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We derive an asymptotic theory of nonparametric estimation for a time series regression model $Z_t=f(X_t)+W_t$, where \ensuremath\{X_t\} and \ensuremath\{Z_t\} are observed nonstationary processes and $\{W_t\}$ is an unobserved stationary…
We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response.…
With the rapid development of high-power petawatt class lasers worldwide, exploring physics in the strong field QED regime will become one of the frontiers for laser-plasma interactions research. Particle-in-cell codes, including quantum…
We present a comprehensive overview of different types of parametric interactions in nonlinear optics which are associated with simultaneous phase-matching of several optical processes in quadratic nonlinear media, the so-called multistep…
Cascaded optical cavities appear in various quantum information processing schemes in which atomic qubits are sitting in separate cavities interconnected by photons as flying qubits. The usual theoretical description relies on a…
Pairs of entangled photons are crucial for photonic quantum technologies. The demand for integrability and multi-functionality suggests 'flat' platforms - ultrathin layers and metasurfaces - as sources of photon pairs. With the success in…
We report an integrated platform for efficient second-order nonlinear interactions based on linearly uncoupled resonators and angular phase matching. The proposed architecture confines phase control to a limited section of the device,…
Nonlinear effects could play a crucial role in addressing optical nonreciprocal behaviors in scattering media. Such behaviors are, however, typically observed within a single transmission channel and predominantly in media with fixed…
We present a method, based on Feynman path integrals, to describe the propagation and properties of the quantised electromagnetic field in an arbitrary, nonlinear medium. We provide a general theory, valid for any order of optical…
In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic electromagnetic fields is established. Our results…
We present a method for describing nonlinear electromagnetic interactions in integrated photonic devices utilizing an asymptotic-in/out field formalism. Our method expands upon previous continuous wave asymptotic treatments by describing…
We describe theoretically the process of spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays in the presence of linear loss. We derive a set of discrete Schrodinger-type equations for the biphoton wave function,…
In our contribution we give a brief overview of two widely discussed quantum processes: electron-positron pairs production off a probe photon propagating through a polarized short-pulsed electromagnetic (e.m.) (e.g.\ laser) wave field or…
We describe an opto-mechanical system in which the coupling between optical and mechanical degrees of freedom takes the form of a fully quantised third-order parametric interaction. Two physical realisations are proposed: a harmonically…
We study the dynamical Casimir effect in a double superconducting cavity in a circuit quantum electrodynamics architecture. Parameters in the quantum circuit are chosen in such a way the superconducting cavity can mimic a double cavity,…
Harnessing nonlinearities strong enough to allow two single photons to interact with one another is not only a fascinating challenge but is central to numerous advanced applications in quantum information science. Currently, all known…
We describe the generation of atom-resonant indistinguishable photon pairs using nonlinear optical techniques, their spectral purification using atomic filters, characterization using multi-photon interference, and application to…
The light force on particles trapped in the field of a high-Q cavity mode depends on the quantum state of field and particle. Different photon numbers generate different optical potentials anddifferent motional states induce different field…
We have developed a rigorous quantum model of spontaneous parametric down-conversion in a nonlinear 1D photonic-band-gap structure based upon expansion of the field into monochromatic plane waves. The model provides a two-photon amplitude…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…