相关论文: Moyal phase-space analysis of nonlinear optical Ke…

The existence of a novel type of solitons in periodic Kerr media constructed as superposition of noninteracting gap-solitons of different kinds (bright, dark and periodic) is first demonstrated. The periodic modulation of the nonlinearity…

We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…

An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…

The very small size of optical nonlinearities places wide ranging restrictions on the types of novel physics one can explore. For an ensemble of multi-level systems one can synthesize a large effective optical nonlinearity using quantum…

Controlling nonequilibrium responses in optically driven quantum materials is essential for advancing applications in energy conversion, ultrafast electronics, and quantum computation. Nonlinear optical spectroscopy serves as a powerful…

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…

The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…

We generalize the Moyal equation, which describes the dynamics of quantum observables in phase space, to quantum systems coupled to a reservoir. It is shown that phase space observables become functionals of fluctuating noise forces…

A spectral singularity is a mathematical notion with an intriguing physical realization in terms of certain zero-width resonances. In optics it manifests as lasing at the threshold gain. We explore the application of their…

Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution…

Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in non-equilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly…

The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general, localized, response function. It is shown that there always exists a finite number of well-separated MI gain bands, with each of them…

In this article we present a full description of the quantum Kerr Ising model---a linear optical network of parametrically pumped Kerr non-linearities. We consider the non-dissapative Kerr Ising model and, using variational techniques, show…

It is shown that the properties of the modulational instability of partially coherent waves propagating in a nonlinear Kerr medium depend crucially on the profile of the incoherent field spectrum. Under certain conditions, the incoherence…

We consider a well-known static, axially symmetric, vacuum solution of Einstein equations belonging to Weyl's class and determine the fundamental frequencies of small harmonic oscillations of test particles around stable circular orbits in…

We propose a comprehensive model describing the Kerr nonlinear dynamics of an electric field in a cylindrical microresonator with an effective radius variation, coupled to a radiation source. The proposed system of equations for coupled…

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation…

In this paper, we investigate the single mode quantum properties of the codirectional Kerr nonlinear coupler when the frequency mismatch is involved and a condition for an exact solution of equations of motion is fulfilled. Particularly, we…

We show two examples in which the dynamical Casimir effect can be achieved by modulating the Kerr or higher order nonlinearities. In the first case the cavity field is coupled to an arbitrary number of qubits or an harmonic oscillator via…

Nonlinear imaging systems can surpass the limits of linear optics, but to date they have all relied on physical media (e.g. crystals) to work. These materials are all constrained by their physical properties, such as frequency selectivity,…