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

Cascading failures in coupled networks with both inner-dependency and inter-dependency links

We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We find that when most of dependency links are inner- or inter-ones, the coupled networks system is fragile and makes a discontinuous percolation transition. However, when the numbers of two types of dependency links are close to each other, the system is robust and makes a continuous percolation transition. This indicates that the high density of dependency links could not always lead to a discontinuous percolation transition as the previous studies. More interestingly, although the robustness of the system can be optimized by adjusting the ratio of the two types of dependency links, there exists a critical average degree of the networks for coupled random networks, below which the crossover of the two types of percolation transitions disappears, and the system will always demonstrate a discontinuous percolation transition. We also develop an approach to analyze this model, which is agreement with the simulation results well.Comment: 9 pages, 4 figure

Cooling mechanical resonators to quantum ground state from room temperature

Ground-state cooling of mesoscopic mechanical resonators is a fundamental requirement for test of quantum theory and for implementation of quantum information. We analyze the cavity optomechanical cooling limits in the intermediate coupling regime, where the light-enhanced optomechanical coupling strength is comparable with the cavity decay rate. It is found that in this regime the cooling breaks through the limits in both the strong and weak coupling regimes. The lowest cooling limit is derived analytically at the optimal conditions of cavity decay rate and coupling strength. In essence, cooling to the quantum ground state requires $Q_{\mathrm{m}}>2.4n_{\mathrm{th}}$, with $Q_{\mathrm{m}}$ being the mechanical quality factor and $n_{\mathrm{th}}$ being the thermal phonon number. Remarkably, ground-state cooling is achievable starting from room temperature, when mechanical $Q$-frequency product $Q_{\mathrm{m}}{\nu>1.5}\times10^{13}$, and both of the cavity decay rate and the coupling strength exceed the thermal decoherence rate. Our study provides a general framework for optimizing the backaction cooling of mesoscopic mechanical resonators