Nonlinearity Induced Entanglement Stability in a Qubit-Oscillator System

We consider a system composed of a qubit interacting with a quartic (undriven) nonlinear oscillator (NLO) through a conditional displacement Hamiltonian. We show that even a modest nonlinearity can enhance and stabilize the quantum entanglement dynamically generated between the qubit and the NLO. In contrast to the linear case, in which the entanglement is known to oscillate periodically between zero and its maximal value, the nonlinearity suppresses the dynamical decay of the entanglement once it is established. While the entanglement generation is due to the conditional displacements, as noted in several works before, the suppression of its decay is related to the presence of squeezing and other complex processes induced by two- and four-phonon interactions. Finally, we solve the respective Markovian master equation, showing that the previous features are preserved also when the system is open.

Nonlinearity as a resource for nonclassicality in anharmonic systems

Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macro- scopic quantum coherence. Considering various exactly-solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the the entropic nonlinearity of the considered potentials and their ground state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing--which is not captured by the negativity of the Wigner function--we focus on the Glauber-Sudarshan P-function and address the nonclassicality/nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.

Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity

Using the numerical solution of the nonlinear Schrodinger equation and a variational method, it is shown that (3+1)-dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity. © 2013 American Physical Society.

PT-symmetric coupler with chi((2)) nonlinearity

We introduce the notion of a 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 and 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.

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems.

The degree of nonlinearity and anisotropy of blood vessel elasticity

Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress–strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress–strain relationship derived from this function represents the sum of a linear stress–strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In the case of canine pulmonary artery in the arch region, Debes and Fung [Debes, J. C. & Fung, Y. C.(1995) Am. J. Physiol. 269, H433–H442] have shown that the linear regime of the stress–strain relationship extends from the zero-stress state to the homeostatic state and beyond. Both vessels, however, are anisotropic in both the linear and nonlinear regimes.

Generation of macroscopic superposition states with small nonlinearity

We suggest a scheme to generate a macroscopic superposition state (Schrodinger cat state) of a free-propagating optical field using a beam splitter, homodyne measurement, and a very small Kerr nonlinear effect. Our scheme makes it possible to reduce considerably the required nonlinear effect to generate an optical cat state using simple and efficient optical elements.

Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation

Recently, there have been several suggestions that weak Kerr nonlinearity can be used for generation of macroscopic superpositions and entanglement and for linear optics quantum computation. However, it is not immediately clear that this approach can overcome decoherence effects. Our numerical study shows that nonlinearity of weak strength could be useful for macroscopic entanglement generation and quantum gate operations in the presence of decoherence. We suggest specific values for real experiments based on our analysis. Our discussion shows that the generation of macroscopic entanglement using this approach is within the reach of current technology.

Physical Insights, Steady Aerodynamic Effects, and a Design Tool for Low-Pressure Turbine Flutter

The successful, efficient, and safe turbine design requires a thorough understanding of the underlying physical phenomena. This research investigates the physical understanding and parameters highly correlated to flutter, an aeroelastic instability prevalent among low pressure turbine (LPT) blades in both aircraft engines and power turbines. The modern way of determining whether a certain cascade of LPT blades is susceptible to flutter is through time-expensive computational fluid dynamics (CFD) codes. These codes converge to solution satisfying the Eulerian conservation equations subject to the boundary conditions of a nodal domain consisting fluid and solid wall particles. Most detailed CFD codes are accompanied by cryptic turbulence models, meticulous grid constructions, and elegant boundary condition enforcements all with one goal in mind: determine the sign (and therefore stability) of the aerodynamic damping. The main question being asked by the aeroelastician, ``is it positive or negative?'' This type of thought-process eventually gives rise to a black-box effect, leaving physical understanding behind. Therefore, the first part of this research aims to understand and reveal the physics behind LPT flutter in addition to several related topics including acoustic resonance effects. A percentage of this initial numerical investigation is completed using an influence coefficient approach to study the variation the work-per-cycle contributions of neighboring cascade blades to a reference airfoil. The second part of this research introduces new discoveries regarding the relationship between steady aerodynamic loading and negative aerodynamic damping. Using validated CFD codes as computational wind tunnels, a multitude of low-pressure turbine flutter parameters, such as reduced frequency, mode shape, and interblade phase angle, will be scrutinized across various airfoil geometries and steady operating conditions to reach new design guidelines regarding the influence of steady aerodynamic loading and LPT flutter. Many pressing topics influencing LPT flutter including shocks, their nonlinearity, and three-dimensionality are also addressed along the way. The work is concluded by introducing a useful preliminary design tool that can estimate within seconds the entire aerodynamic damping versus nodal diameter curve for a given three-dimensional cascade.