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We study the use of the self-Kerr and cross-Kerr nonlinearities to realize strong photon blockade in a weakly driven, four-mode optomechanical system. According to the Born−Oppenheimer approximation, we obtain the cavity self-Kerr coupling and the inter-cavity cross-Kerr coupling, adiabatically separated from the mechanical oscillator. Through minimizing the second-order correlation function, we find out the optimal parameter conditions for the unconventional photon blockade. Under the optimal conditions, the strong photon blockade can appear in the strong or weak nonlinearities.

Discrete spatial solitons are self-consistent solutions of the discrete nonlinear Schrödinger equation that maintain their shape during propagation. Here we show, using a pump-probe technique, that soliton formation can be used to optically induce and control a linear topological end state in the bulk of a Su–Schrieffer–Heeger lattice, using evanescently-coupled waveguide arrays. Specifically, we observe an abrupt nonlinearly-induced transition above a certain power threshold due to an inversion symmetry-breaking nonlinear bifurcation. Our results demonstrate all-optical active control of topological states.

The nonlinearity of semiconductor quantum dots under the condition of low light levels has many important applications. In this study, linear absorption, self-Kerr nonlinearity, fifth-order nonlinearity and cross-Kerr nonlinearity of multiple quantum dots, which are coupled by multiple tunneling, are investigated by using the probability amplitude method. It is found that the linear and nonlinear properties of multiple quantum dots can be modified by the tunneling intensity and energy splitting of the system. Most importantly, it is possible to realize enhanced self-Kerr nonlinearity, fifth-order nonlinearity and cross-Kerr nonlinearity with low linear absorption by choosing suitable parameters for the multiple quantum dots. These results have many potential applications in nonlinear optics and quantum information devices using semiconductor quantum dots.

We demonstrate that higher-order vortex solitons (with larger vortex charges m ) in the nonlinear Schrödinger equation with cubic (defocusing Kerr) nonlinearity can be stabilized by the action of a flat-bottom potential. Such a model can also support the common fundamental (vorticityless) solitons, including the Gaussian-like and flat-top solitons. The effective radii of the fundamental and vortex solitons can be modified by tuning the radius of the flat-bottom part of the potential. We display the contours and phases of vortex solitons with vorticity numbers up to m = 12 . Interestingly, the central holes of vortex solitons increase with the increase of vortex charges, and the central portions of these higher-order vortices become flat. We investigate the existence and stability of both the fundamental and vortex solitons, for different values of the relevant model parameters: the radius of the flat bottom, initial beam power, propagation constant, and the strength of nonlinearity. We also consider the propagation of perturbed initial beams, as well as the propagation in longitudinally modulated flat-bottom potentials. Such a modulated propagation allows for an easy soliton management. We find that the fundamental solitons are completely stable, while the higher-order vortex solitons are prone to the modulation instability, degenerating into m simple vortices that fly away from the inside to the outside of solitons. Eventually, an initial higher-order vortex beam turns into a fundamental (chargeless) soliton.

This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed for this purpose under some parametric constraints. The computational work shows the difference, effectiveness, reliability, and power of the considered scheme. This method can treat several complex higher-order NLSEs that arise in mathematical physics. Graphical illustrations of some obtained solitons are presented.

The emerging technology of quantum neural networks (QNNs) offers a quantum advantage over classical artificial neural networks (ANNs) in terms of speed or efficiency of information processing tasks. It is well established that nonlinear mapping between input and output is an indispensable feature of classical ANNs, while in a QNN the roles of nonlinearity are not yet fully understood. As one tends to think of QNNs as physical systems, it is natural to think of nonlinear mapping originating from a physical nonlinearity of the system, such as Kerr nonlinearity. Here we investigate the effect of Kerr nonlinearity on a bosonic QNN in the context of both classical (simulating an XOR gate) and quantum (generating Schrödinger cat states) tasks. Aside offering a mechanism of nonlinear input-output mapping, Kerr nonlinearity reduces the effect of noise or losses, which are particularly important to consider in the quantum setting. We note that nonlinear mapping may also be introduced through a nonlinear input-output encoding rather than a physical nonlinearity: for example, an output intensity is already a nonlinear function of input amplitude. While in such cases Kerr nonlinearity is not strictly necessary, it still increases the performance in the face of noise or losses.

We present a theoretical study of supercontinuum generation in a Rubidium vapor cell under the conditions of electromagnetically induced transparency (EIT). A weak probe pulse and a strong control laser beam were utilized within a lambda-type excitation scheme. We identified a significant Kerr nonlinearity on the order of 10 3 W −1 m −1 and low group velocity dispersion on the order of 10 −20 s 2 m −1 in the Rubidium vapor cell of length 2.54 cm at a probe wavelength of 781 nm. These parameters facilitated the generation of a 35nm supercontinuum, characterized by pronounced oscillations resulting from self-phase modulation and optical wave breaking. The findings suggest potential applications in nonlinear optical devices and spectroscopy.

We present a new method for the complete analysis of hyperentangled Bell state and Greenberger-Horne-Zeilinger state in polarization and spatial-mode degrees of freedom, resorting to weak cross-Kerr nonlinearity and auxiliary frequency entanglement. The weak cross-Kerr nonlinearity with small phase shift is used to construct quantum nondestructive detector, and it is realizable with the current technology. Compared with the previous schemes, our scheme largely reduces the requirement on nonlinearity with the help of auxiliary entanglement in the third degree of freedom. Our method provides an efficient avenue for the hyperentangled state analysis, and will be useful for high-capacity quantum information processing.

In this article we present a full description of the quantum Kerr Ising model-a linear optical network of parametrically pumped Kerr nonlinearities. We consider the non-dissipative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally, we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities.

We discuss the Kerr nonlinearities of the nonlocally nonlinear system with oscillatory responses by the variational approach. The self-focusing and self-defocusing states are found to dramatically depend on the degree of nonlocality. When the degree of nonlocality goes across a critical value, the nonlinearity can transit to its opposite counterpart, that is, focusing to defocusing or defocusing to focusing. The critical degree of nonlocality for the nonlinearities transition is given analytically, and confirmed by numerical simulations. As a versatile mathematical tool, we also employ the variational approach to analytically address the stabilities of solitons, and obtain the range of the degree of nonlocality for the stable solitons, which is confirmed by the linear stability analysis and the numerical simulation.