Berry Phase of Nonlinear Correction

TL;DR

This paper explores how nonlinearity in Bose-Einstein condensates affects the Berry phase during adiabatic evolution, revealing finite geometric phases contributed by Bogoliubov fluctuations, with broader implications for nonlinear systems.

Contribution

It introduces a theoretical framework for understanding Berry phase modifications in nonlinear quantum systems, specifically in BECs governed by Gross-Pitaevskii equations.

Findings

Nonlinearity modifies the Berry phase in BEC systems.

Bogoliubov fluctuations contribute a finite geometric phase.

The theory applies to other nonlinear physical systems.

Abstract

We investigate the geometric phase or Berry phase of adiabatic quantum evolution in the Bose-Einstein condensate (BEC) systems governed by nonlinear Gross-Pitaevskii(GP) equations. We study how this phase is modified by the nonlinearity and find that the Bogoliubov fluctuations around the eigenstates are accumulated during the nonlinear adiabatic evolution and contribute a finite phase of geometric nature. A two-mode BEC model is used to illustrate our theory. Our theory is applicable to other nonlinear systems such as paraxial wave equation for nonlinear optics and Ginzburg-Landau equations for complex order parameters in condensed-matter physics.