Rosen-Zener Transition in a Nonlinear Two-Level System

TL;DR

This paper investigates how nonlinearity influences Rosen-Zener transitions in a two-level quantum system, revealing conditions for complete population transfer or blockade, with implications for Bose-Einstein condensates.

Contribution

It provides analytical and numerical analysis of nonlinear effects on quantum transitions, highlighting conditions for robust transfer and blockade in two-level systems.

Findings

Complete population transfer at certain nonlinearities

Transition blockade under strong nonlinearity

Analytical expressions for transition probabilities

Abstract

We study Rosen-Zener transition (RZT) in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. We find that the nonlinearity could affect the quantum transition dramatically. At certain nonlinearity the 100% population transfer between two levels is observed and found to be robust over a very wide range of external parameters. On the other hand, the quantum transition could be completely blocked by a strong nonlinearity. In the sudden and adiabatic limits we have derived analytical expressions for the transition probability. Numerical explorations are made for a wide range of parameters of the general case. Possible applications of our theory to Bose-Einstern Condensates (BECs) are discussed.