We introduce the notion of a ${cal PT}$-symmetric dimer with a $chi^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss,
respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain/loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first or the second harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.
In this work, we propose a PT-symmetric coupler whose arms are birefringent waveguides as a realistic physical model which leads to a so-called quadrimer i.e., a four complex field setting. We seek stationary solutions of the resulting linear and non
linear model, identifying its linear point of PT symmetry breaking and examining the corresponding nonlinear solutions that persist up to this point, as well as, so-called, ghost states that bifurcate from them. We obtain the relevant symmetry breaking bifurcations and numerically follow the associated dynamics which give rise to growth/decay even within the PT-symmetric phase. Our obtained stationary nonlinear solutions are found to terminate in saddle-center bifurcations which are analogous to the linear PT-phase transition.
The magnetic phase diagram has been mapped out via the measurements of electronic resistivity, magnetization and specific heat in the cobalt-based layered LnCo1-xFexAsO (Ln=La, Sm) compounds. The ferromagnetic (FM) transition at 63 K for LaCoAsO is r
apidly suppressed upon Fe doping, and ultimately disappears around x=0.3 in the LaCo1-xFexAsO system. When La is replaced by magnetic rare earth element Sm, the 3d electrons first undergo a FM transition at Tc = 75 K, followed by an antiferromagnetic (AFM) transition at a lower temperature TN1 = 45 K. With partial Fe doping on the Co site, both FM (Tc) and AFM (TN1) transition temperatures are significantly suppressed, and finally approach zero kelvin at x = 0.3 and 0.2, respectively. Meanwhile, a third magnetic transition at TN2 = 5.6 K for SmCoAsO, associated with the AFM order of the Sm3+ 4f-oments, is uncovered and TN2 is found to be almost robust against the small Fe-doping. These results suggest that the 4f electrons of Sm3+ have an important effect on the magnetic behavior of 3d electrons in the 1111 type Co-based LnCo1-xFexAsO systems. In contrast, the magnetism of the f-electrons is relatively unaffected by the variation of the 3d electrons. The rich magnetic phase diagram in the Co-rich side of the LnCo1-xFexAsO system, therefore, is established.
In this work we analyze PT-symmetric double-well potentials based on a two-mode picture. We reduce the problem into a PT-symmetric dimer and illustrate that the latter has effectively two fundamental bifurcations, a pitchfork (symmetry-breaking bifur
cation) and a saddle-center one, which is the nonlinear analog of the PT-phase-transition. It is shown that the symmetry breaking leads to ghost states (amounting to growth or decay); although these states are not true solutions of the original continuum problem, the systems dynamics closely follows them, at least in its metastable evolution. Past the second bifurcation, there are no longer states of the original continuum system. Nevertheless, the solutions can be analytically continued to yield a new pair of branches, which is also identified and dynamically examined. Our explicit analytical results for the dimer are directly compared to the full continuum problem, yielding a good agreement.
We investigate superconductivity and transport properties of Co doped SmFe$_{1-x}$Co$_{x}$AsO system. The antiferromagnetic (AFM) spin-density wave (SDW) order is rapidly suppressed by Co doping, and superconductivity emerges as $x$ $geq$ 0.05. $T_c$
$^{mid}$ increases with increasing Co content, shows a maximum of 17.2 K at the optimally doping of $xsim$ 0.10. A phase diagram is derived based on the transport measurements and a dome-like $T_c$ versus $x$ curve is established. Meanwhile we found that the normal state thermopower might consist of two different contributions. One contribution increases gradually with increasing $x$, and the other contribution is abnormally enhanced in the superconducting window 0.05 $leq$ $x$ $leq$ 0.20, and shows a dome-like doping dependence. A close correlation between $T_{c}$ and the abnormally enhanced term of thermopower is proposed.
