Controllable Goos-H\"{a}nchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field

The quantum Goos-H\"{a}nchen shift for ballistic electrons is investigated in a parabolic potential well under a uniform vertical magnetic field. It is found that the Goos-H\"{a}nchen shift can be negative as well as positive, and becomes zero at transmission resonances. The beam shift depends not only on the incident energy and incidence angle, but also on the magnetic field and Landau quantum number. Based on these phenomena, we propose an alternative way to realize the spin beam splitter in the proposed spintronic device, which can completely separate spin-up and spin-down electron beams by negative and positive Goos-H\"{a}nchen shifts.Comment: 6 pages, 6 figure

An efficient non-linear Feshbach engine

We investigate a thermodynamic cycle using a Bose-Einstein condensate with nonlinear interactions as the working medium. Exploiting Feshbach resonances to change the interaction strength of the BEC allows us to produce work by expanding and compressing the gas. To ensure a large power output from this engine these strokes must be performed on a short timescale, however such non-adiabatic strokes can create irreversible work which degrades the engine's efficiency. To combat this, we design a shortcut to adiabaticity which can achieve an adiabatic-like evolution within a finite time, therefore significantly reducing the out-of-equilibrium excitations in the BEC. We investigate the effect of the shortcut to adiabaticity on the efficiency and power output of the engine and show that the tunable nonlinearity strength, modulated by Feshbach resonances, serves as a useful tool to enhance the system's performance.Comment: 8 pages, 5 figures. To Appear New J. Phys. Focus on Shortcuts to Adiabaticit