arXiv subjects

Ivan Gonoskov

Publications and source records attributed to Ivan Gonoskov.

7 recordsLinked to original sources

arXiv2025

Emergence of nonclassical radiation in strongly laser-driven quantum systems

We present an analytical framework for the emergence of nonclassical radiation in strongly laser-driven quantum systems, with a focus on high-order harmonic generation (HHG). Starting from a Pauli-Fierz description, we employ a parametric factorization of the coupled light-matter wavefunction that reduces the dynamics to coupled equations for a field-driven electronic state and a quantized light mode. Within this framework, we identify a simple and predictive mechanism for nonclassicality: it originates from the nonlinear dependence of the electronic dipole response on the light-mode coordinate. An approximately constant dipole yields coherent radiation, a linear dependence produces squeezing, and higher-order nonlinearities give rise to Wigner-function negativity. We illustrate this mechanism for atomic and molecular model systems and analyze its scaling in multi-emitter configurations, indicating routes toward high-photon-number nonclassical radiation in HHG. Our results provide a transparent connection between strong-field dynamics and quantum-optical properties of emitted light, offering a basis for engineering nonclassical states in intense laser-matter interactions.

quant-ph↗

arXiv2023

Compact-form solution to the time-dependent Schr\"odinger equation with an arbitrary potential

We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of finite number of standard mathematical operations with finite (condition-independent) number of variables in a discrete or continous region of consideration. The general approach to obtain the compact-form solutions combines a number of methods in the fields of partial differential equations, enumerative combinatorics, and number theory, which we describe in detail. We discuss their advantages and perspectives for the various fields in physics, mathematics, and advanced calculus.

math-ph↗

arXiv2022

Nonclassical light generation and control from laser-driven semiconductor intraband excitations

We investigate the generation of higher-order harmonics from a quantum optics perspective via the interaction of a semiconductor with a coherent pump field focusing on the regime where strong-field intraband excitations dominate. The related Schr\"odinger equation for the system is solved approximately and the classical and quantum characteristics of the fundamental light mode as well as the higher frequency modes are analyzed. We find intricate but sufficiently mild modifications of the fundamental mode and coherent displacements depending on the position quadrature component of the driving laser field for the harmonic modes within our approximations due to the intricate induced nonlinear interactions. Similar to high-harmonic generation in atoms, all radiation field modes are entangled, allowing for potential novel protocols for quantum information processing with high photon numbers over a large range of frequencies.

quant-ph↗

arXiv2021

Light-matter quantum dynamics of complex laser-driven systems

We propose a novel general approximation to transform and simplify the description of a complex fully-quantized system describing the interacting light and matter. The method has some similarities to the time-dependent Born-Oppenheimer approach: we consider a quantum description of light rather than of nuclei and follow a similar separation procedure. Our approximation allows to obtaing a decoupled system for the light-excited matter and "dressed" light connected parametrically. With these equations at hand, we study how intense light as a quantum state is affected due to the back-action of the interacting matter. We discuss and demonstrate the possibility of the light-mode entanglement and nonclassical light generation during the interaction.

quant-ph↗

arXiv2014

Single-step Propagators for calculation of time evolution in quantum systems with arbitrary interactions

We propose and develop a general method of numerical calculation of the wave function time evolution in a quantum system which is described by Hamiltonian of an arbitrary dimensionality and with arbitrary interactions. For this, we obtain a general n-order single-step propagator, which could be used for the numerical solving of the problem with any prescribed accuracy. We demonstrate an applicability of the proposed approach by considering a propagation of an electron in focused electromagnetic field with vortex electric field component.

physics.atom-ph↗

arXiv2013

Closed-form solution of a general three-term recurrence relation

We present a closed-form solution for n-th term of a general three-term recurrence relation with arbitrary given n-dependent coefficients. The derivation and corresponding proof are based on two approaches, which we develop and describe in detail. First, the recursive-sum theory, which gives the exact solution in a compact finite form using a recursive indexing. Second, the discrete dimensional-convolution procedure, which transforms the solution to the non-recursive expression of n, including a finite number of elementary operations and functions.

math.CA↗

arXiv2012

Cyclic Operator Decomposition for Solving the Differential Equations

We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrödinger equation, and wave equation in dispersive medium.

math.SP↗