Non-linear mixing of Bogoliubov modes in a bosonic Josephson junction

TL;DR

This paper investigates the nonlinear dynamics of Bogoliubov modes in a bosonic Josephson junction, revealing how mode coupling leads to self-trapping and frequency shifts in population oscillations.

Contribution

It introduces a Bogoliubov quasiparticle projection method to analyze mode mixing and nonlinear effects in Bose-Einstein condensates within double-well potentials.

Findings

Mode coupling causes frequency shifts in plasma oscillations.

Nonlinear mixing leads to self-trapping of the condensate.

Results are expected to extend to higher-dimensional systems.

Abstract

We revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For very small imbalance between left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, more excited modes -- though initially not macroscopically occupied -- get coupled during the evolution of the system. Since their population also varies with time, the frequency spectrum of the imbalance turns out to be still peaked around a single frequency, which is continuously shifted towards lower values. The nonlinear mixing between Bogoliubov modes eventually drives the system into the the self-trapping regime, when the population of the ground state can be transferred completely to the excited states at some time during the evolution. For simplicity, here we consider a one-dimensional setup, but the results are expected to hold also in higher dimensions.