterpart; i.e., its mean position appears to have been advanced in time. An array of such potentials makes the "time advance" effect even more pronounced, so that scattered solitons move well ahead of nonscattered ones, fully preserving their initial shape and velocity. A possible application of the obtained results is pointed out.

Electron in the field of a molecule with an electric dipole moment.

In solving the eigenvalue wave equation, we relax the usual diagonal constraint on its matrix representation by allowing it to be tridiagonal. This results in a larger representation space that incorporates an analytic solution for the noncentral electric dipole pole potential cos theta/r2, which was believed not to belong to the class of exactly solvable potentials. Consequently, we obtain closed form solution of the time-independent Schrödinger equation for an electron in the field of a molecule treated as a point electric dipole.