Floquet-engineered quantum walks.

The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas. One prominent application is in computational models capable of performing any quantum computation, in which precisely controlled state transfer is required. It is, however, generally difficult to control the behavior of quantum walks due to stochastic processes. Here we unveil the walking mechanism based on its particle-wave duality and then present tailoring quantum walks using the walking mechanism (Floquet oscillations) under designed time-dependent coins, to manipulate the desired state on demand, as in universal quantum computation primitives. Our results open the path towards control of quantum walks.

Breather-breather interactions in sine-Gordon systems using collective coordinate approach.

We investigate the interaction between breathers in sine-Gordon systems using a collective coordinate approach. Focusing on the in-phase or out-of-phase oscillation mode of two identical breathers, we derive a simple ordinary differential equation for the collective coordinate: the separation between the centers of mass of the two breathers R. Analytic solutions of this equation can reproduce quantitatively the results of a direct numerical simulation of the sine-Gordon equation over the whole parameter range. The interaction between the two breathers is attractive (repulsive) for the in-phase (out-of-phase) oscillation mode with an asymptotic exponential dependence on R. We find that the interaction within the innermost kink-antikink (kink-kink) pair for the in-phase (out-of-phase) case plays the most significant role in determining the sign and the strength of the effective breather-breather interaction. We also find an internal oscillation mode of the in-phase oscillating breather pair and obtain an analytic expression for the angular frequency of the mode.

Time dilation of a bound half-fluxon pair in a long Josephson junction with a ferromagnetic insulator.

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.

Supercurrent through hybrid junctions with anisotropic Cooper-pair condensates.

A general formula for the supercurrent between different internal structures in a wide class of hybrid junctions is derived on the basis of the Andreev-reflection picture. The formula extends existing formulas and also enables us to analyze novel B-phase/A-phase/B-phase junctions in superfluid 3He systems. We propose a mechanism for pi states due to the (circumflex)l texture in the A phase of the junction, which could elucidate major features of the pi states with higher critical current ( H states) discovered in superfluid 3He weak links. The bistability of the pi states is also discussed.