The ability to coherently couple arbitrary harmonic oscillators in a fully-controlled way is an important tool to process quantum information. Coupling between quantum harmonic oscillators has previously been demonstrated in several physical systems
by use of a two-level system as a mediating element. Direct interaction at the quantum level has only recently been realized by use of resonant coupling between trapped ions. Here we implement a tunable direct coupling between the microwave harmonics of a superconducting resonator by use of parametric frequency conversion. We accomplish this by coupling the mode currents of two harmonics through a superconducting quantum interference device (SQUID) and modulating its flux at the difference (~ 7 GHz) of the harmonic frequencies. We deterministically prepare a single-photon Fock state and coherently manipulate it between multiple modes, effectively controlling it in a superposition of two different colours. This parametric interaction can be described as a beam-splitter-like operation that couples different frequency modes. As such, it could be used to implement linear optical quantum computing protocols on-chip.
We report the observation of a highly unusual Hall current in the MnSi in an applied pressure P = 6-12 kbar. The Hall conductivity displays a distinctive step-wise field profile quite unlike any other Hall response observed in solids. We identify the
origin of this Hall current with the effective real-space magnetic field due to chiral spin textures, which may be a precursor of the partial-order state at P>14.6 kbar. We discuss evidence favoring the chiral spin mechanism for the origin of the observed Hall anomaly.
The large magnetic anisotropy in the layered ferromagnet Fe_{1/4}TaS_2 leads to very sharp reversals of the magnetization $bf M$ at the coercive field. We have exploited this feature to measure the anomalous Hall effect (AHE), focussing on the AHE co
nductivity $sigma^A_{xy}$ in the inelastic regime. At low temperature T (5-50 K), $sigma^A_{xy}$ is T-independent, consistent with the Berry-phase/Karplus-Luttinger theory. Above 50 K, we extract an inelastic AHE conductivity $sigma^{in}_{xy}$ that scales as the square of $Deltarho$ (the T dependent part of the resistivity $rho$). The term $sigma^{in}_{xy}$ clarifies the T dependence and sign-reversal of the AHE coefficient R_s(T). We discuss the possible ubiquity of $sigma^{in}_{xy}$ in ferromagnets, and ideas for interpreting its scaling with $(Deltarho)^2$. Measurements of the magnetoresistance (MR) reveal a rich pattern of behavior vs. T and field tilt-angle. We show that the 2 mechanisms, the anisotropic MR effect and field-suppression of magnons, account for the intricate MR behavior, including the bow-tie features caused by the sharp reversals in $bf M$.
