We propose a method to create "spin cat states," i.e., macroscopic superpositions of coherent spin states, in Bose-Einstein condensates using the Kerr nonlinearity due to atomic collisions. Based on a detailed study of atom loss, we conclude that cat sizes of hundreds of atoms should be realistic. The existence of the spin cat states can be demonstrated by optical readout. Our analysis also inc...

Frequency conversion by means of Kerr nonlinearity is one of the most common and exploited nonlinear optical processes in the UV, visible, IR, and mid-IR spectral regions. Here we show that wave mixing of an optical field and a terahertz wave can be achieved in diamond, resulting in the frequency conversion of the terahertz radiation either by sum- or difference-frequency generation. In the lat...

We describe a method to engineer giant nonlinearities in, and probes to measure nonlinear observables of, mesoscopic quantum resonators. This involves tailoring the Hamiltonian of a simple auxiliary system perturbatively coupled to the resonator, and has the potential to engineer a wide range of nonlinearities to high accuracy. We give a number of explicit examples, including a readily realizab...

We experimentally demonstrate cavity field control by another laser beam with three-level L-type atoms inside an optical ring cavity. By adjusting the frequency detuning of the controlling beam ~coupled to one of the atomic transitions!, the intensity of the cavity field interacting with another atomic transition is switched on and off. Such all-optical switching between two steady states is ca...

Optical 10-Gbit / s return-to-zero pulse transmission in cascaded communication systems using dispersion compensation of the standard monomode fiber with large amplifier spacing is examined. It is shown that pulse distortions that are due to Kerr nonlinearity are significantly diminished by symmetrical ordering of the compensation sections when the total number of precompensation and postcompen...

We consider a laser beam incident normally upon a waveguide with a Kerr nonlinearity. Although the laser is uniform in the plane of the waveguide, we show that the waveguide fields can be unstable to growth, forming coherent periodic structures. The initial, exponential time dependence is determined, and we find a steady-state solution. Finally, we note that the mechanism necessary for this ins...

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also...

Using a variational approach we have studied the shape preserving coherent propagation of light pulses in a resonant dispersive medium in the presence of the Kerr nonlinearity. Within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations, we show the existence of a solitary wave. We have tested our analytical solution through numeri...

It is well-known that the nonlinear coupling between a mechanical oscillator and a superconducting resonator or optical cavity can be used to generate a Kerrnonlinearity for the cavity mode. We show that the strength of this Kerr-nonlinearity, as well as the effect of the photon-pressure force can be enormously increased by modulating the strength of the nonlinear coupling. We describe an elect...

We consider a discrete model that describes a linear chain of particles coupled to a single-site defect with instantaneous Kerr nonlinearity. We show that this model can be regarded as a nonlinear generalization of the familiar Fano-Anderson model and it can generate amplitude-dependent bistable resonant transmission or reflection. We identify these effects as the nonlinear Fano resonance and s...