# Quantum versus classical effects in the chirped-drive discrete nonlinear Schrodinger equation

## TL;DR

This paper compares quantum and classical effects in a driven discrete nonlinear Schrödinger system, identifying regimes of efficient excitation via ladder climbing and autoresonance, influenced by system nonlinearities and parameters.

## Contribution

It introduces a combined quantum-classical analysis of a chirped-driven discrete nonlinear Schrödinger equation, highlighting the interplay of two excitation mechanisms and nonlinear effects.

## Key findings

- Identification of regimes for efficient excitation
- Characterization of ladder climbing and autoresonance
- Influence of nonlinearities on excitation borders

## Abstract

A chirped parametrically driven discrete nonlinear Schrodinger equation is discussed. It is shown that the system allows two resonant excitation mechanisms, i.e., successive two-level transitions (ladder climbing) or a continuous classical-like nonlinear phase-locking (autoresonance). Two-level arguments are used to study the ladder-climbing process, and semiclassical theory describes the autoresonance effect. The regimes of efficient excitation in the problem are identified and characterized in terms of three dimensionless parameters describing the driving strength, the dispersion nonlinearity, and the Kerr-type nonlinearity, respectively. The nonlinearity alters the borderlines between the regimes, and their characteristics.