# Adiabatic tracking for photo- and magneto-association of Bose-Einstein condensates with Kerr nonlinearities

## TL;DR

This paper introduces an adiabatic tracking method for Bose-Einstein condensate association that accounts for Kerr nonlinearities, revealing how to maintain efficient transfer despite bifurcations and stability issues.

## Contribution

The study demonstrates how to adapt adiabatic tracking in nonlinear BEC systems with Kerr effects, ensuring effective transfer by choosing appropriate detuning.

## Key findings

- Kerr nonlinearities cause bifurcations affecting adiabatic dynamics.
- Strong fields can compensate for nonlinear destabilization.
- Proper detuning enables efficient adiabatic transfer despite nonlinear effects.

## Abstract

We develop the method of adiabatic tracking for photo- and magneto-association of Bose-Einstein atomic condensates with models that include Kerr type nonlinearities. We show that the inclusion of these terms can produce qualitatively important modifications in the adiabatic dynamics, like the appearance of bifurcations, in which the trajectory that is being tracked loses its stability. As a consequence the adiabatic theorem does not apply and the adiabatic transfer can be strongly degraded. This degradation can be compensated by using fields that are strong enough compared with the values of the Kerr terms. The main result is that, despite these potentially detrimental features, there is always a choice of the detuning that leads to an efficient adiabatic tracking, even for relatively weak fields.